Calendar

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am TBA

Friday, November 14, 1986

Posted December 15, 2024
Last modified February 11, 2025

3:30 pm – 4:30 pm TBA

TBA

Saturday, January 27, 1990

Posted December 12, 2022
Last modified December 26, 2024

10:30 am – 11:20 am

TBA

Saturday, March 31, 1990

Posted January 7, 2023

10:30 am – 11:20 am

Andrea L’Afflitto, Virginia Tech DARPA Young Faculty Awardee

Saturday, September 29, 1990

Posted August 18, 2023
Last modified November 16, 2023

10:30 am – 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

TBA

Sunday, November 18, 1990

Posted August 15, 2022

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Domitilla Del Vecchio, Massachusetts Institute of Technology Donald P. Eckman Awardee, IEEE Fellow
TBA

Saturday, December 8, 1990

Posted August 25, 2023
Last modified September 3, 2023

10:30 am – 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Piermarco Cannarsa, Università degli studi di Roma "Tor Vergata"
TBA

Sunday, September 29, 1991

Posted August 18, 2023
Last modified November 16, 2023

10:30 am – 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

TBA

Sunday, October 27, 1991

Posted August 22, 2023
Last modified November 16, 2023

10:30 am – 11:20 am Test

Test

Friday, January 1, 1999

Posted January 27, 2024

TBA

Saturday, January 1, 2000

Posted December 21, 2024
Last modified March 21, 2025

9:00 am

TBA

Monday, January 17, 2000

Posted September 11, 2024
Last modified October 31, 2024

Control and Optimization Seminar Questions or comments?

(Originally scheduled for Sunday, January 16, 2000, 9:00 am)

Saturday, April 8, 2000

Posted January 23, 2024
Last modified December 26, 2024

11:30 am – 12:20 pm Monday, April 8, 2024 Zoom (click here to join)

Wednesday, October 11, 2000

Posted September 11, 2024
Last modified December 26, 2024

10:30 am – 11:20 am Zoom (click here to join)

TBA

Tuesday, September 18, 2001

Posted November 17, 2003

3:00 pm James E. Keisler Lounge (Room 321 Lockett)

Stanislav Zabic, Louisiana State University Department of Mathematics Graduate Student
Optimizing the Design of the Michelin PAX Tire System

Abstract: This talk analyzes a problem encountered by the Michelin Corporation in the design of a \'run-flat\', or PAX, tire system. A PAX tire system consists of an aluminum wheel of larger-than-conventional radius, a low-profile tire, and a special rubber support ring inside and concentric with the tire. The goal of the support ring is to provide a safe driving transition in case of a flat tire. After the air has deflated from the tire, the support ring carries the entire load of the car. We will discuss ways to optimize the design of the support ring. This research was carried out during the summer of 2001, while the speaker was a visitor at North Carolina State University.

Tuesday, October 2, 2001

Posted September 14, 2003
Last modified May 3, 2010

Control and Optimization Seminar Questions or comments?

3:00 pm 381 Lockett Hall

Michael Malisoff, LSU Roy P. Daniels Professor
Lyapunov Functions and Viscosity Solutions, Part 1

Tuesday, October 16, 2001

Posted September 14, 2003
Last modified May 3, 2010

Control and Optimization Seminar Questions or comments?

3:00 pm 381 Lockett Hall

Michael Malisoff, LSU Roy P. Daniels Professor
Lyapunov Functions and Viscosity Solutions, Part 2

Tuesday, November 6, 2001

Posted September 14, 2003
Last modified May 3, 2010

Control and Optimization Seminar Questions or comments?

3:00 pm 381 Lockett Hall

Michael Malisoff, LSU Roy P. Daniels Professor
Lyapunov Functions and Viscosity Solutions, Part 3

Monday, September 23, 2002

Posted October 14, 2003
Last modified October 1, 2021

3:30 pm – 4:30 pm Tuesday, September 23, 2003 Lockett 240

Stephen Shipman, Mathematics Department, LSU
Boundary projections and Helmholtz resonances 1

Monday, September 30, 2002

Posted October 14, 2003
Last modified October 1, 2021

3:30 pm – 4:30 pm Tuesday, September 30, 2003 Lockett 240

Stephen Shipman, Mathematics Department, LSU
Boundary projections and Helmholtz resonances 2

Monday, October 14, 2002

Posted October 23, 2003

3:30 pm Lockett 240

Harris Wong, Department of Mechanical Engineering
A d-function model of facets and its applications

Monday, October 21, 2002

Posted October 24, 2003

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 240

Stephanos Venakides, Department of Mathematics, Duke University
The Semiclassical Limit of the Focusing Nonlinear Schroedinger Equation

Tuesday, October 22, 2002

Posted March 25, 2004
Last modified March 26, 2004

3:40 pm 381 Lockett Hall

Vinicio Rios, LSU Department of Mathematics PhD Student
A Theorem on Lipschitzian Approximation of Differential Inclusions

Monday, October 28, 2002

Posted October 24, 2003

3:30 pm Lockett 240

Robert Lipton, Mathematics Department, LSU
Field Fluctuations, Spectral Measures, and Moment Problems

Monday, November 11, 2002

Posted October 24, 2003
Last modified November 6, 2003

3:30 pm Lockett 240

Christo Christov, University of Louisiana at Lafayette
Nonlinear Waves and Quasi-Particles: The Emerging of a New Paradigm

Monday, November 18, 2002

Posted October 24, 2003
Last modified November 6, 2003

3:30 pm Lockett 240

Karsten Thompson, Department of Chemical Engineering, Louisiana State University
Modeling Multiple-scale Phenomena in Porous Materials

Monday, November 25, 2002

Posted October 24, 2003

3:30 pm Lockett 240

Endel Iarve, Materials Directorate Wright Patterson Air Force Base and the University of Dayton Research Institute, Dayton Ohio
Mesh-independent modeling of cracks by using higher-order shape functions

Tuesday, November 26, 2002

Posted October 24, 2003

3:30 pm The Deans conference room 3225, CEBA

Endel Iarve, Materials Directorate Wright Patterson Air Force Base and the University of Dayton Research Institute, Dayton Ohio
Effect of splitting on tensile strength distribution of unidirectional carbon fiber composites

Special Civil Engineering and Applied Analysis Seminar

Monday, January 13, 2003

Posted October 24, 2003

2:00 pm Lockett 285

Boris Baeumer, University of Otago, New Zealand
Fractal Transport and Dispersion: Limits of Continuous Time Random Walks

Monday, January 27, 2003

Posted October 24, 2003

3:30 pm Lockett 240

Ricardo Estrada, Mathematics Department, LSU
Distributional Solutions of Singular Integral Equations

Friday, February 7, 2003

Posted October 24, 2003

3:30 pm Lockett 240

Wilfrid Gangbo, Department of Mathematics, Georgia Institute of Technology
Inequalities for generalized entropy and optimal transportation

Monday, February 10, 2003

Posted October 24, 2003

3:30 pm Lockett 240

Yitshak Ram, Department of Mechanical Engineering, Louisiana State University
Inverse Problems and Eigenvalue Assignment in Vibration and Control

Monday, February 17, 2003

Posted October 24, 2003

Lockett 240

Yuri Antipov, Mathematics Department, LSU
Functional-difference equations and applications

Monday, February 24, 2003

Posted October 24, 2003

3:30 pm Lockett 240

Jay Walton, Department of Mathematics, Texas A&M University
Dynamic Fracture Models in Viscoelasticity

Monday, March 10, 2003

Posted October 24, 2003

3:30 pm Lockett 240

Manuel Tiglio, Department of Physics, Louisiana State University
Summation by parts and dissipation for black hole excision

Tuesday, March 18, 2003

Posted October 24, 2003

3:30 pm Lockett 240

Stephen McDowall, Department of Mathematics, Western Washington University Priklonsky
Total boundary determination of electromagnetic material parameters from boundary data

Thursday, March 20, 2003

Posted October 8, 2003
Last modified January 27, 2004

Anton Deitmar, Mathematical Sciences Department, University of Exeter
Class number asymptotics in degree 3

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Friday, March 21, 2003

Posted October 24, 2003

3:30 pm Lockett Hall

Oscar Bruno, Department of Applied and Computational Mathematics, California Institute of Technology
New high-order, high-frequency methods in computational electromagnetism

Monday, March 24, 2003

Posted October 24, 2003

3:30 pm Lockett Hall 240

Mayank Tyagi, Mechanical Engineering Department, Louisiana State University.
Issues in Large Eddy Simulations of Complex Turbulent Flows

Monday, March 31, 2003

Posted October 24, 2003

3:30 pm Lockett Hall 240

Vladimir Priklonsky, Moscow State University
Tidal Flow and Transport Model

Monday, April 7, 2003

Posted October 24, 2003

3:30 pm Lockett Hall 240

Paul Martin, Department of Mathematical and Computer Science, Colorado School of Mines, Golden
Fundamental solutions and functionally graded materials

Thursday, April 10, 2003

Posted September 10, 2003
Last modified March 2, 2021

8:30 am – Sunday, April 13, 2003 TBA

Louisiana Conference on Mathematical Control Theory (MCT'03)

Conference Web Page: https://www.math.lsu.edu/~malisoff/LCMCT/

Monday, April 14, 2003

Posted October 24, 2003

Control and Optimization Seminar Questions or comments?

3:00 pm Lockett Hall 240

Boris Belinskiy, Department of Mathematics, University of Tennessee at Chattanooga
Boundary Value Contact Problems

Tuesday, April 29, 2003

Posted September 19, 2003
Last modified March 2, 2021

3:30 pm 381 Lockett Hall

Peter Wolenski, LSU Department of Mathematics Russell B. Long Professor
Clarke's New Necessary Conditions in Dynamic Optimization

Monday, May 5, 2003

Posted October 24, 2003

3:30 pm Lockett Hall 240

Jannette Frandsen, Department of Civil & Environmental Engineering, LSU
A Tuned Liquid Damper Model for Frequency Response Predictions of a Coupled System

Thursday, August 21, 2003

Posted August 20, 2003

Teachers of Math 1111/1201/1202

10:00 am – 11:00 am 244 Lockett Hall

Pre-service Teachers in Elementary Education

Posted August 7, 2003

2:00 pm – 3:30 pm Lockett 15

Guillermo Ferreyra, Mathematics Department, LSU
The year ahead

Monday, August 25, 2003

Posted August 20, 2003
Last modified September 17, 2003

LSU Academic Calendar Official LSU Academic Calendar Page

4:00 pm – 5:00 pm Lockett 277

Gunter Lumer, University of Mons-Hainaut and Solvay Institute for Physics and Chemistry, Brussels
Multiparameter dynamics in macrophysics of clouds on flat and general surfaces, or in certain supply-management aspects

Posted July 31, 2003

Classes begin

Wednesday, August 27, 2003

Posted August 22, 2003
Last modified August 28, 2003

Committee Meeting

10:00 am – 11:00 am Conference Room (301D)

Executive Committee Meeting

Posted August 26, 2003

Control and Optimization Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 277

Jesus Pascal, Universidad del Zulia, Venezuela
Free Boundary Control Problem

Monday, September 1, 2003

Posted July 31, 2003

LSU Academic Calendar Official LSU Academic Calendar Page

Labor Day Holiday

Tuesday, September 2, 2003

Posted July 31, 2003

LSU Academic Calendar Official LSU Academic Calendar Page

Final day for dropping courses without receiving a grade of W

Wednesday, September 3, 2003

Posted September 2, 2003

LSU Academic Calendar Official LSU Academic Calendar Page

12:40 pm – 1:30 pm Lockett 381

Gestur Olafsson, Mathematics Department, LSU
Square Integrable Representations and Frames

Thursday, September 4, 2003

Posted August 11, 2003

Final date for adding courses and section changes

Monday, September 8, 2003

Posted September 4, 2003
Last modified January 6, 2021

4:00 pm – 5:00 pm 277, Lockett Hall

Jung-Han Kimn, Mathematics Department, LSU
Overlapping Domain Decomposition Methods

Wednesday, September 10, 2003

Posted September 5, 2003
Last modified September 8, 2003

12:40 pm – 1:30 pm Lockett 381

Gestur Olafsson, Mathematics Department, LSU
Square Integrable Representations and Frames II

Posted September 8, 2003

3:40 pm – 4:30 pm Lockett 381

Eric Hillebrand, Economics Department, LSU
Unknown Parameter Changes in GARCH and ARMA Models

Thursday, September 11, 2003

Posted August 15, 2003

2:00 pm – 3:30 pm B6 Lockett Hall

M. Jane Collins, College of Arts and Sciences
Chair Evaluations

Meeting by the Dean of A&S with the Mathematics Department faculty.

Posted September 2, 2003
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 243

Yuri Antipov, Mathematics Department, LSU
Functional-difference equations and applications

Friday, September 12, 2003

Posted September 11, 2003

Fall Fest

11:00 am – 1:00 pm The Quadrangle

Music, food, and festivities to welcome students, staff, and faculty to LSU for the 2003 Fall Semester

Posted September 5, 2003
Last modified March 31, 2024

Algebra and Number Theory Seminar Questions or comments?

3:00 pm Lockett 2

Undergraduate Courses

Tuesday, September 16, 2003

Posted September 10, 2003
Last modified January 27, 2004

3:40 pm – 4:30 pm Lockett 237

Marco Schlichting, Universität Essen, Germany
Negative K-theory of derived categories

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Wednesday, September 17, 2003

Posted September 8, 2003

12:40 pm – 1:30 pm Lockett 381

Gestur Olafsson, Mathematics Department, LSU
Square Integrable Representations and Frames III

Thursday, September 18, 2003

Posted August 26, 2003
Last modified October 4, 2021

3:40 pm – 4:30 pm 243 Lockett Hall

Amha Lisan, Mathematics Department, LSU
Transitive flows and associated congruences and groups

Refreshments will be served in the lounge one half hour before the talk.

Friday, September 19, 2003

Posted September 4, 2003
Last modified October 4, 2021

3:40 pm – 4:30 pm 243 Lockett Hall

Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Non-commutative Analysis

Refreshments will be served in the lounge one half hour before the talk.
Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Monday, September 22, 2003

Posted September 18, 2003
Last modified January 27, 2004

12:40 pm – 1:30 pm Lockett 381

Karl Heinrich Hofmann, Darmstadt University, Germany Professor Emeritus
How did the adjoint functor theorem get into Lie theory?

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Posted September 4, 2003
Last modified January 6, 2021

4:00 pm – 5:00 pm 277, Lockett Hall

Blaise Bourdin, Department of Mathematics and Center for Computation & Technology, LSU
Brittle fracture seen as a free discontinuities problem

Tuesday, September 23, 2003

Posted September 10, 2003
Last modified January 27, 2004

3:40 pm – 4:30 pm 243 Lockett Hall

Marco Schlichting, Universität Essen, Germany
Hermitian K-theory and Algebraic Bott Periodicity

Refreshments will be served in the lounge one half hour before the talk.
Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Thursday, September 25, 2003

Posted August 26, 2003
Last modified October 4, 2021

3:40 pm – 4:30 pm 243 Lockett Hall

Michael M. Tom, Mathematics Department, LSU
Kadomtsev-Petviashvili and RLW-KP models

Refreshments will be served in the lounge one half hour before the talk.

Monday, September 29, 2003

Posted September 17, 2003
Last modified January 6, 2021

Algebra and Number Theory Seminar Questions or comments?

4:00 pm – 5:00 pm 277, Lockett Hall

Horst Beyer, Max Planck Institute for Gravitational Physics, Golm, Germany, and Dept. of Mathematics, LSU
On the Stability of the Kerr Black Hole

Tuesday, September 30, 2003

Posted September 8, 2003
Last modified September 17, 2003

3:40 pm – 4:30 pm Lockett 282

Helena Verrill, Mathematics Department, LSU
Examples of rigid Calabi-Yau 3-folds

Wednesday, October 1, 2003

Posted September 4, 2003
Last modified July 25, 2021

LSU Academic Calendar Official LSU Academic Calendar Page

until Thursday, October 2, 2003 Tickfaw State Park

Graduate Student Day

Thursday, October 2, 2003

Posted August 11, 2003

until Friday, October 3, 2003

Fall Holiday

Offices remain open

Monday, October 6, 2003

Posted September 23, 2003
Last modified March 2, 2021

4:00 pm – 5:00 pm 277, Lockett Hall

Olivier Sarbach, Dept. of Mathematics and Dept. of Physics & Astronomy, LSU
The initial-boundary value formulation of Einstein's equations

Tuesday, October 7, 2003

Posted October 1, 2003

3:30 pm – 4:30 pm Lockett 243

Patrick Gilmer, Mathematics Department, LSU
Integrality for TQFTs

Wednesday, October 8, 2003

Posted October 6, 2003

LSU Academic Calendar Official LSU Academic Calendar Page

12:40 pm – 1:30 pm Lockett 381

Shijun Zheng, LSU
The Perturbation of the Fourier Transform and Schroedinger Operators (continued)

Monday, October 13, 2003

Posted August 11, 2003

until Saturday, October 18, 2003

Midterms

Tuesday, October 14, 2003

Posted September 11, 2003
Last modified September 17, 2003

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 282

Paul van Wamelen, Mathematics Department, LSU
Analytic Jacobians in Magma

Wednesday, October 15, 2003

Posted October 8, 2003

3:40 pm 240 Lockett Hall

Meeting of the Full Professors

The meeting is to consider promotion cases. Anthony has the files for review.

Thursday, October 16, 2003

Posted October 3, 2003

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm Lockett 381

Guoli Ding, Mathematics Department, LSU
Some new problems on graph embeddings

Monday, October 20, 2003

Posted October 19, 2003

Committee Meeting

10:40 am Conference Room

Hiring Committee Meeting

Tuesday, October 21, 2003

Posted October 15, 2003

3:40 pm – 4:30 pm Room 239

Paul van Wamelen, Mathematics Department, LSU
Analytic Jacobians in Magma II

Posted August 11, 2003

LSU Academic Calendar Official LSU Academic Calendar Page

Midterm grades due

Wednesday, October 22, 2003

Posted October 17, 2003

12:40 pm – 1:30 pm Lockett 381

Shijun Zheng, LSU
The wavelet decomposition for operator multiplication

Posted October 15, 2003

3:40 pm – 4:30 pm

Padmanabhan Sundar, Mathematics Department, LSU
Stochastic Navier-Stokes

Tuesday, October 28, 2003

Posted October 21, 2003
Last modified January 10, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 243

Richard A. Litherland, Mathematics Department, LSU
On the Ozsváth-Szabó homology theory

Posted September 12, 2003
Last modified March 2, 2021

3:40 pm – 4:30 pm Lockett 282

Charles Neal Delzell, Mathematics Department, LSU
A generalization of Polya's theorem to signomials with rational exponents

Wednesday, October 29, 2003

Posted October 24, 2003

12:40 pm – 1:30 pm Lockett 381

Yongdo Lim, Kyungpook National University
Best Approximation in Riemannian Geodesic submanifolds of Positive Definite Matrices

Posted October 27, 2003

3:40 pm Lockett 277

Guillermo Ferreyra, Mathematics Department, LSU
Professorial faculty (tenured and tenure-track) meeting

Agenda: Discussion of hiring and teaching plans

Thursday, October 30, 2003

Posted October 14, 2003
Last modified October 4, 2021

3:40 pm – 4:30 pm 243 Lockett Hall

Horst Beyer, Max Planck Institute for Gravitational Physics, Golm, Germany, and Dept. of Mathematics, LSU
On the Completeness of the Resonance Modes of the Pöschl–Teller Potential

Refreshments will be served in the lounge one half hour before the talk.

Monday, November 3, 2003

Posted November 3, 2003

2:40 pm – 3:30 pm 240 Lockett

Guillermo Ferreyra, Mathematics Department, LSU
Professorial faculty meeting

Posted August 14, 2003
Last modified January 6, 2021

4:00 pm – 5:00 pm 277, Lockett Hall

Gilles Francfort, Université Paris Nord, France
Brittle fracture evolution: a variational standpoint.

Wednesday, November 5, 2003

Posted October 30, 2003

12:40 pm – 1:30 pm Lockett 381

Mark Davidson, Mathematics Department, LSU
Generating Functions and Representation Theory

Friday, November 7, 2003

Posted October 14, 2003

3:40 pm – 4:40 pm 243 Lockett Hall

Charles Frohman, University of Iowa
Symplectic measure, Reidemeister torsion and the Jones polynomial

Monday, November 10, 2003

Posted August 14, 2003
Last modified January 6, 2021

Algebra and Number Theory Seminar Questions or comments?

4:00 pm – 5:00 pm 277, Lockett Hall

Yonggang Huang, Dept. of Mechanical Engineering, University of Illinois at Urbana-Champaign
The fundamental solution of intersonic crack propagation

Tuesday, November 11, 2003

Posted November 3, 2003

3:40 pm – 4:30 pm Lockett 282

Eric Baxter, University of New Orleans
Prime time

Wednesday, November 12, 2003

Posted November 7, 2003

12:40 pm – 1:30 pm

Mark Davidson, Mathematics Department, LSU
Generating Functions and Representation Theory

Posted November 11, 2003

3:40 pm – 4:30 pm Lockett 381

Stochastic Navier-Stokes II: Some Basic Estimates

Friday, November 14, 2003

Posted October 28, 2003

LSU Academic Calendar Official LSU Academic Calendar Page

4:00 pm – 5:00 pm 235, Lockett Hall

Andrej Cherkaev, University of Utah
TBA

To be followed by a \"Special Fluid Dynamic\" seminar at the Chimes.

Posted August 11, 2003

Final date for resigning/dropping courses

Monday, November 17, 2003

Posted August 27, 2003
Last modified January 6, 2021

Control and Optimization Seminar Questions or comments?

4:00 pm – 5:00 pm 277, Lockett hall

Andri Gretarsson, California Institute of Technology and LIGO Livingston Observatory
Detecting Gravitational Waves

Wednesday, November 19, 2003

Posted September 24, 2003
Last modified January 10, 2022

2:30 pm 240 Lockett Hall

Yuan Wang, Florida Atlantic University
A Relaxation Theorem for Differential Inclusions with Applications to Stability Properties

The fundamental Filippov-Ważewski Relaxation Theorem states that the solution set of an initial value problem for a locally Lipschitz differential inclusion is dense in the solution set of the same initial value problem for the corresponding relaxation inclusion on compact intervals. In this talk, I will discuss a complementary result which says that the approximation can be carried out over non-compact or infinite intervals provided one does not insist on the same initial values. To illustrate the motivations for studying such approximation results, I will briefly discuss some quick applications of the result to various stability and uniform stability properties.
Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Posted November 18, 2003

3:40 pm – 4:30 pm Lockett 381

Vochita Mihai, Department of Mathematics, LSU Graduate Student
The Radon-Gauss Transform

Posted November 14, 2003

Ramadan Dinner

5:00 pm James E. Keisler Lounge (Room 321 Lockett)

3rd Traditional Ramadan Dinner

Suat Namli and his Turkish friends will generously make a Turkish Ramadan dinner for our faculty, students, and families. We look forward to another fabulous feast!

Thursday, November 20, 2003

Posted September 24, 2003
Last modified October 4, 2021

3:40 pm – 4:40 pm 243 Lockett

Yuan Wang, Florida Atlantic University
Input-to-State Stability of Nonlinear Control Systems

Refreshments will be served in the lounge one half hour before the talk.
Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Friday, November 21, 2003

Posted November 17, 2003

1:30 pm James E. Keisler Lounge (room 321 Lockett)

Angie Traumonte, Blue Cross Blue Shield

This is the first meeting of the Actuarial Student Association. There will be pizza and refreshments served at the meeting.

Monday, November 24, 2003

Posted October 23, 2003
Last modified January 6, 2021

Control and Optimization Seminar Questions or comments?

4:00 pm – 5:00 pm 277, Lockett Hall
(Originally scheduled for Monday, October 27, 2003)

Peter Y Huang, LSU, Department of Mechanical Engineering
Direct Numerical Simulation of Multiphase Flows in Newtonian and Non-Newtonian Fluids

Wednesday, November 26, 2003

Posted November 18, 2003
Last modified November 24, 2003

2:30 pm 240 Lockett Hall

Tzanko Donchev, University of Architecture and Civil Engineering, BULGARIA
Singular Perturbations in Infinite Dimensional Control Systems

Abstract: We consider a singularly perturbed control system involving differential inclusions in Banach spaces with slow and fast solutions. Using the averaging approach, we obtain sufficient conditions for the Hausdorff convergence of the set of slow solutions in the sup norm. We present applications of the theorem to prove convergence of the fast solutions in terms of invariant measures and convergence of equi-Lipschitz solutions. We also present some illustrative examples.

Thursday, November 27, 2003

Posted August 11, 2003

LSU Academic Calendar Official LSU Academic Calendar Page

until Friday, November 28, 2003

Thanksgiving Holiday

Offices closed

Wednesday, December 3, 2003

Posted August 11, 2003

LSU Academic Calendar Official LSU Academic Calendar Page

until Sunday, December 7, 2003

Concentrated study period

Saturday, December 6, 2003

Posted August 11, 2003

LSU Academic Calendar Official LSU Academic Calendar Page

Classes end

Monday, December 8, 2003

Posted November 17, 2003

LSU Academic Calendar Official LSU Academic Calendar Page

4:00 pm – 5:00 pm 277, Lockett Hall

Darko Volkov, Department of Mathematical Sciences, New Jersey Institute of Technology
Integral equation methods for the statics and the dynamics of an electrified fluid bridge

Posted August 11, 2003

until Saturday, December 13, 2003

Final exams

Tuesday, December 9, 2003

Posted December 5, 2003
Last modified March 2, 2021

Holiday Party

12:00 pm Keisler Lounge

Everyone is invited to share in the Season's Spirit

We will have beverages and turkey. Bring a dish to share.

Monday, December 15, 2003

Posted December 14, 2003
Last modified January 27, 2022

2:30 pm – 3:30 pm 285 Lockett

David Levin, University of Utah
Modern Topics in Random Walks

I will survey some of my work relating to random walks: dynamical random walks and reconstruction of sceneries visited by a random walk. Dynamical random walks are easily constructed "coin tossing" analogues of infinite dimensional diffusions. We discuss the existence of times where atypical random walk behavior is seen, and give connections to the Ornstein-Uhlenbeck process on Wiener space. (Joint work with Khoshnevisan and Mendez.) Hidden Markov chains are widely applicable probabilistic models: a noisy function of an underlying stochastic process is seen, while the process itself is unobserved. We describe such models where an unknown scenery is explored by a hidden random walk, and discuss when reconstruction of this underlying scenery is possible. (Joint work with Pemantle and Peres.)

Refreshments at 2:00 in the Keisler Lounge.

Wednesday, December 17, 2003

Posted December 17, 2003
Last modified March 3, 2021

LSU Academic Calendar Official LSU Academic Calendar Page

2:30 pm – 3:30 pm

Patricia Hersh, University of Michigan
A GL_n(q) analogue of the partition lattice and discrete Morse theory for posets

Coffee at 2:00 in the Keisler Lounge

Friday, December 19, 2003

Posted August 11, 2003

Commencement

Tuesday, January 13, 2004

Posted January 8, 2004

LSU Academic Calendar Official LSU Academic Calendar Page

2:40 pm – 3:30 pm Lockett 285

Diane Maclagan, Stanford University
Toric Hilbert schemes

Abstract: Toric Hilbert schemes have broad connections to other areas of mathematics, including optimization, geometric combinatorics, algebraic geometry, and representations of finite groups and quivers. They parameterize all ideals in a a polynomial ring with the simplest possible multigraded Hilbert function. I will introduce these objects, and discuss some of the applications.

Monday, January 19, 2004

Posted January 16, 2004

Martin Luther King Day

Offices closed

Tuesday, January 20, 2004

Posted January 16, 2004

LSU Academic Calendar Official LSU Academic Calendar Page

Classes begin

Thursday, January 22, 2004

Posted January 15, 2004
Last modified March 3, 2021

3:30 pm – 4:30 pm 285 Lockett

Scott Baldridge, Louisiana State University
Elementary Mathematics for Teachers: A mathematician's perspective

This talk describes a mathematics course, designed by mathematicians, for prospective elementary teachers. I will describe three unique features of the course: the extensive use of the Primary Mathematics books from Singapore, the idea of a “teaching sequence”, and the use of “teacher's solutions” in class and in homework. The course is based on a new textbook I wrote with T. Parker: Elementary Mathematics for Teachers. The goal of the textbook and the course is to present the mathematics clearly and correctly while keeping the focus on material that elementary school teachers will be addressing in their classrooms.

Refreshments in the Lounge at 3:00

Friday, January 23, 2004

Posted January 15, 2004
Last modified January 16, 2004

3:30 pm – 4:30 pm 285 Lockett

Scott Baldridge, Louisiana State University
Seiberg-Witten invariants of 4--manifolds with circle actions, with applications to symplectic topology.

Ever since the introduction of Donaldson invariants in the early 1980's, efforts to calculate diffeomorphism invariants of 4-manifolds centered upon large classes of smooth manifolds that have some additional structure. One such class of manifolds thought to have promise was 4-manifolds with effective circle actions, but the extra structure given by such manifolds turned out to be insufficient for calculating Donaldson invariants. However, it is possible to calculate their Seiberg-Witten invariants. In this talk I will give an overview of the Seiberg-Witten invariants and describe formulas for calculating the Seiberg-Witten invariant of 4-manifolds with circle actions. I will also discuss some results on the topology of symplectic 4-manifolds which follow from those calculations.

Refreshments in the Lounge at 3:00

Monday, January 26, 2004

Posted January 15, 2004
Last modified January 26, 2004

2:30 pm – 3:30 pm Lockett 237

Malabika Pramanik, University of Wisconsin–Madison
Averaging and maximal operators for curves in R^3

We consider the L^p regularity of an averaging operator over a curve in R^3 with nonvanishing curvature and torsion. We also prove related local smoothing estimates, which lead to L^p boundedness of a certain maximal function associated to these averages. The common thread underlying the proof of these results is a deep theorem of T. Wolff on cone multipliers. This is joint work with Andreas Seeger of University of Wisconsin, Madison.

Refreshments in Lounge at 2:00

Posted January 8, 2004
Last modified January 6, 2021

LSU Academic Calendar Official LSU Academic Calendar Page

3:30 pm – 4:30 pm 277, Lockett Hall

Petr Kloucek, Computational and Applied Mathematics department, Rice University
Stochastic Modeling of the Functional Crystalline Materials

Tuesday, January 27, 2004

Posted January 16, 2004

Final day for dropping courses without receiving a grade of W

Thursday, January 29, 2004

Posted January 15, 2004
Last modified January 27, 2004

LSU Academic Calendar Official LSU Academic Calendar Page

3:30 pm – 4:30 pm Lockett 285

Susan Wilson, Michigan State University, College of Education
Reforming Mathematics Education; Lessons from California

Refreshments in the Lounge at 3:00

Posted January 16, 2004

Final date for adding courses and section changes

Monday, February 2, 2004

Posted January 27, 2004

3:00 pm – 3:50 pm Lockett 381

Jimmie Lawson, Mathematics Department, LSU
The symplectic group, the symplectic semigroup, and the Ricatti Equation

Posted January 27, 2004
Last modified January 30, 2004

3:30 pm – 4:30 pm Lockett 285

Tara Brendle, Department of Mathematics, LSU
On finite order generators of the mapping class group

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents LEQSF(2002-04)-ENH-TR-13

Wednesday, February 4, 2004

Posted February 2, 2004

4:30 pm James Keisler lounge (Room 321 Lockett)

Actuarial Student Association Meeting

There will be opportunities to sign-up for study groups preparing for the actuarial exams. Refreshments will be served.

Thursday, February 5, 2004

Posted January 29, 2004
Last modified October 5, 2023

3:40 pm – 4:30 pm Lockett 285

Pramod Achar, University of Chicago
Equivariant K-theory of the unipotent variety

The equivariant K-theory of the unipotent variety in a complex algebraic group has two natural bases, one indexed by the set $\Lambda^+$ of dominant weights, the other by the set $\Omega$ of irreducible representations of centralizers of unipotent elements. Lusztig's work on cells in affine Weyl groups led him to conjecture that the change-of-basis matrix relating these two bases is upper-triangular, and that in particular there is a natural bijection between $\Lambda^+$ and $\Omega$. This question has been treated in the work of Bezrukavnikov, Ostrik, Xi, and others. I will discuss an approach to the problem that, in the case of $GL(n)$, results in an explicit combinatorial algorithm for computing the bijection. I will also discuss connections to the Springer correspondence, duality, and other topics.

Monday, February 9, 2004

Posted January 27, 2004

3:00 pm – 3:50 pm Monday, February 2, 2004 Lockett 381

Jimmie Lawson, Mathematics Department, LSU
The symplectic group, the symplectic semigroup, and the Ricatti Equation II

Tuesday, February 10, 2004

Posted February 4, 2004
Last modified February 9, 2004

3:30 pm Lockett 15

Meeting of the professorial faculty.

The meeting is to discuss hiring for this year and a 3rd year review file.

Wednesday, February 11, 2004

Posted January 29, 2004
Last modified February 11, 2004

2:40 pm – 3:30 pm Lockett 243

Tatyana Foth, University of Michigan
Quantization, Kahler manifolds, and automorphic forms

Abstract:
I shall talk about results and problems that appear in the interplay between three subjects:
1. quantization (which can be regarded as an attempt to construct a finite-dimensional representation of the Lie algebra of smooth functions on a compact symplectic manifold with the Poisson bracket);
2. varying Kahler structure on a compact Kahler manifold with the symplectic form being kept fixed;
3. holomorphic automorphic forms on a bounded symmetric domain in C^n (for example, on the open unit ball in C^n with the Bergman metric).

Refreshments served in Keisler Lounge at 2pm.

Thursday, February 12, 2004

Posted January 22, 2004
Last modified January 6, 2021

3:30 pm – 4:30 pm 235, Lockett Hall
(Originally scheduled for Wednesday, February 11, 2004)

Vladimir Mityushev, Institute de Physique du Globe de Paris (France), and Pedagogical University in Slupsk (Poland)
Effective properties of composites with unidirectional cylindrical fibers

Friday, February 13, 2004

Posted February 4, 2004

3:40 pm – 4:30 pm Lockett 285

Irina Mitrea, Cornell University
On the Spectral Radius Conjecture in Two Dimensions

Monday, February 16, 2004

Posted February 12, 2004

3:00 pm – 5:50 am Lockett 381

Jimmie Lawson, Mathematics Department, LSU
The symplectic group, the symplectic semigroup, and the Ricatti Equation III

Posted February 12, 2004

3:30 pm – 4:30 pm Lockett 285

Ian Agol, University of Illinois, Chicago
Tameness of hyperbolic 3-manifolds

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents LEQSF(2002-04)-ENH-TR-13

Wednesday, February 18, 2004

Posted February 16, 2004

3:40 pm – 4:30 pm Lockett 285

Ruhai Zhou, University of North Carolina at Chapel Hill
Analysis and computations of nematic polymers

Friday, February 20, 2004

Posted January 9, 2004
Last modified March 2, 2021

LSU Academic Calendar Official LSU Academic Calendar Page

3:30 pm – 4:30 pm 235, Lockett Hall

Marcus Sarkis, Institito de Matematica Pura e Aplicada (IMPA, Brazil) and Worcester Polytechnic Institute
Schwarz Methods for Partial Differential Equations

Monday, February 23, 2004

Posted January 16, 2004

until Wednesday, February 25, 2004

Mardi Gras holiday

Offices remain open on Monday and Wednesday

Friday, February 27, 2004

Posted February 9, 2004
Last modified September 17, 2021

Deadline

Annual Reports Due Today

Monday, March 1, 2004

Posted January 14, 2004
Last modified March 2, 2022

3:40 pm 235 Lockett Hall
(Originally scheduled for Monday, February 9, 2004)

Ricardo Estrada, Mathematics Department, LSU
Distributional Radius of Curvature

We show that any continuous plane path that turns to the left has a well-defined distribution, that corresponds to the radius of curvature of smooth paths. As a byproduct, we will learn to divide by 0! These ideas were inspired by a talk by Professor H. Wong in the Applied Analysis Seminar some months ago, where he showed how to use Dirac delta functions to model facets in crystals.

Wednesday, March 3, 2004

Posted February 27, 2004

4:45 pm – 6:00 pm 319 Lockett Hall

Actuarial Student Association Meeting

Guest speakers will be Phillip Clesi, Truman Breithaupt and Gregg Schneider. These are professional actuaries working in the New Orleans area. Refreshments will be available.

Monday, March 8, 2004

Posted March 7, 2004

LSU Academic Calendar Official LSU Academic Calendar Page

3:00 pm – 3:50 am Lockett 381

Gestur Olafsson, Mathematics Department, LSU
The Fuglede conjecture and related problems.

Posted February 2, 2004
Last modified March 8, 2004

Student Math Club Talk

4:15 pm – 5:30 pm Lockett 243

Serge Lang, Yale University Member, National Academy of Sciences; Recipient, Frank Nelson Cole Prize in Algebra
Dirac Families

Math Majors and other interested students are especially encouraged to come to this talk.
Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents LEQSF(2002-04)-ENH-TR-13

Posted January 16, 2004

until Saturday, March 13, 2004

Midterms

Tuesday, March 9, 2004

Posted February 2, 2004

3:40 pm – 4:30 pm Wednesday, March 10, 2004 Lockett 285

Serge Lang, Yale University Member, National Academy of Sciences; Recipient, Frank Nelson Cole Prize in Algebra
The Heat Kernel and Theta Inversion Formulas

Visit supported by Visiting Experts Program in Mathematics, Louisiana
Board of Regents LEQSF(2002-04)-ENH-TR-13

Wednesday, March 10, 2004

Posted January 30, 2004
Last modified March 1, 2004

3:40 pm – 4:30 pm Lockett 285
(Originally scheduled for Thursday, February 26, 2004)

Carl Mueller, University of Rochester
Properties of the Random String

Visit supported by Visiting Experts Program in Mathematics, Louisiana

Board of Regents LEQSF(2002-04)-ENH-TR-13

Thursday, March 11, 2004

Posted March 5, 2004

2:30 pm Lockett 2

Meeting of the Tenured Faculty

Posted January 29, 2004
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 285

Stig Larsson, University of Gothenburg, Chalmers University
The finite element method for a linear stochastic parabolic partial differential equation driven by additive noise

Visit supported by Visiting Experts Program in Mathematics, Louisiana

Board of Regents LEQSF(2002-04)-ENH-TR-13

Friday, March 12, 2004

Posted March 8, 2004

2:40 pm – 3:30 pm Lockett 381

Graham Denham, University of Western Ontario
The Homotopy Lie Algebra of an Arrangement

Posted March 4, 2004
Last modified March 20, 2004

3:40 pm – 4:30 pm Lockett 285

Mark Meerschaert, University of Nevada, Reno
The Fractal Calculus Project

Monday, March 15, 2004

Posted February 3, 2004
Last modified March 2, 2022

2:40 pm – 3:30 pm Lockett Hall 235

Gregory Kriegsmann, New Jersey Institute of Technology
Complete Transmission Through a Two-Dimensional Diffraction Grating

The propagation of a normally incident plane electromagnetic wave through a two-dimensional metallic grating, is modeled and analyzed using S-Matrix theory. The period of the structure $A$ is on the order of the incident wave length $\lambda$, but the height of the channel $H$ separating the grating elements is very small in comparison. Exploiting the small parameter $H/A$ an approximate transmission coefficient is obtained for the grating. For a fixed frequency this coefficient is $O(H/A)$ due to the thinness of the channel. However, near resonant lengths it is $O(1)$. That is, for certain widths the structure is transparent. Similarly, for a fixed length the transmission coefficient has the same resonant features as a function of frequency. This latter feature makes this grating potentially useful as a selective filter.

Posted March 8, 2004

3:03 pm – 3:52 pm Lockett 381

Simon Gindikin, Rutgers University
Some explicit formulas in integral geometry

Posted March 4, 2004
Last modified February 14, 2023

3:40 pm – 4:30 pm Lockett 285

Loukas Grafakos , University of Missouri, Columbia
Calderón's program, the bilinear Hilbert transforms, and the Carleson-Hunt theorem

Tuesday, March 16, 2004

Posted January 27, 2004
Last modified October 4, 2021

LSU Academic Calendar Official LSU Academic Calendar Page

3:40 pm – 4:30 pm Lockett 285

John Willis, Cambridge University Fellow, Royal Society of London (FRS)
Bounds for the Effective Constitutive Relation of a Nonlinear Composite

For a nonlinear composite, a bound on its effective energy density does not induce a corresponding bound on its constitutive relation, because differentiating a bound on a function does not automatically bound its derivative. In this work, a method introduced by G.W. Milton and S.K. Serkov for bounding directly the constitutive relation is refined by employing a linear comparison material, in a similar way that Talbot and Willis introduced such a material to obtain bounds of “Hashin–Shtrikman” type for the effective energy of a nonlinear composite. The original Milton–Serkov approach produces bounds with a close relationship to the classical energy bounds, of Voigt and Reuss type. The bounds produced in the present implementation are closely related to bounds of Hashin–Shtrikman type for the composite. It is demonstrated by means of examples that the approximate constitutive relation that is obtained by differentiating the energy bound can be on the boundary of the bounding set, obtained here, for the exact constitutive relation, but a simple counterexample is presented to show that this is not always the case.

(This talk reports on joint work with D R S Talbot.)
Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents LEQSF(2002-04)-ENH-TR-13

Posted January 16, 2004

Midterm grades due

Thursday, March 18, 2004

Posted March 2, 2004

3:40 pm – 4:30 pm Lockett 285

Simon Gindikin, Rutgers University
Complex geometry and complex analysis on real symmetric spaces

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents LEQSF(2002-04)-ENH-TR-13

Monday, March 22, 2004

Posted March 15, 2004

3:00 pm – 3:50 pm Lockett 381

Karl Heinrich Hofmann, Darmstadt University, Germany Professor Emeritus
Commuting exponential matrices and Lie theory

Posted February 11, 2004
Last modified January 6, 2021

3:30 pm – 4:30 pm 235, Lockett Hall

John Strain, University of California Berkeley
High-order fractional step methods for constrained differential equations

Posted March 3, 2004
Last modified March 20, 2004

3:40 pm – 5:00 pm Lockett 285

K Saito, Meijo University
Levy Laplacian and its Applications

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents.
LEQSF(2002-04)-ENH-TR-13

Posted March 3, 2004
Last modified March 12, 2004

3:40 pm – 4:30 pm tba

Neal Stoltzfus, Mathematics Department, LSU
Diagonalization of the Lickorish Form on Non-crossing Chord Diagrams

Tuesday, March 23, 2004

Posted March 4, 2004
Last modified March 2, 2021

3:40 pm – 4:30 pm Lockett 285

Fritz Gesztesy, University of Missouri, Columbia
On the spectrum of Schrödinger operators with quasi-periodic algebro-geometric KdV potential

Refreshments will be served in Keisler lounge at 3pm.

Wednesday, March 24, 2004

Posted March 3, 2004
Last modified March 20, 2004

3:40 pm – 4:30 pm Lockett 285

Alberto Setti, Università dell'Insubria, Como
Maximum principle on Riemannian manifolds: an overview

Refreshments will be served in Keisler lounge at 3pm.
Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents.
LEQSF(2002-04)-ENH-TR-13

Thursday, March 25, 2004

Posted February 11, 2004
Last modified October 4, 2021

3:30 pm – 4:30 pm Lockett Hall 285

Thomas Kerler, Ohio State University
Topological Quantum Field Theories

TQFT can be thought of as measures on topological spaces that behave nicely functorially under the gluing of spaces. We will motivate the formalism and give an elementary construction of TQFTs starting from nothing more than the basic Seifert–van Kampen Theorem. From there we will expand on more general TQFT properties, formalisms and constructions, sketch some problems of finiteness and quantization, and present a few typical applications of TQFTs.

Refreshments will be served in the lounge one half hour before the talk.
Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Monday, March 29, 2004

Posted March 22, 2004
Last modified March 25, 2004

3:30 pm – 4:30 pm 285 Lockett

Thomas Kerler, Ohio State University
Mapping Class Group Representations from TQFT

Abstract: The TQFTs of Witten Reshetikhin Turaev imply representations of the mapping class
groups over the cyclotomic integers Z[\\zeta] for \\zeta a prime root of unity. These
representations are highly structured and allow \"perturbative\" filtrations due to the
rich ideal structure of Z[\\zeta]. It is not too surprising that they are related to
well known filtrations of the mapping class groups, given, for example, by the
Johnson subgroups. We will describe such explicit relations in \"low order\" examples.

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents.
LEQSF(2002-04)-ENH-TR-13

Tuesday, March 30, 2004

Posted March 4, 2004
Last modified March 28, 2004

Control and Optimization Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 285

Salah-Eldin Mohammed, Southern Illinois University, Carbondale
The Stable Manifold Theorem for Stochastic Partial Differential Equations

Wednesday, March 31, 2004

Posted March 3, 2004

2:30 pm 240 Lockett Hall

Zhijun Cai, Department of Mechanical Engineering, LSU PhD Candidate
Adaptive Stabilization of Parametric Strict-Feedback Systems with Additive Disturbance

Abstract: This talk deals with the output regulation of uncertain, nonlinear, parametric strict-feedback systems in the presence of additive disturbance. A new continuous adaptive control law is proposed using a modified integrator backstepping design that ensures the output is asymptotically regulated to zero. Despite the disturbance, the adaptation law does not need the standard robustifying term (e.g., sigma-modification or e1-modification) to ensure the aforementioned stability result. A numerical example illustrates the main result.

Posted March 5, 2004

3:40 pm – 4:30 pm Lockett 285

David Kirshner, Department of Curriculum and Instruction, LSU
What Ails Elementary Algebra Education: Historical, Psychological, and Philosophical Perspectives

Refreshments in Keisler Lounge at 3pm

Thursday, April 1, 2004

Posted March 31, 2004

3:30 pm 285 Lockett Hall

Meeting of the tenured and tenure-track faculty

The purpose of the meeting is to discuss a senior hire at the level of full professor. A ballot will follow.

Monday, April 12, 2004

Posted April 1, 2004
Last modified March 2, 2021

3:00 pm – 3:50 pm Lockett 381

Shijun Zheng, LSU
Operator representation in wavelet bases and Application in PDEs, Part 2

We give a short review on recent development on wavelet-based numerical solution of time-dependent partial differential equations. The fundamental idea is to use wavelet to give sparse matrix representations of the solution operators involved. Thus it leads to a fast algorithm for efficient approximation of the solution to the equation. We demonstrate the general scheme by considering the anisotropic diffusion problem arising in modeling thin film image processing. Other examples are advection-diffusion equations in $CFD$, including the connection with the incompressible Navier-Stokes equations in semigroup formulation.

Posted April 12, 2004
Last modified March 2, 2022

LSU Academic Calendar Official LSU Academic Calendar Page

3:40 pm – 4:30 pm 235 Lockett Hall

Horst Beyer, Max Planck Institute for Gravitational Physics, Golm, Germany, and Dept. of Mathematics, LSU
On some vector analogues of Sturm-Liouville operators

The talk considers a general class of densely defined, linear symmetric operators in Hilbert space, which originate from the separation of vector partial differential operators (PDO) in three dimensions, which are invariant under the rotation group. Those PDO describe spheroidal Lagrangian adiabatic oscillations of spherically symmetric newtonian stars (treated as ideal fluids) in the so-called “Cowling approximation” in stellar pulsation theory. Their extension properties turn out to be very similar to that of minimal Sturm–Liouville operators. In particular close analogues of Weyl's famous theorems hold. On the other hand the spectral properties of their self-adjoint extensions are quite different. In particular every extension has a non-trivial essential spectrum. Finally, a result is given which allows to determine the resolvent of the self-adjoint extensions, which are perturbed by a “matrix” of integral operators of a specific general type. Those perturbed operators are generalizations of operators governing spheroidal adiabatic oscillations of spherically symmetric stars.

Posted January 16, 2004

Final date for resigning/dropping courses

Wednesday, April 14, 2004

Posted February 15, 2004
Last modified March 1, 2004

Control and Optimization Seminar Questions or comments?

2:30 pm Lockett Hall, Room 240

Frederic Mazenc, Institut National de Recherche en Informatique et en Automatique, FRANCE
Stabilization of Nonlinear Systems with Delay in the Input

Abstract: We present three results on the problem of globally uniformly and locally exponentially stabilizing nonlinear systems with delay in the input through differentiable bounded feedbacks: 1) We solve the problem for chains of integrators of arbitrary length. No limitation on the size of the delay is imposed. An exact knowledge of the delay is not required. 2) We solve the problem for an oscillator with an arbitrary large delay in the input. A first solution follows from a general result on the global stabilization of null controllable linear systems with delay in the input by bounded control laws with a distributed term. Next, it is shown through a Lyapunov analysis that the stabilization can be achieved as well when the distributed terms are neglected. It turns out that this main result is intimately related to the output feedback stabilization problem. 3) We solve the problem for a family of nonlinear feedforward systems when there is a delay in the input. No limitation on the size of the delay is imposed. An exact knowledge of the delay is not required.

This visit is supported by the Visiting Experts Program in Mathematics, Louisiana Board of Regents Grant LEQSF(2002-04)-ENH-TR-13.

Thursday, April 15, 2004

Posted January 9, 2004
Last modified January 6, 2021

3:30 pm – 4:30 pm Friday, April 16, 2004 235, Lockett Hall

Guillermo Goldsztein , School of Mathematics, Georgia Institute of Technology
Perfectly plastic heterogeneous materials

Posted March 23, 2004
Last modified March 3, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm

Ronald Stanke, Baylor University
Differential Operators, SL(2,R) Invariance and Special Functions

Refreshments in the Lounge one half hour before talk. Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents, LEQSF(2002-04)-ENH-TR-13.

Posted April 13, 2004

Mathematics-Physics Joint Colloquium

3:40 pm – 4:30 pm 152 Coates Hall

Ravi Rau, Department of Physics and Astronomy, LSU
Supersymmetry in Quantumn Mechanics

Monday, April 19, 2004

Posted March 23, 2004
Last modified April 16, 2004

2:40 pm – 3:30 pm Lockett 235
(Originally scheduled for 3:40 pm)

Ling Long, Iowa State University
On Atkin-Swinnerton-Dyer congruence relations

Visit supported by Visiting Experts Program in Mathematics, Louisiana

Board of Regents LEQSF(2002-04)-ENH-TR-13

Posted March 1, 2004
Last modified January 6, 2021

3:30 pm – 4:30 pm 235, Lockett Hall

Daniel Sage, Mathematics Department, LSU
Racah coefficients, subrepresentation semirings, and composite materials--An application of representation theory to material science

Wednesday, April 21, 2004

Posted April 2, 2004

3:40 pm 15 Lockett Hall

A question-and-answer session with the two candidates for chair

The meeting is open to Mathematics Department professors and instructors.

Candidates’ answers to written questions will be available to professors and instructors shortly after Spring Break.

Thursday, April 22, 2004

Posted March 28, 2004

3:40 pm – 4:30 pm Lockett 281

Boris Rubin, The Hebrew University of Jerusalem
Selected problems of integral geometry and small denominators on the sphere

Monday, April 26, 2004

Posted April 20, 2004

3:00 pm – 3:50 pm Lockett 381

Boris Rubin, Louisiana State University
Zeta integrals and Radon transforms on the space of rectangular matrices

Posted April 7, 2004
Last modified April 25, 2004

3:30 pm – 4:30 pm 285 Lockett Hall

Paul Saylor, University of Illinois
What Does Radar Have to Do with Solving Sets of Linear Equations?

Tuesday, April 27, 2004

Posted March 31, 2004
Last modified April 26, 2004

3:40 pm – 4:30 pm Lockett 281

Thierry Lévy, École normale supérieure and CNRS
Two-dimensional Yang-Mills theory is almost a topological field theory

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents LEQSF(2002-04)-ENH-TR-13

Wednesday, April 28, 2004

Posted February 15, 2004
Last modified November 16, 2023

2:30 pm Lockett Hall, Room 240

Michael Malisoff, LSU Roy P. Daniels Professor
Remarks on the Strong Invariance Property for Non-Lipschitz Dynamics

Abstract: Topics in flow invariance theory provide the foundation for considerable current research in modern control theory and optimization.Starting from strong invariance and its Hamiltonian characterizations, one can develop uniqueness results and regularity theory for proximal solutions of Hamilton-Jacobi-Bellman equations, stability theory, infinitesimal characterizations of monotonicity, and many other applications. On the other hand, it is well appreciated that many important dynamics are non-Lipschitz, and may even be discontinuous, and therefore are beyond the scope of the known strong invariance characterizations. Therefore, the development of conditions guaranteeing strong invariance under less restrictive assumptions is a problem that is of considerable ongoing research interest. In this talk we will report on some recently developed sufficient conditions for strong invariance for discontinuous differential inclusions. This talk is based in part on the speaker\'s joint work with Mikhail Krastanov and Peter Wolenski.

Thursday, April 29, 2004

Posted March 16, 2004
Last modified April 13, 2004

3:30 pm – 4:30 pm 285 Lockett

Paulo Lima-Filho, Texas A&M
Applications of operads and ternary trees to polynomial map

Using ternary trees we build operads and use them to define a family of ideals in the (non-commutative) algebra generated by pointed ternary trees. These constructions have several applications to iterations of polynomial maps and conjectures in algebraic geometry. This is an essentially self-contained talk, accessible to a general audience and to graduate students. Refreshments will be served in the lounge one half hour before the talk.

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents.

LEQSF(2002-04)-ENH-TR-13

Friday, April 30, 2004

Posted April 30, 2004

2:00 pm Lockett 301 D

Costel Ionita, Mathematics Department, LSU
Class Groups and Norms of Units

Graduate Advisor: Jurgen Hurrelbrink

Posted April 20, 2004

Algebra and Number Theory Seminar Questions or comments?

2:30 pm – 3:30 pm Lockett 381

Ziemowit Rzeszotnik, University of Texas, Austin
Norm of the Fourier transform on finite abelian groups

Posted April 26, 2004
Last modified April 27, 2004

3:40 pm – 4:30 pm Lockett 235

Paulo Lima-Filho, Texas A&M
On the RO(Z/2)-graded equivariant cohomology ring of real quadrics

ABSTRACT: We provide a complete presentation of the RO(Z/2)-graded
equivariant cohomology ring of real quadrics under the action of the
Galois group. Then we exhibit its relation to classical objects in
topology and to motivic cohomology over the reals.

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of
Regents LEQSF(2002-04)-ENH-TR-13

Monday, May 3, 2004

Posted April 27, 2004

3:00 pm – 3:50 pm Lockett 381

Dave Larson, Texas A&M
Wavelet sets and Frames

Wednesday, May 5, 2004

Posted March 29, 2004
Last modified April 1, 2004

3:00 pm – 4:30 pm Hill Memorial Library

Reception for Dr. Richard Anderson

Please join us for a reception honoring Dr. Richard Anderson and his accomplishments in mathematics and mathematics education.

Refreshments will be served.

Sponsored by the Cain Center and the Department of Mathematics

Thursday, May 6, 2004

Posted May 3, 2004

3:00 pm James Kiesler Lounge, 319 Lockett Hall

Spring Math Awards Ceremony

The Porcelli Scholarships, The Betti and Robert Giles Senior Mathematics Award, The David Oxley Memorial Graduate Student Teaching Award, and Certificates of Teaching Excellence (for graduate assistants) will be awarded. Refreshments will be provided. This will also serve as the colloquium tea for the colloquium which follows.

Posted April 3, 2004

3:30 pm – 4:30 pm 285 Lockett Hall

Milton C. Lopes Filho, Penn State University and UNICAMP, Brazil
Open problems on mathematical hydrodynamics

Abstract: Mathematical hydrodynamics is primarily concerned with the behavior of solutions of the incompressible Euler and Navier-Stokes equations. These nonlinear systems of PDEs have a rich mathematical structure that keeps hydrodynamics a topic of current interest in mathematical research. One illustration of the cogency of this topic is the choice of the singularity problem for the Navier-Stokes equations as one of the seven Millenium Prize Problems. Problems in the field of mathematical hydrodynamics often reduce to proving that solutions of the incompressible flow equations behave as actual fluids are known to behave. In this talk we will examine a few instances where the known behavior of real fluids leads to open problems on the behavior of solutions of the incompressible flow equations, exploring the power, and the limitations, of modern analytic techniques used in the treatment of these problems.

Refreshments will be served in the lounge one half hour before the talk. Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Friday, May 7, 2004

Posted April 26, 2004
Last modified January 6, 2021

3:30 pm – 4:30 pm 235, Lockett Hall

Helena Nussenzveig Lopes, Universidade Estadual de Campinas (Brasil) and Penn State University
On vortex sheet evolution

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Tuesday, May 11, 2004

Posted May 7, 2004

3:30 pm Lockett 285

Faculty Meeting

The agenda is a report on the upcoming program review and hiring.

Friday, May 14, 2004

Posted May 13, 2004

3:30 pm – 4:30 pm Lockett 285

Cun-Quan Zhang, West Virginia University
Some Results about Integer Flows

Refreshments in Keisler Lounge at 3pm

Tuesday, May 18, 2004

Posted May 7, 2004

10:00 am Lockett 301 D

Vochita Mihai, Department of Mathematics, LSU Graduate Student
The Radon-Gauss Transform

Graduate Advisor: Ambar Sengupta

Monday, June 28, 2004

Posted June 7, 2004

3:00 pm 301D Lockett Hall

Troels Johansen, Mathematics Department, LSU Graduate Student
Orbit structure on the Silov boundary of a tube domain and the Plancherel decomposition of a causally compact symmetric space, with emphasis on the rank one case

Graduate Advisor: Gestur Olafsson

Thursday, July 8, 2004

Posted June 18, 2004

11:30 am 301D Lockett Hall

Mihaly Kovacs, Mathematics Department, LSU Graduate Student
On qualitative properties and convergence of time-discretization methods for semigroups

Graduate Advisors: Frank Neubrander (LSU) and Istvan Farago (Eotvos Lorand University, Budapest, Hungary)

Thursday, August 12, 2004

Posted July 19, 2004
Last modified July 25, 2021

until Friday, August 13, 2004 LSU Union Building

International Graduate Student Orientation Meetings

New International Student Orientation for the Fall semester of 2004 will be held on Thursday and Friday, August 12-13, 2004. International Orientation begins Thursday, August 12, 2004 from 8:00 a.m. - 4:30 p.m. in the Royal-Cotillion Ballroom of the LSU Union. At 8:15 a.m. on Friday, August 13, new international students are to report to 51 Himes Hall for Michigan English testing (written English). Appointments will be scheduled for Spoken English Interviews for all International Graduate Assistants.

Monday, August 16, 2004

Posted July 19, 2004
Last modified July 21, 2004

9:00 am – 3:00 pm Friday, August 20, 2004 386 Lockett Hall

Registration of New Graduate Students, Monday through Friday

All new graduate students in mathematics should visit the Director in 386 Lockett Hall to register for courses between Monday and Friday this week. A list of other items to which new students must attend that week will be provided at that office, so please visit early rather than late!

Posted July 19, 2004

1:30 pm – 4:00 pm 285 Lockett Hall

Core-1 Comprehensive Exam in Analysis

This is part of the PhD Qualifying Exam. Graduate students need to pass the three Core-1 tests and any one of the six possible Core-2 tests by January of the second year of study. All students taking Comprehensive Exams should pre-register for them with the Graduate Director.

Tuesday, August 17, 2004

Posted July 19, 2004

1:30 pm – 4:00 pm 285 Lockett Hall

Core-1 Comprehensive Exam in Topology

Wednesday, August 18, 2004

Posted July 19, 2004

8:15 am – 12:30 pm LSU Union Theater Lobby

Graduate Student Orientation

This is the Graduate School's required Orientation Meeting for all new graduate students at LSU. Coffee, donuts and juice will be served at 8:15 AM and lunch will be served later. There will be an Information and Resource Fair included in the Cotillion Ballroom starting at 11 AM.

Thursday, August 19, 2004

Posted July 21, 2004
Last modified August 10, 2004

10:00 am – 12:00 pm Room 235, Lockett Hall

Orientation Meeting for Graduate Students leading recitations in Math 1431 and 1022

Graduate Students assigned to lead recitation sections for Math 1431 (Business Calculus) and 1022 (Trigonometry) will learn how to help undergraduates with MAPLE TA, a computer program which will be used this fall to support instruction in those subjects. Graduate Students who have been assigned to lead recitations in these subjects will receive a note about this in their letter boxes in Room 301 in August.

Posted July 19, 2004

1:30 pm – 4:00 pm 285 Lockett Hall

Core-1 Comprehensive Exam in Algebra

Friday, August 20, 2004

Posted July 19, 2004

Control and Optimization Seminar Questions or comments?

1:00 pm – 4:30 pm 285 Lockett Hall

Core-2 Comprehensive Exams

Graduate students need to pass the three Core-1 tests and any one of the six possible Core-2 tests by January of the second year of study. All students taking Comprehensive Exams should pre-register for them with the Graduate Director. Since there is a choice of Core-2 Exam subjects, Core-2 Exams will be offered only according to the requests of students who have registered.

Wednesday, September 1, 2004

Posted August 27, 2004

3:00 pm 381 Lockett Hall

Stanislav Zabic, Louisiana State University Department of Mathematics Graduate Student
Impulsive Systems

Wednesday, September 8, 2004

Posted August 20, 2004

3:30 pm Lockett 5

Provost Palm speaks to the faculty.

The Provost and Executive Vice Chancellor, Risa Palm, will visit the Mathematics Department and discuss the National Flagship Agenda.

Friday, September 10, 2004

Posted August 23, 2004

Control and Optimization Seminar Questions or comments?

3:00 pm – 4:00 pm Atchafalaya Room of the Union

A&S Assistant Professor Meeting

Come Meet the Deans! Refreshments will be served

Monday, September 13, 2004

Posted September 3, 2004
Last modified September 10, 2004

3:00 pm 381 Lockett Hall
(Originally scheduled for Wednesday, September 8, 2004, 3:00 pm)

Stanislav Zabic, Louisiana State University Department of Mathematics Graduate Student
Impulsive Systems, Part II

Posted September 8, 2004

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 243 Lockett

Graduate Student Seminar

Bill Schellhorn will speak.

Tuesday, September 14, 2004

Posted September 9, 2004
Last modified September 13, 2004

3:10 pm – 4:00 pm Lockett 282

Helena Verrill, Mathematics Department, LSU
Finding the Picard Fuchs differential equations of certain families of Calabi-Yau varieties

Posted September 8, 2004

4:10 pm – 5:00 pm Lockett 284

Scott Baldridge, Louisiana State University
Introduction to 4-Manifold Theory, I

Posted August 24, 2004

4:30 pm The James Keisler Lounge (321 Lockett)

Actuarial Student Association Meeting

Organizing meeting to set up study groups, propose speakers, and introduce new officers.

Wednesday, September 15, 2004

Posted September 9, 2004

Control and Optimization Seminar Questions or comments?

2:40 pm – 3:30 pm Lockett 381

Jens Christensen, Mathematics Department, LSU
Uncertainty principles generated by Lie-groups

Monday, September 20, 2004

Posted September 20, 2004

3:00 pm 381 Lockett Hall

Norma Ortiz, Mathematics Department, LSU PhD Student
An Existence Theorem for the Neutral Problem of Bolza

Posted September 8, 2004

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 243 Lockett

Graduate Student Seminar

Steven Wallace will speak.

Tuesday, September 21, 2004

Posted September 17, 2004

3:10 pm – 4:00 pm Lockett 282

Jerome W. Hoffman, Mathematics Department, LSU
Modular forms on noncongruence subgroups and Atkin-Swinnerton_Dyer congruences

Posted September 20, 2004

4:10 pm – 5:00 pm Lockett 284

Scott Baldridge, Louisiana State University
Introduction to 4-manifold theory, II

Wednesday, September 22, 2004

Posted September 17, 2004

2:40 pm – 3:30 pm Lockett 381

Jens Christensen, Mathematics Department, LSU
Uncertainty principles generated by Lie-groups

Thursday, September 23, 2004

Posted September 17, 2004

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 277

Daniel Sage, Mathematics Department, LSU
Group and quantum group actions on algebras and composite materials

Monday, September 27, 2004

Posted September 21, 2004

3:10 pm – 4:00 pm Lockett 381

Norma Ortiz, Mathematics Department, LSU PhD Student
An existence theorem for the neutral problem of Bolza, Part II

Tuesday, September 28, 2004

Posted September 9, 2004
Last modified March 2, 2021

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm Lockett 282

Marco Schlichting, Louisiana State University
Higher algebraic K-theory of forms and Karoubi's fundamental theorem

Posted September 21, 2004

4:10 pm – 5:00 pm Lockett 284

Scott Baldridge, Louisiana State University
Introduction to 4-Manifolds III

Wednesday, September 29, 2004

Posted September 22, 2004

2:40 pm – 3:30 pm Lockett 381

Jens Christensen, Mathematics Department, LSU
An Uncertainty Principle Related to the Euclidean motion group

I will show that a well known uncertainty principle for functions on the circle can be derived from the generators of the Euclidean motion group.

Thursday, September 30, 2004

Posted September 23, 2004

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 277

Ricardo Estrada, Mathematics Department, LSU
On the regularization of generalized functions

Monday, October 4, 2004

Posted September 29, 2004
Last modified October 1, 2004

3:10 pm – 4:00 pm 381 Lockett Hall

Vinicio Rios, LSU Department of Mathematics PhD Student
Strong Invariance for Dissipative Lipschitz Dynamics

Posted September 8, 2004

3:30 pm – 4:30 pm 243 Lockett

Graduate Student Seminar

Jean Bureau will speak.

Tuesday, October 5, 2004

Posted September 30, 2004

3:30 pm – 4:30 pm Lockett 239

Mark Davidson, Mathematics Department, LSU
Generating functions associated to Highest Weight Representations

Wednesday, October 6, 2004

Posted September 30, 2004

2:40 pm – 3:30 pm Lockett 381

Daniel Sage, Mathematics Department, LSU
Group and Hopf algebra actions on central simple algebras.

Monday, October 11, 2004

Posted August 4, 2004

Control and Optimization Seminar Questions or comments?

3:00 pm Lockett 2

Meeting with the Dean of the College.

Dean Ferreyra will meet with faculty members to discuss the chair\'s evaluation.

Posted October 6, 2004

3:10 pm – 4:00 pm 381 Lockett Hall

Vinicio Rios, LSU Department of Mathematics PhD Student
Strong Invariance for Dissipative Lipschitz Dynamics, Part II

Tuesday, October 12, 2004

Posted October 4, 2004

Refreshments

2:30 pm – 3:00 pm Keisler Lounge

Refreshments before talk of Gregor Masbaum

Scheduled not to conflict with Algebra Seminar Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents LEQSF(2002-04)-ENH-TR-13

Posted September 9, 2004
Last modified September 30, 2004

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm Tuesday, October 5, 2004 Lockett 282

Ambar Sengupta, Mathematics Department, LSU
Calculus Reform, or How (super)Algebra simplifies Calculus (on manifolds)

Posted October 8, 2004
Last modified March 2, 2021

3:30 pm – 4:30 pm Lockett 277

Kiseop Lee, University of Louisville
Insider's hedging in a jump diffusion model

Posted September 24, 2004
Last modified October 1, 2004

4:00 pm – 5:00 pm Lockett 284

Gregor Masbaum, University Paris 7
Integral lattices in TQFT

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents LEQSF(2002-04)-ENH-TR-13

Wednesday, October 13, 2004

Posted September 24, 2004

Control and Optimization Seminar Questions or comments?

3:00 pm Allen 35

Meeting of the Tenured Faculty

Promotion Cases: One to associate professor, two to full professor, and one tenure only.

Monday, October 18, 2004

Posted October 13, 2004
Last modified October 14, 2004

3:10 pm – 4:00 pm 381 Lockett Hall

George Cazacu, LSU Department of Mathematics PhD student
A characterization of stability for dynamical polysystems via Lyapunov functions

Posted September 22, 2004

3:30 pm – 4:30 pm Lockett 243

Graduate Student Seminar

Debra Czarneski will speak on Zeta functions for graphs

Wednesday, October 20, 2004

Posted October 18, 2004

Algebra and Number Theory Seminar Questions or comments?

2:40 pm – 3:30 pm Lockett 312

Daniel Sage, Mathematics Department, LSU
Group and Hopf algebra actions on central simple algebras. II

Posted September 17, 2004
Last modified October 19, 2004

3:40 pm – 4:30 pm Lockett 282

Pramod Achar, Mathematics Department, LSU
Hecke algebras and complex reflection groups

Saturday, October 23, 2004

Posted July 19, 2004
Last modified July 25, 2021

Control and Optimization Seminar Questions or comments?

9:30 am – 4:30 am Tickfaw State Park
(Originally scheduled for Saturday, September 18, 2004, 9:00 am)

Graduate Student Day

Monday, October 25, 2004

Posted October 20, 2004

3:10 pm – 4:00 pm 381 Lockett Hall

George Cazacu, LSU Department of Mathematics PhD student
Closed relations and Lyapunov functions for polysystems

Posted October 12, 2004

3:30 pm – 4:30 pm Lockett 243

Graduate Student Seminar

Jeremy J. Becnel will give a talk on \"Windows 2020: Built on Quantum Technology\"

Tuesday, October 26, 2004

Posted October 20, 2004

3:00 pm Lockett 284

Hiring Plan

The IRC is finishing their hiring plan and will release the document soon. The meeting is to discuss the plan.

Wednesday, October 27, 2004

Posted October 22, 2004

2:40 pm – 3:30 pm Lockett 281

Daniel Sage, Mathematics Department, LSU
Group and Hopf algebra actions on central simple algebras. III

Thursday, October 28, 2004

Posted October 20, 2004
Last modified March 2, 2021

3:40 pm – 4:30 pm Lockett 277

Fernando Rodriguez-Villegas, University of Texas at Austin
The Many Aspects of Mahler's Measure

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents LEQSF(2002-04)-ENH-TR-13. Refreshments will be served in the lounge at 3pm.

Friday, October 29, 2004

Posted October 25, 2004
Last modified March 2, 2021

Joint Topology and Algebra/Number Theory Seminar

3:30 pm – 4:30 pm Lockett 243

Fernando Rodriguez-Villegas, University of Texas at Austin
Mahler's measure and the Dilogarithm

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents LEQSF(2002-04)-ENH-TR-13

Monday, November 1, 2004

Posted October 22, 2004
Last modified December 13, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 243

Graduate Student Seminar

Khaled Qazaqzeh will give a talk on “The Parity of the Maslov Index” (joint work with P. Gilmer)

Tuesday, November 2, 2004

Posted September 10, 2004
Last modified March 2, 2021

3:10 pm – 4:00 pm Tuesday, October 26, 2004 Lockett 282
(Originally scheduled for Monday, October 4, 2004)

Robert Perlis, Mathematics Department, LSU
Disconnected thoughts on Klein's four group

Wednesday, November 3, 2004

Posted November 3, 2004

2:40 pm – 3:30 pm Lockett 381

Daniel Sage, Mathematics Department, LSU
Group and Hopf algebra actions on central simple algebras. IV

Friday, November 5, 2004

Posted September 10, 2004
Last modified January 6, 2021

3:30 pm – 4:30 pm 239, Lockett Hall

Enrique Reyes, University of New Orleans
Practical finite difference modeling approaches to environmental problems: Louisiana coastal land loss.

Wednesday, November 10, 2004

Posted November 3, 2004

2:40 pm – 3:30 pm Lockett 381

Daniel Sage, Mathematics Department, LSU
Group and Hopf algebra actions on central simple algebras. V

Friday, November 12, 2004

Posted October 13, 2004

Control and Optimization Seminar Questions or comments?

3:30 pm 239, Lockett Hall

Stephen Shipman, Mathematics Department, LSU
Anomalous electromagnetic transmission mediated by guided modes

Monday, November 15, 2004

Posted November 8, 2004
Last modified November 9, 2004

Computational Mathematics/CCT Seminar

3:00 pm 338, Johnston Hall

Oren Livne, School of Computing, University of Utah
A Multigrid Overview

Posted November 10, 2004
Last modified November 16, 2023

3:00 pm 381 Lockett Hall

Michael Malisoff, LSU Roy P. Daniels Professor
New Constructions of Strict Input-to-State Stable Lyapunov Functions for Time-Varying Systems

This talk is based on the speaker's joint work “Further Remarks on Strict Input-to-State Stable Lyapunov Functions for Time-Varying Systems” with Frederic Mazenc (arXiv math.OC/0411150).

Monday, November 22, 2004

Posted November 3, 2004
Last modified November 17, 2004

3:10 pm – 4:00 pm 381 Lockett Hall

Peter Wolenski, LSU Department of Mathematics Russell B. Long Professor
Introduction to control Lyapunov functions and feedback

Posted November 11, 2004
Last modified December 13, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 243

Graduate Student Seminar

Michael Aristidou will talk about “Laguerre Functions for the Cone of Positive Definite Real Matrices”

Monday, November 29, 2004

Posted November 25, 2004

3:10 pm – 4:00 pm 381 Lockett Hall

Peter Wolenski, LSU Department of Mathematics Russell B. Long Professor
Introduction to control Lyapunov functions and feedback, Part II

Tuesday, November 30, 2004

Posted November 18, 2004
Last modified November 29, 2004

3:10 pm Lockett 277

Meeting of the Tenured and Tenure-Track Faculty

online voting, delegating hiring authority, promotion/tenure/evaluation discussion

Friday, December 3, 2004

Posted October 26, 2004

3:30 pm 239, Lockett Hall

Jonathan Dowling, Louisiana State University, Department of Physics Hearne Professor of Theoretical Physics at LSU, Quantum Sciences and Technologies Group
Effective densities of state

Wednesday, December 8, 2004

Posted November 29, 2004

Party

12:00 pm James Keisler lounge (Room 321 Lockett)

Christmas Party

Food, Awards, and Food.

Posted November 29, 2004
Last modified March 3, 2021

3:40 pm – 4:30 pm 277 Lockett

Christopher Leininger, Columbia University Candidate for Assistant Professor Position in Topology
Teichmüller disks in geometry and topology

Refreshments in Keisler Lounge at 3:00 PM

Friday, December 10, 2004

Posted October 26, 2004

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 239, Lockett Hall

Petr Plechak, Mathematics Institute, University of Warwick Candidate for Associate Professor Position in Scientific Computation
TBA

Sunday, January 9, 2005

Posted December 9, 2005

Locket 285

Marie-José Bertin, Université Pierre et Marie Curie, Paris
TBA

Monday, January 10, 2005

Posted January 3, 2005

1:30 pm – 4:00 pm Room 285 Lockett Hall

Core-I Analysis

Comprehensive (PhD Qualifying) Exam

Tuesday, January 11, 2005

Posted January 3, 2005

1:30 pm – 4:00 pm Room 285 Lockett Hall

Core-I Topology

Comprehensive (PhD Qualifying) Exam

Thursday, January 13, 2005

Posted December 27, 2005
Last modified July 25, 2021

1:30 pm 285 Lockett Hall

Core-1 Analysis Comprehensive/PhD Qualifying Exam

This is the first of the three component tests of the Core-1 part of the PhD Qualifying Exam.

Posted January 3, 2005

1:30 pm – 4:00 pm Room 285 Lockett Hall

Core-I Algebra

Comprehensive (PhD Qualifying) Exam

Friday, January 14, 2005

Posted January 3, 2005

1:00 pm – 4:30 pm Room 285 Lockett

Core-II Exams (all)

Comprehensive (PhD qualifying) Exam

Tuesday, January 18, 2005

Posted December 13, 2004
Last modified January 5, 2005

3:40 pm Lockett 285

Selim Esedoglu, UCLA Candidate for Assistant Professor Position in Applied Math
Threshold dynamics for the piecewise constant Mumford-Shah

Wednesday, January 19, 2005

Posted January 5, 2005
Last modified January 12, 2005

3:40 pm Lockett 285

Burak Aksoylu, University of Texas at Austin, Institute for Computational Eng. and Science Candidate for Assistant Professor Position in Scientific Computation
Local refinement and single/multi level preconditioning with applications in biophysics, computer graphics, and geosciences

Friday, January 21, 2005

Posted October 3, 2004
Last modified October 26, 2004

3:30 pm – 4:30 pm

Michel Jabbour, University of Kentucky
TBA

Tuesday, January 25, 2005

Posted December 13, 2004
Last modified January 14, 2005

3:40 pm Lockett 285
(Originally scheduled for Thursday, January 20, 2005, 3:40 pm)

Valeriy Slastikov, Carnegie Mellon University Candidate for Assistant Professor Position in Applied Math
Geometrically Constrained Walls

Wednesday, January 26, 2005

Posted January 25, 2005

10:40 am – 11:30 am Lockett 282

Jimmie Lawson, Mathematics Department, LSU
Symmetric Spaces with Seminegative Curvature

Friday, January 28, 2005

Posted January 24, 2005
Last modified January 27, 2005

1:40 pm Lockett 138

Tara Brendle, Mathematics Department, Cornell University Candidate for Assistant Professor Position in Topology
Mapping class groups and complexes of curves

Posted October 27, 2004
Last modified January 6, 2021

3:30 pm – 4:30 pm 235, Lockett Hall

Asher Rubinstein, Department of Mechanical Engineering, Tulane University
Failure Analysis of Thermal Barrier Coatings

Posted January 24, 2005
Last modified January 26, 2005

3:40 pm Lockett 285

Brendan Owens, Mathematics Department, Cornell University Candidate for Assistant Professor Position in Topology
Four-manifolds with prescribed boundary and applications to knot theory

Tuesday, February 1, 2005

Posted January 21, 2005
Last modified January 26, 2005

3:40 pm Lockett 285

Masako (Marta) Asaeda, Mathematics Department, University of Iowa Candidate for Assistant Professor Position in Topology
Generalizations of Khovanov homology

Posted January 21, 2005

4:00 pm Keisler Lounge

Spring Organizational Meeting of the ASA

Wednesday, February 2, 2005

Posted January 25, 2005

10:40 am – 11:30 am Lockett 282

Jimmie Lawson, Mathematics Department, LSU
Symmetric Spaces of Seminegative Curvature

Posted January 26, 2005
Last modified January 31, 2005

3:40 pm Lockett 285

Hongyu He, Mathematics Department, LSU
Tensor Products of Oscillator Representations

Friday, February 11, 2005

Posted January 26, 2005
Last modified February 3, 2005

3:40 pm Lockett 285

Ai-Ko Liu, U. C. Berkeley, Mathematics Candidate for Assistant Professor in Geometric Analysis
Cosmic String, Family Seiberg-Witten theory and Harvey-Moore Conjecture

Monday, February 14, 2005

Posted February 11, 2005

3:40 pm Lockett 285

Meeting of the tenured and tenure-track faculty

The VIGRE grant and the Friday site visit.

Tuesday, February 15, 2005

Posted January 31, 2005
Last modified February 1, 2005

3:40 pm Lockett 285

Justin Sawon, Department of Mathematics, SUNY at Stony Brook Candidate for Assistant Professor in Topology
Derived equivalence of algebraic varieties

Wednesday, February 16, 2005

Posted February 4, 2005

10:40 am – 11:30 am Lockett 282

Jimmie Lawson, Mathematics Department, LSU
Symmetric Spaces of seminegative curvature

Posted February 10, 2005
Last modified February 15, 2005

1:00 pm – 2:00 pm Life Sciences A 663 Access Grid Video Conference Room

Daniel C. Cohen, Mathematics Department, LSU
Topology and Combinatorics of boundary manifolds of arrangements

Joint Virtual Seminar with the University of Iowa

Posted January 31, 2005
Last modified February 1, 2005

3:40 pm Lockett 285

Yann Rollin, MIT, Department of Mathematics Candidate for Assistant Professor in Geometric Analysis
Construction of Kaehler surfaces with constant scalar curvature

Friday, February 18, 2005

Posted February 16, 2005

VIGRE panel site

8:00 am – 4:45 pm James E. Keisler Mathematics Lounge

VIGRE panel site visit

The VIGRE panel will interview with various students, faculty, and administrators throughout the day.

Posted October 26, 2004
Last modified January 6, 2021

3:30 pm – 4:30 pm 239, Lockett Hall

Susanne Brenner, Department of Mathematics, University of South Carolina
Additive Multigrid Theory

Monday, February 21, 2005

Posted February 12, 2005

3:30 pm Lockett 285

Meeting of the Tenured Faculty

Discuss the third year review cases.

Tuesday, February 22, 2005

Posted February 16, 2005
Last modified March 3, 2021

3:30 pm – 4:30 pm Lockett 285

Leticia Barchini, Oklahoma State University at Stillwater
Positivity of Zeta distributions and small representations

We study positivity of zeta distributions associated to noneuclidean Jordan algebras. The values of the complex parameter s for which the distributions are positive is determined. A theory analogous to the classical theory of Riesz distributions and Wallach set is developed. We calculate the distributions when they are positive. For each value of s for which the zeta distribution is positive we build a Hilbert space. These Hilbert spaces are representations spaces for the conformal groups of the Jordan algebras involved. In this way we build an explicit family of small (non holomorphic) representations.

Wednesday, February 23, 2005

Posted February 16, 2005

10:40 am – 11:30 am Lockett 282

Leticia Barchini, Oklahoma State University at Stillwater
Remarks on the characteristic cycle of discrete series of SU(p,q)

Posted February 20, 2005

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 285

William Schellhorn, LSU
Virtual Strings for Closed Curves with Multiple Components

Abstract: A Gauss paragraph is a combinatorial formulation of a generic closed curve with multiple components on some surface. A virtual string is a collection of circles with arrows that represent the crossings of such a curve. Every closed curve has an underlying virtual string and every virtual string has an underlying Gauss paragraph. A word-wise partition is a partition of the alphabet set of a Gauss paragraph that satisfies certain conditions with respect to the Gauss paragraph. This talk will discuss how the theory of virtual strings can be used to obtain necessary and sufficient conditions for a Gauss paragraph and word-wise partition to represent a closed curve in the 2-sphere.

Posted February 21, 2005
Last modified February 25, 2005

3:30 pm 2150 CEBA

Michael Malisoff, LSU Roy P. Daniels Professor
An Introduction to Input-to-State Stability

Thursday, February 24, 2005

Posted February 21, 2005

2:00 pm – 2:50 pm Lockett 277

Stephen(Steve) Bryson, NASA Ames Research Center Candidate for Assistant Professor Position in Scientific Computation
Central Methods for Balance Laws

Saturday, February 26, 2005

Posted December 2, 2004
Last modified February 21, 2005

LSU High School Math Contest

9:00 am – 4:00 pm

LSU High School Math Contest

This year the contest is being organized by Jacek Cygan. More information is at the Contest Website.

Monday, February 28, 2005

Posted February 26, 2005
Last modified February 27, 2005

Student Seminar

5:00 pm – 6:00 pm 3rd floor lounge, Lockett Hall

Michael Aristidou Graduate Student
Consistency, Probability and Human Rationality

Intended for all students, both graduate and undergraduate.

Wednesday, March 2, 2005

Posted February 22, 2005

10:40 am – 11:30 am Lockett 282

Boris Rubin, Louisiana State University
The Composite Cosine Transform on the Stiefel Manifold

Thursday, March 3, 2005

Posted February 23, 2005
Last modified February 25, 2005

3:40 pm Lockett 285

Yaniv Almog, Department of Mathematics, Technion I.I.T. Candidate for Assistant Professor Position in Applied Math
Abrikosov lattices in finite domain

Friday, March 4, 2005

Posted October 26, 2004
Last modified January 6, 2021

3:30 pm – 4:30 pm 235, Lockett Hall

Béatrice Rivière, Department of Mathematics, University of Pittsburgh
Discontinuous Galerkin methods for incompressible flows

Monday, March 7, 2005

Posted February 23, 2005
Last modified March 4, 2005

Algebra and Number Theory Seminar Questions or comments?

3:40 pm Lockett 285

Petr Plechak, Mathematics Institute, University of Warwick Candidate for Associate Professor Position in Scientific Computation
Approximation and coarse-graining of stochastic lattice systems

Posted March 6, 2005

Student Seminar

5:00 pm Math Lounge, third floor of Lockett

Martin Laubinger, LSU Graduate Student
Card Shuffling

In \"Proofs from THE BOOK,\" Martin Aigner and Gunter M. Ziegler discuss various methods of Card Shuffling, inclduing Top-in-at-random shuffles and riffle shuffles. Learn some basic Combinatorics or learn how to analyze random\" shuffling using combinatorial reasoning. Bring your favorite deck of cards or your favorite card trick, and we\'ll discuss the mathematics of cards before the talk begins. There will be pizza, as usual, but all are encouraged to bring their own drinks.

Tuesday, March 8, 2005

Posted March 4, 2005

2:30 pm – 3:30 pm Lockett 282

Augusto Nobile, Mathematics Department, LSU
Algorithmic equiresolution

Posted March 1, 2005
Last modified October 1, 2021

3:30 pm – 4:30 pm Lockett 239

Kee Lam, University of British Columbia
Low dimensional spinor bundles over projective spaces

Given a k-dimensional vector bundle E over a real projective space, the "geometric dimension problem" asks for the maximal s such that E contains an s-dimensional trivial sub-bundle. This problem originates from the study of immersions of projective spaces into Euclidean space, and has been much pursued by topologists over the last 40 years. As a general phenomenon, k-s will be smaller when k is divisible by a higher power of 2. In this talk we shall examine such a phenomenon from the view point of spinor representations, and obtain some partial results. Some of these results turn out to be best possible.

Posted March 1, 2005
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 285

Brian Hall, University of Notre Dame
The range of the heat operator

I will consider the heat operator both on Euclidean space and on certain symmetric manifolds such as spheres and hyperbolic spaces. I will begin by reviewing the heat equation itself, which describes how temperature distributions evolve in time. Then I will consider the following question: What class of functions does one obtain by taking an arbitrary initial temperature distribution and then running the heat equation for some fixed time t? The heat equation is very smoothing: the diffusion of heat smoothes out any rough edges in the initial temperature distribution. Thus the functions obtained must be very nice ones and I will characterize them in terms of their analyticity properties. My talk will follow a recent reprint, available at www.arxiv.org/abs/math.DG/0409308.

Wednesday, March 9, 2005

Posted March 3, 2005

Control and Optimization Seminar Questions or comments?

10:40 am – 11:30 am Lockett 282

Boris Rubin, Louisiana State University
The Composite Cosine Transform on the Stiefel Manifold II

Posted March 8, 2005
Last modified March 9, 2005

3:30 pm – 4:30 pm 2150 CEBA

Rafal Goebel, University of California, Santa Barbara
Hybrid dynamical systems: solution concepts, graphical convergence, and robust stability

Hybrid dynamical systems, that is systems in which some variables evolve continuously while other variables may jump, are an active area of research in control engineering. Basic examples of such systems include a bouncing ball (where the velocity \"jumps\" every time the ball hits the ground) and a room with a thermostat (where the temperature changes continuously while the heater is either \"on\" or \"off\"), much more elaborate cases are studied for example in robotics and automobile design.

The talk will present some challenges encountered on the way to a successful stability theory of hybrid systems, and propose a way to overcome them. In particular, we will motivate the use
of generalized time domains, show how the nonclassical notion of graphical convergence appears to be the correct concept to treat sequences of solutions to hybrid systems, and how various other tools of set-valued and nonsmooth analysis may and need to be used.

Monday, March 14, 2005

Posted March 14, 2005

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 5:00 pm Keisler Lounge

Bogdan Oporowski, Mathematics Department, LSU
A Brief Introduction to Graph Theory

Tuesday, March 15, 2005

Posted March 9, 2005
Last modified March 11, 2005

3:10 pm – 4:00 pm Lockett 282

Jean Bureau, Louisiana State University
The Four Conjecture

Posted March 9, 2005
Last modified March 11, 2005

4:00 pm – 5:00 pm Lockett 285

Patrick Gilmer, Mathematics Department, LSU
Integral Lattices in TQFT

Thursday, March 17, 2005

Posted March 11, 2005

3:40 pm – 4:30 pm Lockett 381

Habib Ouerdiane, University of Tunis
Solutions of stochastic heat equations of convolution type

Friday, March 18, 2005

Posted March 11, 2005

Algebra and Number Theory Seminar Questions or comments?

11:10 am – 12:00 pm Lockett 381

Habib Ouerdiane, University of Tunis
Infinite dimensional entire functions and applications to stochastic differential equations

Tuesday, March 29, 2005

Posted March 15, 2005

3:10 pm – 4:00 pm Lockett 282

Jurgen Hurrelbrink, Mathematics Department, LSU
Quadratic Forms over Fields: The Splitting Pattern Conjecture

Wednesday, March 30, 2005

Posted March 29, 2005

1:30 pm – 2:30 pm

Xiao-Song Lin, University of California Riverside
Representations of Braid Groups and Colored Homfly Polynomials

Virtual Seminar together with U Iowa

Thursday, March 31, 2005

Posted March 28, 2005

2:00 pm Lockett 277

Meeting of the tenured and tenure-track faculty

Meeting of the tenured and tenure track faculty to discuss the possibility of a Math-Biology program.

Posted February 22, 2005
Last modified March 28, 2005

3:30 pm – 4:30 pm Lockett 285

Alexander Figotin, University of California at Irvine
Nonlinear dispersive media

We study the basic properties of the Maxwell equations for nonlinear inhomogeneous media. Assuming the classical nonlinear optics representation for the nonlinear polarization as a power series, we show that the solution exists and is unique in an appropriate space if the excitation current is not too large. The solution to the nonlinear Maxwell equations is represented as a power series in terms of the solution of the corresponding linear Maxwell equations. This representation holds at least for the time period inversely proportional to the appropriate norm of the solution to the linear Maxwell equation. We derive recursive formulas for the terms of the power series for the solution including an explicit formula for the first significant term attributed to the nonlinearity. Coffee will be served in the Keisler Lounge at 3:00pm

Friday, April 1, 2005

Posted February 9, 2005
Last modified January 6, 2021

3:40 pm 239, Lockett Hall

Alexander Figotin, University of California at Irvine
Conservative extensions of dispersive dissipative systems

Monday, April 4, 2005

Posted March 29, 2005

3:30 pm – 4:30 pm Lockett 285

Khaled Qazaqzeh, LSU
Integral Bases for the SU(2)-TQFT-modules in genus one

Posted March 30, 2005

Student Seminar

5:00 pm 3rd floor Lounge, Lockett Hall

Natalia Ptitsyna, LSU Graduate Student
Traffic Flow Along a Highway

Pizza will be served.

Posted April 4, 2005

Algebra and Number Theory Seminar Questions or comments?

5:00 pm James E. Keisler Mathematics Lounge

Natalia Ptitsyna, LSU Graduate Student
Traffic Flow on a Highway

The problem will be approached in analogy to fluid flow.

Tuesday, April 5, 2005

Posted March 15, 2005
Last modified May 8, 2021

3:10 pm – 4:00 pm Lockett 282

Preeti Raman, Rice University
Hasse Principle for Classical groups

I will discuss a conjecture due to Colliot-Thélène about Hasse principle for algebraic groups defined over the function field of a curve over a number field. I will also describe its relation to the classification of hermitian forms over such fields.

Wednesday, April 6, 2005

Posted March 31, 2005

Control and Optimization Seminar Questions or comments?

10:40 am – 11:30 am Lockett 282

Daniel Sage, Mathematics Department, LSU
Racah Coefficients and Subrepresentation Semirings

Thursday, April 7, 2005

Posted March 29, 2005
Last modified March 2, 2021

2:00 pm – 3:00 pm Lockett 381

Vladimir Gaitsgory, School of Mathematics and Statistics, University of South Australia
TBA

Friday, April 8, 2005

Posted March 29, 2005
Last modified March 30, 2005

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm CEBA 2150

Vladimir Gaitsgory, School of Mathematics and Statistics, University of South Australia
Limits of Occupational Measures and Averaging of Singularly Perturbed

Monday, April 11, 2005

Posted March 28, 2005
Last modified April 7, 2005

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 285

Xiao-Song Lin, University of California Riverside
A folding problem of polygonal arcs in 3-space

Tuesday, April 12, 2005

Posted April 4, 2005
Last modified January 6, 2021

2:40 pm – 3:30 pm Lockett 282

Debra Czarneski, LSU
Zeta Functions of Finite Graphs

Posted April 7, 2005
Last modified March 2, 2021

LSU Chancellor's Distinguished Lecture Series

4:00 pm – 5:00 pm Design Building Auditorium

John Willis, Cambridge University Fellow, Royal Society of London (FRS)
New Waves in Solids

Wednesday, April 13, 2005

Posted April 11, 2005

10:40 am – 11:30 am Lockett 282

Daniel Sage, Mathematics Department, LSU
Racah Coefficients and Subrepresentation semigroups. II

Posted March 31, 2005
Last modified January 6, 2021

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 285

John Willis, Cambridge University Fellow, Royal Society of London (FRS)
Radon transforms in Solid Mechanics

Posted April 11, 2005

3:40 pm – 4:40 pm Lockett 381

Jesus Pascal, Universidad del Zulia, Venezuela
On the Hamilton Jacobi Bellman Equation for a Deterministic Optimal Control Problem

Thursday, April 14, 2005

Posted March 1, 2005
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 241

Dror Bar-Natan, University of Toronto
Local Khovanov Homology

Visit supported by Visiting Experts Program in Mathematics, Louisiana
Board of Regents LEQSF(2002-04)-ENH-TR-13

Posted April 16, 2005

3:40 pm James E. Keisler Mathematics Lounge

Meeting of the Actuarial Student Association

There is a visit by a consulting actuary. Refreshments will be served.

Friday, April 15, 2005

Posted March 15, 2005
Last modified October 1, 2021

3:30 pm – 4:30 pm Life Science A663

Dror Bar-Natan, University of Toronto
I don't understand Khovanov-Rozansky homology

Visit supported in part by Visiting Experts Program in Mathematics, Louisiana, Board of Regents LEQSF(2002-04)-ENH-TR-13.

Monday, April 18, 2005

Posted April 15, 2005

Algebra and Number Theory Seminar Questions or comments?

11:00 am Coates 202

Martin Olbrich, Universität Göttingen
Automorphic distributions and dynamical zeta functions

Tuesday, April 19, 2005

Posted April 11, 2005
Last modified January 6, 2021

3:10 pm – 4:00 pm Lockett 282

James Madden, Mathematics Department, LSU
Ways of ordering real algebras

Wednesday, April 20, 2005

Posted April 19, 2005

10:40 am – 11:30 am Lockett 282

Daniel Sage, Mathematics Department, LSU
Racah Coefficients and Subrepresentation Semirings III

Posted April 6, 2005
Last modified April 19, 2005

Control and Optimization Seminar Questions or comments?

1:40 pm – 2:30 pm Life Science A 663

Cameron Gordon, University of Texas, Austin
Knots with Unknotting Number 1 and Conway Spheres

Virtual Seminar with U Iowa.
Cameron Gordon is visiting U Iowa.

Posted April 15, 2005

3:30 pm – 4:30 pm CEBA 2150

Steven Hall, Louisiana State University, Department of Biological and Agricultural Engineering
Challenges in Measurement and Control with Biological Systems

Monday, April 25, 2005

Posted April 20, 2005

Algebra and Number Theory Seminar Questions or comments?

3:40 pm Lockett 285

Meeting of the tenured and tenure-track faculty

The purpose is to discuss Peter\'s Math Biology proposal.

Tuesday, April 26, 2005

Posted April 20, 2005
Last modified January 6, 2021

2:40 pm – 3:30 pm Lockett 282

Helena Verrill, Mathematics Department, LSU
More modular Calabi-Yau threefolds

Posted April 19, 2005

3:30 pm – 4:30 pm Lockett 285

Ambar Sengupta, Mathematics Department, LSU
Quantum Physics from Pure Logic

Wednesday, April 27, 2005

Posted April 20, 2005

10:40 am – 11:30 am Lockett 282

Gestur Olafsson, Mathematics Department, LSU
The Image of the Heat Transform on Symmetric Spaces

Posted April 26, 2005
Last modified March 2, 2022

3:40 pm – 4:40 pm CEBA 2150

Blaise Bourdin, Department of Mathematics and Center for Computation & Technology, LSU
From Geman and Geman to Mumford–Shah

This talk focuses on the issues raised by an apparently simple problem: extending Geman and Geman's weak-membrane model for the segmentation of signals to that of images. I will briefly describe the problems of image and signal segmentation, then present Geman and Geman's approach. I will illustrate the issue with its intuitive multi-dimensional extension. Then, I will present how one can derive the Mumford–Shah functional as the Gamma limit of a weak-membrane energy, and then extend it to the 2D and 3D cases. Time permitting, I will then present numerical schemes based on the Mumford–Shah problem.

Thursday, April 28, 2005

Posted March 15, 2005
Last modified January 27, 2022

11:00 am – 12:00 pm 104 Hill Memorial Library
(Originally scheduled for Tuesday, April 12, 2005)

Roger Howe, Yale University
More than Mathematics for Teaching

There has been substantial agreement among professionals concerned with mathematics education that the mathematical skills of the teaching corps needs to be substantially upgraded. This is an urgent project which will require huge effort. At the same time we work on this, however, we should not lose sight of the fact that there are certain jobs, in particular, mathematics supervisor, which require substantially higher levels of expertise than classroom teaching. Furthermore, the system as a whole needs means to improve its understanding of both mathematics teaching practice and curriculum. This talk will discuss these issues, and some possible means for addressing them.

Friday, April 29, 2005

Posted March 27, 2005
Last modified April 27, 2005

3:30 pm – 4:30 pm Lockett 285

Abhijit Champanerkar, University of South Alabama
Scissors congruence and Bloch invariants of hyperbolic 3-manifolds.

Abstract: I will give a background of scissors congruence in various geometries. The complexified Dehn invariant for scissors congruence in hyperbolic 3-space gives rise to invariants of hyperbolic 3-manifolds called Bloch invariants introduced by Neumann and Yang. I will talk about the variation of the Bloch invariant and its relation to the PSL A-polynomial.

Tuesday, May 3, 2005

Posted April 25, 2005

3:10 pm 285 Lockett

Meeting of Instructors with Chair and ACI

Posted April 27, 2005
Last modified January 10, 2022

4:00 pm – 5:00 pm Lockett 232

Tom Mark, Southeastern Louisiana University
Heegaard Floer invariants for fibered manifolds.

Heegaard Floer invariants, introduced by Ozsváth and Szabó several years ago, are proving to be valuable tools in low-dimensional topology: in particular the theory reproduces and extends many results obtained previously using Seiberg-Witten and/or Donaldson gauge theory, as well as yielding novel results. I will discuss an ongoing project, joint with Slaven Jabuka, whose goal is to understand the Ozsváth-Szabó invariants of Lefschetz fibered 4-manifolds. A natural place to start is to study the Heegaard Floer homology groups of 3-manifolds that fiber over the circle, particularly in terms of the expression of their monodromy as a product of Dehn twists. We give some preliminary results in this area and indicate some directions for future work.

Thursday, May 5, 2005

Posted April 21, 2005

3:00 pm James Kiesler Lounge, 319 Lockett Hall

Spring Math Awards Ceremony

Wednesday, May 11, 2005

Posted May 3, 2005

Control and Optimization Seminar Questions or comments?

10:00 am Allen 102

Dean Ferreyra Meets with the Faculty

The Dean will speak with the Mathematics faculty about the chair\'s evaluation.

Friday, June 24, 2005

Posted June 17, 2005

10:30 am EE117

Li Qiu, Hong Kong University of Science and Technology
Perturbation Analysis beyond Singular Values -- A Metric Geometry on the Grassmann Manifold

Friday, July 15, 2005

Posted July 15, 2005

Control and Optimization Seminar Questions or comments?

10:00 am EE 117

Boumediene Hamzi, University of California, Davis
The Controlled Center Dynamics

Friday, August 12, 2005

Posted June 29, 2005

8:30 am – 4:30 pm LSU Student Union Building

International Student Orientation

New international students should have been notified of this meeting in the packets containing I-20 forms for visas. This meeting is required for all new international students beginning their studies at LSU. Students will be informed when and where to take the required written English test and when and where to report for a spoken English interview with a faculty member from the ESL Program. If you did not receive notification or arrive late, go to International Services at 102 Hatcher Hall to find out what is required.

Monday, August 15, 2005

Posted July 12, 2005

1:30 pm – 4:00 pm Room 285 Lockett

Core-1 Comprehensive Exam in Analysis

Tuesday, August 16, 2005

Posted June 29, 2005
Last modified July 21, 2005

9:00 am – 12:00 pm Pleasant Hall, Room 148

Workshop & Orientation for TAs Assigned to the R2R Program

Ms. Rouse will hold a required R2R workshop on Tuesday and Thursday morning from 9 AM to noon for all TAs assigned to the R2R Program this fall semester. This includes both TAs who are assigned to tutor in the R2R Program and those assigned to teach in the R2R Program.

Posted July 12, 2005

1:30 pm – 4:00 pm Room 285 Lockett

Core-1 Comprehensive Exam in Topology

Wednesday, August 17, 2005

Posted June 29, 2005
Last modified July 12, 2005

8:30 am – 12:30 pm LSU Student Union Building

Orientation Meeting for All New Graduate Students at LSU

This is the Graduate School's required orientation meeting for all new graduate students at LSU.

Thursday, August 18, 2005

Posted June 29, 2005
Last modified July 21, 2005

9:00 am – 12:00 pm Pleasant Hall, Room 148

Orientation & Workshop for TAs Assigned to R2R Program, Continued

Ms. Rouse\'s Orientation & Workshop for TAs assigned to the R2R Program will continue today from the Tuesday Orientation. This includes both TAs who are assigned to tutor in the R2R Program and those assigned to teach in the R2R Program.

Posted July 12, 2005

1:30 pm – 4:00 pm Room 285 Lockett

Core-1 Comprehensive Exam in Algebra

Friday, August 19, 2005

Posted June 29, 2005

9:00 am – 12:00 pm Lockett 235

Orientation for TAs Assigned Duties supporting Math 1431

Ms. Clement will begin the meeting in Room 235. After about an hour or more, the group will move to the computer lab on the 3rd floor.

Posted July 21, 2005

9:00 am – 12:00 pm Pleasant Hall, Room 148

Orientation for TAs assigned to TEACH in the R2R Program

Ms. Rouse will hold a required R2R workshop for all TAs assigned to teach in the R2R Program this fall semester. Those assigned only to tutor need not attend this meeting.

Posted June 29, 2005
Last modified July 21, 2005

12:00 pm – 2:45 pm Lockett 237 at noon, followed by the Computer Lab at Pleasant Hall at 12:45.
(Originally scheduled for 9:00 am)

Orientation for TAs Assigned to Math 1022

This meeting is required for those TAs who will be teaching Math 1022 labs. Meet in Lockett 237. Ms. Neal will go over the way the course is run via Maple, Semester Book, etc. At 12:45 the meeting will move to the Computer Lab in Pleasant Hall.

Posted July 12, 2005

1:00 pm – 4:30 pm Room 285 Lockett

Core-2 Comprehensive Exams

Core-2 Comprehensive Exams will be offered in each Core-2 subject which has been requested.

Friday, August 26, 2005

Posted August 22, 2005

10:40 am conference room, Lockett 301D

Meeting of the new Assistant Professors

The meeting is for our new assistant professors but all the assistant professors are invited.

Tuesday, September 6, 2005

Posted August 16, 2005
Last modified September 6, 2005

4:10 pm – 5:00 pm Lockett 285

Nathan Broaddus, Cornell University
Non-cyclic covers of knot complements

Wednesday, September 7, 2005

Posted August 26, 2005
Last modified August 31, 2005

3:40 pm Lockett 284

Grant Writing

The meeting is for our new assistant professors and those looking for guidance in writing their grant applications.

Thursday, September 8, 2005

Posted August 24, 2005

Algebra and Number Theory Seminar Questions or comments?

5:00 pm James E. Keisler Lounge, Lockett 321

First ASA Meeting

Organizational Meeting

Monday, September 12, 2005

Posted September 12, 2005

3:30 pm – 4:30 pm 285 Lockett Hall

Jerome W. Hoffman, Mathematics Department, LSU
Koszul Duality

Tuesday, September 13, 2005

Posted September 8, 2005
Last modified September 13, 2005

4:10 pm – 5:00 pm Lockett 285

Brendan Owens, LSU
Floer homology of double branched covers

Wednesday, September 14, 2005

Posted September 8, 2005

2:40 pm – 3:30 pm Lockett 381

Mark Davidson, Mathematics Department, LSU
Differential Recursion Relations for Laguerre Functions on Symmetric Cones

Posted September 8, 2005

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 381

Hui-Hsiung Kuo, Mathematics Department, LSU
Interacting Fock spaces associated with probability measures

Monday, September 19, 2005

Posted September 14, 2005

2:35 pm – 3:30 pm Lockett 285

Jerome W. Hoffman, Mathematics Department, LSU
Koszul Duality II

continuation of previous algebra seminar

Posted September 9, 2005

3:40 pm Lockett 241

Meeting of the Full Professors

A presentation and discussion about a promotion to full professor.

Tuesday, September 20, 2005

Posted September 9, 2005

4:10 pm – 5:00 pm Lockett 285

Brendan Owens, LSU
Floer homology of double branched covers, Part II

Wednesday, September 21, 2005

Posted September 18, 2005

2:40 pm – 3:30 pm Lockett 381

Mark Davidson, Mathematics Department, LSU
Differential Recursion Relations for Laguerre Functions on Symmetric Cones II

Posted September 17, 2005

3:40 pm – 4:30 pm Lockett 381

Jae Gil Choi , Louisiana State University, Baton Rouge (Visiting Faculty)
Generalized analytic Feynman integrals and conditional generalized analytic Feynman integrals on function space

Friday, September 23, 2005

Posted September 20, 2005

10:40 am – 11:30 am conference room, Lockett 301D

Meeting of the new Assistant Professors

The meeting is for our new assistant professors and post doc but all the assistant professors are invited.

Monday, September 26, 2005

Posted September 19, 2005
Last modified February 20, 2022

4:00 pm – 5:00 pm 1030 Magnolia Wood Avenue

Si Si, Aichi Prefectural University, Japan
Some aspects of Poisson noise

Tuesday, September 27, 2005

Posted September 13, 2005

4:10 pm – 5:00 pm Lockett 285

Brendan Owens, LSU
Floer homology of double branched covers, Part III

Wednesday, September 28, 2005

Posted September 21, 2005

2:40 pm – 3:30 pm Lockett 381

Gestur Olafsson, Mathematics Department, LSU
The Image of the Segal-Bargman Transform

Thursday, September 29, 2005

Posted September 2, 2005
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 235

Jacob Rubinstein, Indiana University
The weighted least action principle

Monday, October 3, 2005

Posted September 29, 2005

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett 277

Meeting of the Instructors

The agenda will be to discuss teaching needs and assignments for the spring.

Posted September 21, 2005
Last modified September 28, 2005

3:35 pm – 4:30 pm Monday, September 26, 2005 Locket 285

Jerome W. Hoffman, Mathematics Department, LSU
Koszul Duality III

continuation of previous algebra seminar

Posted September 20, 2005
Last modified February 17, 2022

3:40 pm – 4:30 pm Lockett 381

Jeremy Becnel, Stephen F. Austin State University
Delta Function for an Affine Subspace

Tuesday, October 4, 2005

Posted September 19, 2005

4:10 pm – 5:00 pm Lockett 285

Scott Baldridge, Louisiana State University
Symplectic 4-manifolds with prescribed fundamental group

Wednesday, October 5, 2005

Posted October 3, 2005

Dissertation defense rehearsal

1:40 pm – 2:30 pm Lockett 235

Tong Yi, LSU, Mathematics Graduate student
Broadcast in sparse optical networks using fewest converters

Posted September 28, 2005

Algebra and Number Theory Seminar Questions or comments?

2:40 pm – 3:30 pm Lockett 381

Gestur Olafsson, Mathematics Department, LSU
The Image of the Segal-Bargman Transform II

Monday, October 10, 2005

Posted October 4, 2005

3:30 pm Locket 285

Marco Schlichting, Louisiana State University
Algebraic K-theory of singular varieties and a conjecture of Weibel

Posted October 5, 2005

3:40 pm – 4:30 pm Lockett 381

Jeremy Becnel, Stephen F. Austin State University
The Delta Function for an Affine Subspace II

Tuesday, October 11, 2005

Posted October 4, 2005

4:10 pm – 5:00 pm Lockett 285

Scott Baldridge, Louisiana State University
Symplectic 4-manifolds with prescribed fundamental group, Part II

Wednesday, October 12, 2005

Posted October 7, 2005

2:40 pm – 3:30 pm Lockett 381

Gestur Olafsson, Mathematics Department, LSU
The Image of the Segal-Bargman Transform III

Friday, October 14, 2005

Posted September 29, 2005
Last modified October 6, 2005

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm 241 Lockett Hall

Robert Lipton, Mathematics Department, LSU
Multi-scale Stress Analysis

Many structures are hierarchical in nature and are made up of substructures distributed across several length scales. Examples include aircraft wings made from fiber reinforced laminates and naturally occurring structures like bone. From the perspective of failure initiation it is crucial to quantify the load transfer between length scales. The presence of geometrically induced stress or strain singularities at either the structural or substructural scale can have influence across length scales and initiate nonlinear phenomena that result in overall structural failure. In this presentation we examine load transfer between length scales for hierarchical structures when the substructure is known exactly or only in a statistical sense. New mathematical objects dubbed macrostress modulation functions are presented that facilitate a quantitative description of the load transfer in hierarchical structures. Several concrete physical examples are provided illustrating how these quantities can be used to quantify the stress and strain distribution inside multi-scale structures. It is then shown how to turn the problem around and use the macrostress modulation functions to design graded microstructures for control of local stress.

Monday, October 17, 2005

Posted October 4, 2005
Last modified March 2, 2021

3:40 pm Locket 285

Helena Verrill, Mathematics Department, LSU
Modular forms and Ramanujan's series for 1/pi

Tuesday, October 18, 2005

Posted October 12, 2005
Last modified October 15, 2005

4:10 pm – 5:00 pm Lockett 285

Tara Brendle, Department of Mathematics, LSU
The Birman-Craggs-Johnson homomorphism and the homology of the Johnson Kernel

Wednesday, October 19, 2005

Posted October 13, 2005
Last modified March 3, 2021

2:40 pm – 3:30 pm Lockett 381

Hongyu He, Mathematics Department, LSU
Some problems concerning positive definite functions

I will give an introduction about positive definitive function and its relation to unitary representation theory, Bochner's Theorem, Gelfand-Naimark-Segal construction etc. Then I will define positive definite distributions and introduce the extension problems, square root problems and the positivity problem of Godement. This talk will be accessible to graduate students.

Thursday, October 20, 2005

Posted October 13, 2005

5:00 pm James E. Keisler Lounge, Lockett 321

Actuarial Student Association Meeting

Friday, October 21, 2005

Posted October 11, 2005

Algebra and Number Theory Seminar Questions or comments?

3:30 pm 241 Lockett Hall

Robert Lipton, Mathematics Department, LSU
Differentiation of G-limits and weak L-P estimates for sequences

Monday, October 24, 2005

Posted October 14, 2005

3:40 pm Locket 285

Pramod Achar, Mathematics Department, LSU
Koszul duality in representation theory

Tuesday, October 25, 2005

Posted October 12, 2005
Last modified October 14, 2005

4:10 pm – 5:00 pm 285 Lockett

Tara Brendle, Department of Mathematics, LSU
The Birman-Craggs-Johnson homomorphism and the homology of the Johnson Kernel, Part II

Posted October 17, 2005

Ramadan Dinner

6:30 pm James E. Keisler Lounge (Room 321 Lockett)

5th Traditional Ramadan Dinner

Suat Namli and his Turkish friends will generously make a Turkish Ramadan dinner for our faculty, students, and families. We look forward to another fabulous feast!

Thursday, October 27, 2005

Posted October 21, 2005

3:40 pm – 4:30 pm 381 Lockett Hall

Carolyn Chun, Victoria University in Wellington, New Zealand Former LSU graduate student
Unavoidable Parallel Minors of Large, 4-Connected Graphs

Saturday, October 29, 2005

Posted July 14, 2005
Last modified July 25, 2021

10:00 am – 3:00 pm Hilltop Arboretum, 11855 Highland Rd, Baton Rouge

Graduate Student Day & Orientation Conference

Wednesday, November 2, 2005

Posted October 20, 2005

2:40 pm – 1:30 pm Lockett 381

Boris Rubin, Louisiana State University
The generalized Busemann-Petty problem on sections of convex bodies.

The generalized Busemann-Petty problem asks whether origin-symmetric convex bodies in $R^n$ with smaller $i$-dimensional central sections necessarily have smaller volume. This problem has a long history. For $i=2$ and $3$, the answer is still unknown if $n>4$. The problem is intimately connected with the spherical Radon transform. I am planning to give a survey of known results and methods, discuss some generalizations and difficulties.

Thursday, November 3, 2005

Posted October 28, 2005

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm 381 Lockett Hall

Brian Beavers, Mathematics Department, LSU Graduate student
Finding Cycles of All Sizes in Large Graphs and Matroids

Monday, November 7, 2005

Posted October 15, 2005
Last modified November 2, 2005

3:40 pm Locket 285

Jorge Morales, Mathematics Department, LSU
Quaternion orders, ternary quadratic forms and hyperelliptic curves

Tuesday, November 8, 2005

Posted November 1, 2005

4:10 pm – 5:00 pm Lockett 285

Tara Brendle, Department of Mathematics, LSU
The Birman-Craggs-Johnson homomorphism and the homology of the Johnson Kernel, Part III

Wednesday, November 9, 2005

Posted October 27, 2005
Last modified October 28, 2005

2:40 pm – 3:30 pm 381 Lockett Hall

Boris Rubin, Louisiana State University
The generalized Busemann-Petty problem on sections of convex bodies.II

Thursday, November 10, 2005

Posted November 9, 2005

1:40 pm Lockett 284

Meeting of the Faculty

Update on the post Katrina budget situation.

Posted September 28, 2005
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 235
(Originally scheduled for Thursday, October 20, 2005, 3:00 pm)

Richard Anderson, Louisiana State University (Emeritus) Emeritus Boyd Professor
My Three Lives in Mathematics

Refreshments will be served in the James E. Keisler Lounge one half hour before the talk.

Friday, November 11, 2005

Posted October 6, 2005
Last modified March 2, 2022

Algebra and Number Theory Seminar Questions or comments?

3:40 pm 241 Lockett Hall

Itai Shafrir, Department of Mathematics, Technion - Israel Institute of Technology
On the distance between homotopy classes of $S^1$-valued maps

Certain Sobolev spaces of $S^1$-valued functions can be written as a disjoint union of homotopy classes. The problem of finding the distance between different homotopy classes in such spaces is considered. In particular several types of one-dimensional and two-dimensional domains are studied. Lower bounds are derived for these distances. Furthermore, in many cases it is shown that the lower bounds are sharp but are not achieved.

Monday, November 14, 2005

Posted November 9, 2005

3:40 pm Locket 285

Jorge Morales, Mathematics Department, LSU
Quaternion orders, ternary quadratic forms and hyperelliptic curves, part II

Wednesday, November 16, 2005

Posted October 28, 2005

Algebra and Number Theory Seminar Questions or comments?

2:40 pm – 3:30 pm 338 Johnston Hall

Eric Todd Quinto, Mathematics Department, Tufts University
LIMITED DATA TOMOGRAPHY AND MICROLOCAL ANALYSIS

In this talk, we will describe limited data tomography problems that come up in applications, including electron microscopy and diagnostic radiology. In each of these tomography problems, certain singularities (boundaries, cracks, etc.) of the object are easily visible in the reconstruction and others are not. We will show how this phenomenon is reflected in the singular functions for the corresponding tomographic problems. A theoretical framework, microlocal analysis, will be given to explain the phenomenon, and we will include an elementary introduction to this idea. If time, we will outline our basic algorithm.

Monday, November 21, 2005

Posted November 9, 2005

3:40 pm Locket 285

Pramod Achar, Mathematics Department, LSU
How I learned to stop worrying and love stacks

Monday, November 28, 2005

Posted November 4, 2005
Last modified November 9, 2005

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Locket 285
(Originally scheduled for Monday, November 14, 2005, 3:30 pm)

Planning meeting to decide graduate courses in algebra for next year

Tuesday, November 29, 2005

Posted November 14, 2005

4:10 pm – 5:00 pm Lockett 285

Khaled Qazaqzeh, LSU
Integral Bases for Certain TQFT-Modules of the Torus

Wednesday, November 30, 2005

Posted October 28, 2005

2:40 pm – 3:30 pm 381 Lockett Hall

Ricardo Estrada, Mathematics Department, LSU
Average local behavior of functions and Fourier Series

Posted November 9, 2005
Last modified November 22, 2005

3:40 pm – 4:30 pm Lockett 381

Jeremy Becnel, Stephen F. Austin State University
An Infinite Dimensional Integral Identity for the Segal-Bargmann Transform

Friday, December 2, 2005

Posted November 11, 2005
Last modified March 2, 2022

Algebra and Number Theory Seminar Questions or comments?

3:40 pm 239 Lockett Hall

Corey Redd, Department of Mathematics, LSU
Capturing Deviation from Ergodicity at Different Scales

Many researchers are interested in the topics of ergodicity and mixing, and more importantly in methods by which these quantities can be measured. As these properties may register differently based upon the space under observation, it is also important that any measure be able to be applied at different scales. Up to now, an energy based measure (L-2 norm) has traditionally been used to assess the ergodicity and/or mixing of a system. This method is less than ideal in part due to its non-uniqueness and difficulty with assessment on varying scales. I will present a Lagrangian based, multiscale method for measuring ergodicity that will attempt to address these issues. This talk will begin with background information on ergodicity and mixing and the relationship between the two. From the abstract definitions, I will derive an equation that will measure ergodicity on multiple scales. Following that, results will be presented from some initial computations of the metric on several test maps. Finally, computational issues will be discussed that are specific to measuring ergodicity, as well as in comparison to a mixing measure.

Monday, December 5, 2005

Posted December 2, 2005

3:30 pm Locket 285

Pramod Achar, Mathematics Department, LSU
Stacks II

Before the talk, we will have a 15 minute discussion of graduate courses for next year. Graduate students welcome.

Tuesday, December 6, 2005

Posted November 20, 2005

4:10 pm – 5:00 pm 285 Lockett

Atle Hahn, University of Bonn and LSU
Towards a path integral derivation of the Reshetikhin-Turaev invariants

Monday, December 12, 2005

Posted November 30, 2005
Last modified January 27, 2022

3:40 pm – 4:30 pm Lockett 285

Changyou Wang, University of Kentucky Candidate for an Associate/Full Professor Position in Partial Differential Equations
Calculus of variations in L-infinity and Aronsson's equation

In this talk, I will discuss the basic issues for L-infinity variational problems, where one considers minimization problem of the supernorm functional: $$F(u,\Omega)=\esssup H(x,u(x),\nabla u(x)), u\in W^{1,\infty}(\Omega).$$ We will survey some recent developments on: (1) the existence of absolute minimizers (AMs), (2) the PDE characterization of AMs (i.e., Aronsson's equation or AE), (3) the relationship between AM and AE, and (4) regularity and uniqueness of AE.

We will also discuss its connection with image interpolation, random game theory.

Wednesday, December 14, 2005

Posted December 11, 2005

Algebra and Number Theory Seminar Questions or comments?

12:00 pm Keisler Lounge

Christmas Party

The sign up sheet for dishes is on Karen\'s door (Lockett 304) not on the mail
room door. Please sign up for a dish. We will have two turkeys (one baked
and one fried) as well as the shared dishes.

Tuesday, January 10, 2006

Posted December 9, 2005
Last modified December 18, 2005

2:30 pm

Marie-José Bertin, Université Pierre et Marie Curie, Paris
Lehmer's problem and Mahler measure

Friday, January 13, 2006

Posted December 27, 2005
Last modified July 25, 2021

1:30 pm

Core-1 Analysis Comprehensive/PhD Qualifying Exam

This is the first of the three component tests of the Core-1 part of the PhD Qualifying Exam.

Saturday, January 14, 2006

Posted December 27, 2005
Last modified July 25, 2021

1:00 pm 285 Lockett
(Originally scheduled for 1:00 pm)

Core-1 Topology Comprehensive/PhD Qualifying Exam

This is the second of the three component tests of the Core-1 part of the PhD Qualifying Exam.

Posted December 27, 2005
Last modified July 25, 2021

1:00 pm 285 Lockett

Core-1 Topology Comprehensive/PhD Qualifying Exam

This is the second of the three component tests of the Core-1 part of the PhD Qualifying Exam.

Monday, January 16, 2006

Posted December 27, 2005
Last modified July 25, 2021

1:30 pm

Core-1 Algebra Comprehensive/PhD Qualifying Exam

This is the third of the three component tests of the Core-1 part of the PhD Qualifying Exam.

Saturday, January 21, 2006

Posted December 27, 2005
Last modified July 25, 2021

Algebra and Number Theory Seminar Questions or comments?

12:30 pm 285 Lockett

Core-2 Components (all) of the PhD Qualifying Exam

These are the Core-2 component parts of the PhD Qualifying Exam.

Monday, January 30, 2006

Posted January 23, 2006
Last modified March 2, 2021

2:30 pm Locket 285

Marco Schlichting, Louisiana State University
Stabilized Witt groups, Ranicki's lower L groups, and blow ups

Tuesday, January 31, 2006

Posted January 24, 2006
Last modified January 26, 2006

4:30 pm – 5:30 pm Lockett 284

Daniel C. Cohen, Mathematics Department, LSU
tba

Wednesday, February 1, 2006

Posted January 13, 2006
Last modified January 16, 2006

3:40 pm – 4:30 pm Lockett 284

David Damanik, California Institute of Technology Candidate for Full Professor Position
Structures of intermediate complexity and quantum dynamics

Abstract: We discuss the spreading properties of quantum particles in structures of intermediate complexity. Examples of interest include quasicrystals. We carry out a complete analysis for the Fibonacci Hamiltonian, which is the most prominent object in the mathematics and physics literature on quasicrystals.

Friday, February 3, 2006

Posted January 27, 2006

Algebra and Number Theory Seminar Questions or comments?

1:30 pm Lockett 137

Meeting of the tenured and tenure-track faculty

Candidate discussion.

Monday, February 6, 2006

Posted February 1, 2006

2:30 pm Locket 276

James Madden, Mathematics Department, LSU
Orderings of commutative rings with nilpotents

Posted January 18, 2006

4:00 pm Keisler Lounge

Actuarial Student Association Meeting

Spring Organizational Meeting of the ASA

Tuesday, February 7, 2006

Posted February 3, 2006

3:00 pm – 4:00 pm Lockett 284

Dana Scott, Carnegie Mellon University
Parametric Sets and Virtual Classes

Posted January 26, 2006
Last modified February 1, 2006

4:40 pm – 5:30 pm Lockett 284

Neal Stoltzfus, Mathematics Department, LSU
Root Posets and Temperley-Lieb Algebras

Wednesday, February 8, 2006

Posted January 24, 2006

3:40 pm – 4:30 pm Lockett 381

Gestur Olafsson, Mathematics Department, LSU
Determining Intertwining Operators

Thursday, February 9, 2006

Posted January 23, 2006
Last modified January 6, 2021

12:30 pm – 1:30 pm 277 Lockett

Robert B. Haber, Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign
Space-time Discontinuous Galerkin Methods for Multi-scale Solid Mechanics

Tuesday, February 14, 2006

Posted February 8, 2006

4:40 pm – 5:30 pm Lockett 284

Ben McReynolds, UT Austin
Separable subgroups of mapping class groups

Wednesday, February 15, 2006

Posted February 8, 2006

Diffeological Spaces Seminar

3:40 pm – 4:30 pm Lockett 381

Gestur Olafsson, Mathematics Department, LSU
Determining Intertwining Operators II

Monday, February 20, 2006

Posted February 17, 2006

3:40 pm – 4:30 pm Lockett 232

Martin Laubinger, LSU Graduate Student
Cartesian Closedness and Diffeological Spaces

This seminar is intended to be widely accessible to graduate students and
faculty, with a minimum of background assumed. During this semester we will
primarily develop the basic theory of diffeological spaces.

Tuesday, February 21, 2006

Posted January 30, 2006
Last modified February 16, 2006

Control and Optimization Seminar Questions or comments?

10:00 am EE 117

Patrick De Leenheer, Department of Mathematics, University of Florida
Bistability and Oscillations in the Feedback-Controlled Chemostat

The chemostat is a biological reactor used to study the dynamics of species competing for nutrients. If there are n>1 competitors and a single nutrient, then at most one species survives, provided the control variables of the reactor are constant. This result is known as the competitive exclusion principle. I will review what happens if one of the control variables--the dilution rate--is treated as a feedback variable. Several species can coexist for appropriate choices of the feedback. Also, the dynamical behavior can be more complicated, exhibiting oscillations or bistability.

Posted February 21, 2006

3:40 pm 277 Lockett

Faculty meeting

To consider proposals on several math concentrations, and faculty 3rd-year review

Wednesday, February 22, 2006

Posted February 15, 2006
Last modified March 3, 2021

3:30 pm – 4:30 pm Lockett 284

Dorin Dutkay, Rutgers University
Wavelets and self-similarity

In the past twenty years the theory of wavelets has proved to be extremely successful, with important applications to image compression and signal processing. The theory involves the construction of orthonormal bases in euclidean spaces generated by translations and dilations. A key feature of these constructions is the property of self-similarity. We exploit this property and, using operator algebra methods, we offer a wider perspective on the subject. We show how techniques from the theory of wavelets can be used in many other contexts such as fractals, dynamical systems, or endomorphisms of von Neumann algebras. Thus, we can construct rich multiresolution structures with scaling functions and wavelets on fractals, solenoids, super-wavelets for Hilbert spaces containing L^2(R), or harmonic bases on fractal measures.

Thursday, February 23, 2006

Posted February 22, 2006

Research Presentation

10:00 am 381 Lockett Hall

Patrick De Leenheer, Department of Mathematics, University of Florida
Michael Malisoff, LSU Roy P. Daniels Professor
An Informal Seminar on Monotone Systems

Posted February 17, 2006
Last modified January 27, 2022

11:40 am – 12:30 pm Johnston 338

Susanne Brenner, Department of Mathematics, University of South Carolina
Fast Solvers for $C^0$ Interior Penalty Methods

In this talk we will discuss fast solvers for $C^0$ interior penalty methods for fourth order elliptic boundary value problems. We will give a brief introduction to $C^0$ interior penalty methods, and present convergence results for the V-cycle, W-cycle and F-cycle multigrid algorithms, and also condition number estimates for two-level additive Schwarz preconditioners. Numerical results will also be reported.

Posted February 15, 2006
Last modified March 3, 2021

1:40 pm – 2:30 pm Lockett 16

Dave Larson, Texas A&M
Wavelet Sets and Interpolation

A wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a collection, or "system", of unitary operators defined in terms of translation and dilation operations. We will begin by describing an operator-interpolation approach to wavelet theory using the local commutant of a unitary system that was developed by the speaker and his collaborators a few years ago. This is really an abstract application of the theory of operator algebras, mainly von Neumann algebras, to wavelet theory. The concrete applications of operator-interpolation to wavelet theory include results obtained and partially published results, and some brand new results, that are due to this speaker and his former and current students, and other collaborators.

Posted February 16, 2006
Last modified January 27, 2022

3:40 pm – 4:30 pm Lockett 284

Chris Hruska, University of Chicago Candidate for an Assistant Professor Position in Topology
Nonpositively curved spaces with isolated flats

In the 1980s Gromov popularized the study of finitely generated groups using geometric techniques. He introduced and popularized notions of negative and nonpositive curvature in group theory, which have been highly influential in shaping the field of geometric group theory over the last two decades. The theory of negatively curved groups is extremely rich and exhibits many strong stability properties. On the other hand, the theory of nonpositively curved groups is much more delicate and less understood. In my thesis, I introduced the class of nonpositively curved groups with “isolated flats”. These groups occur naturally throughout group theory and low-dimensional topology and can be considered as the simplest nontrivial generalization of a negatively curved group. They have many properties in common with negatively curved groups. In particular, in joint work with Bruce Kleiner, I have shown that such a group is relatively hyperbolic with respect to virtually abelian subgroups.

Friday, February 24, 2006

Posted February 16, 2006
Last modified January 27, 2022

1:40 pm – 2:30 pm Lockett 16

(Jennifer) Suzanne Hruska, Indiana University Candidate for an Assistant Professor Position in Analysis
The Dynamics of Polynomial Skew Products of C^2

Our goal is to develop and use rigorous computer investigations to study the dynamics of polynomial skew products of $C^2$; i.e., maps of the form $f(z,w) = (p(z), q(z,w))$, where $p$ and $q$ are polynomials of the same degree $d \ge 2$. The skew products we are most interested in studying are those maps which are Axiom A. Such maps have the “simplest” chaotic dynamics, and stability under small perturbation, thus are amenable to computer investigation. In this talk, we will describe a new class of skew products with interesting dynamics, and sketch how we have proven using rigorous computer techniques that sample maps from this class are Axiom A. This leads us to conjecture that all (or nearly all) maps in this class are Axiom A.

Posted February 17, 2006

3:40 pm – 4:30 pm Lockett 284

Li-yeng Sung, University of South Carolina Candidate for Possible Senior Professor Position
Fokas Transforms

Just as initial value problems for evolution partial differential equations in one spatial variable can be solved by means of the Fourier transform on the full-line, initial-boundary value problems on the half-line can be solved using Fokas transforms. In this talk we will present unified derivations of these transforms and discuss their applications to linear and nonlinear partial differential equations.

Posted February 2, 2006
Last modified February 22, 2006

until Sunday, February 26, 2006

See program announcement
Workshop in Harmonic Analysis and Fractal Geometry

http://www.math.lsu.edu/~olafsson/workshop06.html

Friday, March 3, 2006

Posted February 23, 2006

1:40 pm – 2:30 pm Lockett 277

Olga Plamenevskaya, Massachusetts Institute of Technology Candidate for Assistant Professor Position in Topology
Heegaard Floer theory, knots, and contact structures

Abstract: Heegaard Floer theory is one of the most significant recent developments in low-dimensional topology. Reminiscent of gauge theory, it provides powerful invariants for 3-manifolds. Although defined via holomorphic disks, these 3-manifold invariants have an unexpected connection to combinatorial knot invariants developed by Khovanov. I will outline the construction of Heegaard Floer and Khovanov theories, as well as their relation (due to Ozsvath and Szabo). Then, I will expand these results to the world of contact topology, providing a new invariant for transversal knots, and bringing the correspondence between the two theories to a new level.

Posted February 23, 2006

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 284

Alexander Retakh, University of Texas at Arlington Candidate for Assistant Professor Position in Algebra
Structure Theory and Representations of Conformal Algebras

The last several decades saw a great deal of interaction between representation theory and modern mathematical physics. The search for rigorous algebraic formalism in areas such as string theory and conformal field theory led Kac and others to the concept of a conformal algebra. Apart from their physical applications, conformal algebras also turned out to be extremely useful in the study of infinite-dimensional Lie algebras. I will define conformal algebras, explain their relation to vertex algebras and superconformal algebras of string theory, the connection to Hamiltonian formalism in calculus of variations, and describe recent progress and conjectures in the field.

Monday, March 6, 2006

Posted January 31, 2006
Last modified January 6, 2021

2:30 pm Locket 276

Edith Adan-Bante, University of Southern Mississippi Gulf Coast
On Conjugacy Classes and Finite Groups

Tuesday, March 7, 2006

Posted February 23, 2006

4:40 pm – 5:30 pm Lockett 284

Matilde Lalin, University of British Columbia
Some aspects of the Multivariable Mahler Measure

Friday, March 10, 2006

Posted March 3, 2006

8:30 am Lockett 6 (in basement)

Guillermo Ferreyra, Mathematics Department, LSU
Faculty Forum with Dean Ferreyra

Posted February 27, 2006
Last modified March 6, 2006

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 284

Chris Larsen, WPI and California Institute of Technology
Epsilon Stability - A new tool for studying local minimizers

Monday, March 13, 2006

Posted March 2, 2006

2:30 pm Locket 276

Juan Marco Cervino, University of Göttingen
The Minkowski-Siegel formula for quadratic bundles on curves

Tuesday, March 14, 2006

Posted March 9, 2006

4:40 pm – 5:30 pm Lockett 284

Patrick Gilmer, Mathematics Department, LSU
Lollipop trees in TQFT

Wednesday, March 15, 2006

Posted March 13, 2006

3:40 pm Lockett 15

Meeting of the tenured and tenure-track faculty

Discussion of two senior candidates. A vote will follow.

Friday, March 17, 2006

Posted March 17, 2006

3:40 pm – 4:30 pm Lockett 284

Leonid V. Berlyand, Department of Mathematics, Pennsylvania State University
The discrete network approximation and asymptotic fictitious fluid approach in modeling of highly packed composites

Tuesday, March 21, 2006

Posted March 21, 2006
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 284

Achim Jung, Department of Computer Science, University of Birmingham, England
Semantic domains, or the curious inapplicability of mathematics in computer science

In the mid-60s, Christopher Strachey and others began a program of describing the meaning of computer programs in a mathematical style. The approach is known as denotational semantics. From the beginning, Strachey was aware that set theory is not a good basis for such an endeavor, but it was not until Dana Scott developed his domain theory several years later that there was any mathematical basis at all.

In this talk, I will try to explain why sets—without further structure—do not reflect well the realities of computing, and I will try to motivate why the domains of Scott, which carry an order and a topology, do a better job. There are several further computational phenomena which required Scott to restrict the concept of domain even further, but once this is done, a fairly pleasing and flexible semantic universe is obtained.

In the spirit of this lecture, I will not dwell too much on the successes that domain theory has had in modeling computation, but rather present those phenomena which have resisted being incorporated into the model. One issue that is still not completely understood is the treatment of exact real numbers. On the one hand, real numbers seem ideally suited for a topological model but recent work by Escardó, Hofmann, and Streicher suggests that there is an inherent conflict between efficiency of the programming language and faithfulness to the mathematical concept.

Wednesday, March 22, 2006

Posted March 21, 2006

Special Guest Lecture (CCT)

3:30 pm 338 Johnston Hall

Bertil Gustafsson, University of Uppsala
High order one-step difference methods for wave propagation

Posted March 14, 2006

3:40 pm – 4:30 pm Lockett 381

Gestur Olafsson, Mathematics Department, LSU
Determining Intertwining Operators III

Friday, March 24, 2006

Posted March 8, 2006
Last modified March 21, 2006

3:30 pm – 4:30 pm Johnston 338

Ken Mattsson, Center for Integrated Turbulence Simulations, Stanford University
Towards time stable and high order accurate schemes for realistic applications

For wave propagation problems, the computational domain is often large compared to the wavelengths, which means that waves have to travel long distances during long times. As a result, high order accurate time marching methods, as well as efficient high order spatially accurate schemes (at least 3rd order) are required. Such schemes, although they might be G-K-S stable (convergence to the true solution as delta x -> 0), may exhibit a non-physical growth in time, for realistic mesh sizes. It is therefore important to device schemes, which do not allow a growth in time that is not called for by the differential equation. Such schemes are called strictly (or time) stable. We are particularly interested in efficient methods with a simple data structure that parallelize easily on structured grids. High order accurate finite difference methods fulfill these requirements. Traditionally, a successful marriage of high order accurate finite difference and strict stability was a complicated and highly problem dependent task, especially for realistic applications. The major breakthrough came with the construction (Kreiss et al., in 1974) of non-dissipative operators that satisfy a summation by parts (SBP) formulation, and later with the introduction of a specific procedure (Carpenter et al., in 1994) to impose boundary conditions as a penalty term, referred to as the Simultaneous Approximation Term (SAT) method. The combination of SBP and SAT naturally leads to strictly stable and high order accurate schemes for well-posed linear problems, on rectangular domains. During the last 10 years, the methodology has been extended to handle complex geometries and non-linear problems. In this talk I will introduce the original SBP and SAT concepts, and further discuss the status today and the focus on future applications. In particular I will discuss some recent developments towards time stable and accurate hybrid combinations of structured and unstructured SBP schemes, making use of the SAT method.

Saturday, March 25, 2006

Posted March 18, 2006
Last modified February 11, 2022

Algebra and Number Theory Seminar Questions or comments?

until Sunday, March 26, 2006 Lockett Hall, Room 241

First Louisiana-Texas-Topology-Retreat

Speakers: Tara Brendle (LSU),
Abhijit Champanerkar (USA),
Tim Cochran (Rice),
Stefan Friedl (Rice),
Gregor Masbaum (Paris VII),
Neal Stoltzfus (LSU)

Detailed Program

Monday, March 27, 2006

Posted March 22, 2006

2:40 pm Locket 276

Jerome W. Hoffman, Mathematics Department, LSU
Koszul duality for multigraded algebras

Posted March 9, 2006

3:40 pm – 4:30 pm Johnston 338

Qian-Yong Chen, University of Minnesota Candidate for Assistant Professor Position
A new basis for spectral methods

Abstract: The spectral methods have been very successful in many applications, such as weather prediction, seismic imaging and etc. The main reason for their success is the exponential accuracy: For smooth problems on simple domains, spectral methods can achieve 10 digits accuracy, compared to 2 ~ 3 digits for finite difference or finite element methods with similar computational cost. However, there are still two issues with the Legendre/Chebyshev polynomials based spectral methods for non-periodic problems: the time-step size and the number of points needed to resolve a wave. In this talk, I address this two issues by using a new basis, the prolate spheroidal wave functions (PSWFs), for spectral methods. The relevant approximation theory will be covered. The advantage of the new basis over Legendre/Chebyshev polynomials will be showed for marginally resolved broadband solutions.

Posted March 8, 2006
Last modified March 2, 2021

4:40 pm – 5:30 pm Lockett 381

K Saito, Meijo University
Constructions of stochastic processes

Wednesday, March 29, 2006

Posted March 24, 2006

3:40 pm – 4:30 pm Lockett 381

Boris Rubin, Louisiana State University
On MATH 7390-1: Applied Harmonic Analysis (Fall 2006)

Abstract. I am planning to review a tentative content of this course which will be suggested to graduate students in Fall 2006. This is an introductory course in the theory of the Radon transform, one of the main objects in integral geometry and modern analysis. Topics to be studied include fractional integration and differentiation of functions of one and several variables, Radon transforms in the n-dimensional Euclidean space and on the unit sphere, selected aspects of the Fourier analysis in the context of its application to integral geometry and tomography. The talk will be illustrated by examples of mathematical problems that fall into the scope of this course.

Thursday, March 30, 2006

Posted March 21, 2006

8:45 am – 4:30 pm Hill Memorial Library

1st Louisiana Joint Workshop for Academia and Industry.

website

Friday, March 31, 2006

Posted March 24, 2006
Last modified January 27, 2022

Algebra and Number Theory Seminar Questions or comments?

9:00 am – 10:00 am 338 Johnston Hall/CCT

Christopher King, Northeastern University
Mathematical problems in quantum information theory

Attempts to extend Shannon's noisy coding theorem to a quantum setting have led to interesting mathematical questions concerning products of completely positive maps on matrix algebras. Specifically for trace-preserving maps it is conjectured that the output state with minimal entropy is always a product state—this is equivalent to the statement that minimal output entropy is additive for such maps. I will review the background to this problem, and describe its relation to some inequalities that arose in different contexts, including strong subadditivity and Hanner's inequality. I will then show how some new matrix inequalities can be used to prove special cases of this result.

Posted March 21, 2006

9:00 am – 12:00 pm Middleton Library, Conference Room 241 A

1st Louisiana Joint Workshop for Academia and Industry.

website

Monday, April 3, 2006

Posted March 27, 2006

2:40 pm Locket 276

Marco Schlichting, Louisiana State University
Koszul duality and the derived category of coherent sheaves on a quadric (after Kapranov)

Wednesday, April 5, 2006

Posted March 28, 2006

3:40 pm – 4:30 pm Lockett 381

Genkai Zhang, Department of Mathematics, Gothenburg University, Sweden
Radon, cosine and sine transforms on Grassmannians.

Posted March 29, 2006
Last modified February 20, 2022

6:00 pm James E. Keisler Lounge Lockett 321

Lawrence Smolinsky, Mathematics Department, LSU
Ancient Constructions and the Modern Formulation

This talk is part I of “Geometric Constructions with Ellipses.” Part II will be given on April 19th by Aliska Gibbins.

Mathematicians and philosophers of Ancient Greece studied the problems of trisecting a general angle, doubling the cube, and squaring the circle. They tried to accomplish these constructions using only a straight edge and compass. While these methods were unsuccessful, they also examined allowing other constructions, devices, and curves. These problems were a major force in the development of mathematics. For example, Menaechmus, the discoverer of conic sections, made his discovery while working on the problem of doubling the cube.

We are most concerned with constructions with straight edge, compass, and conics. Pappus (290–350) gave two trisection constructions with hyperbolas. Another trisection construction—this time with a parabola—is due to René Descartes in his 1637 La Géométrie. Among the results we show is that one can trisect a general angle and double the cube using ellipses. (One can also construct the heptagon and determine the field of elliptically constructible numbers.)

Thursday, April 6, 2006

Posted March 27, 2006
Last modified April 6, 2006

Algebra and Number Theory Seminar Questions or comments?

3:40 pm Lockett 112

Meeting of the tenured and tenure-track faculty

The topics of the meeting will be a discussion of the graduate program and VIGRE.

Monday, April 17, 2006

Posted April 13, 2006

Computing the Future Lecture sponsored by CCT

11:00 am 338 Johnston Hall

D. C. Sorensen, Rice University, Department of Computation and Applied Mathematics
Gramian Based Model Reduction for Dynamical Systems

Here is the abstract. Please come for refreshments at 10:30 AM.

Posted April 5, 2006
Last modified April 6, 2006

3:45 pm Locket 276

Jeonghun Kim, Mathematics Department, LSU LSU graduate student of Robert Perlis
Arf equivalence of quadratic fields

Note this is an hour later than the usual algebra seminar time.

Wednesday, April 19, 2006

Posted March 29, 2006
Last modified February 20, 2022

6:00 pm James E. Keisler Lounge Lockett 321

Aliska Gibbins, Tulane
Elliptic Constructions

This talk is part II of “Geometric Constructions with Ellipses.” Part I was given on April 5th by Larry Smolinsky.

Mathematicians and philosophers of Ancient Greece studied the problems of trisecting a general angle, doubling the cube, and squaring the circle. They tried to accomplish these constructions using only a straight edge and compass. While these methods were unsuccessful, they also examined allowing other constructions, devices, and curves. These problems were a major force in the development of mathematics. For example, Menaechmus, the discoverer of conic sections, made his discovery while working on the problem of doubling the cube.

We are most concerned with constructions with straight edge, compass, and conics. Pappus (290–350) gave two trisection constructions with hyperbolas. Another trisection construction—this time with a parabola—is due to René Descartes in his 1637 La Géométrie. Among the results we show is that one can trisect a general angle and double the cube using ellipses. (One can also construct the heptagon and determine the field of elliptically constructible numbers.)

Thursday, April 20, 2006

Posted April 10, 2006

3:40 pm – 4:30 pm Lockett 284

Atle Hahn, University of Bonn and LSU
Towards a path integral derivation of 3-manifold quantum invariants

Abstract: The study of the heuristic Chern-Simons path integral by E. Witten inspired (at least) two general approaches to quantum topology. Firstly, the perturbative approach based on the CS path integral in the Landau gauge and, secondly, the quantum group approach by Reshetikhin and Turaev. While for the first approach the relation to the CS path integral is obvious for the second approach it is not. In particular, it is not clear if and how one can derive the relevant R-matrices or quantum 6j-symbols directly from the CS path integral. In my talk, I will sketch a strategy that should lead to a clarification of this issue in the special case where the base manifold is of product form. This strategy is based on the torus gauge fixing procedure introduced by Blau and Thompson for the study of the partition function of CS models. I will show that the formulas of Blau and Thompson can be generalized to Wilson lines and that the evaluation of the expectation values of these Wilson lines leads to the same state sum expressions in terms of which shadow invariant of Turaev is defined. Finally, I will sketch how one can obtain a rigorous realization of the path integral expressions appearing in this treatment.

Friday, April 21, 2006

Posted January 26, 2006
Last modified March 11, 2006

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 235

Yaniv Almog, Department of Mathematics, LSU
Boundary layers in superconductivity and smectic liquid crystals

Posted April 19, 2006
Last modified April 20, 2006

CCT Computing the Future Series

4:00 pm 338 Johnston Hall

James Lambers, Petroleum Engineering, Stanford
A Multi-Pronged Research Strategy for Numerical Solution of Variable-Coefficient PDE

The abstract is posted here.

Monday, April 24, 2006

Posted April 5, 2006
Last modified April 6, 2006

3:45 pm Locket 276

Jeonghun Kim, Mathematics Department, LSU LSU graduate student of Robert Perlis
Arf equivalence of quadratic fields, Part II

Part I, given the previous week, is related to this talk, but not essential for understanding part II.

Posted April 13, 2006
Last modified April 24, 2006

4:40 pm James E. Keisler Lounge in Lockett 321

Hank Frantz, Blue Cross Blue Shield of Louisiana
Actuarial Mathematics: On the Job Examples

The speaker is an Associate Actuary BCBS of Louisiana. He will discuss mathematics from three examples in his work.

Wednesday, April 26, 2006

Posted April 19, 2006
Last modified March 2, 2021

1:30 pm – 2:30 pm Life Science A663

David Futer, Michigan State University
Geometry and combinatorics of arborescent link complements

Virtual Seminar together with U Iowa

Posted April 20, 2006

Report on 1000-level Mathematics Courses

3:40 pm Lockett 285

Report on the Computer-based and Large Lecture Courses

Results from the fall semester assessments.

Thursday, April 27, 2006

Posted April 21, 2006
Last modified April 26, 2006

3:40 pm – 4:30 pm Lockett 284

Tomasz Przebinda, University of Oklahoma
Invariant Eigen-Distributions and Howe's Correspondence

Abstract: The notions of a group reduction, a character and an invariant eigen distribution play a crucial role in Harmonic Analysis on a Real Reductive Group. The classical groups may be organized in pairs. This leads to a correspondence of representations, which is compatible with Capelli identities. We shall explain a recent microlocal construction of invariant eigen distributions which is also compatible with Capelli identities. The hope is that this construction explains the behavior of the characters under Howe's correspondence.

Friday, April 28, 2006

Posted April 25, 2006
Last modified March 2, 2021

2:40 pm – 3:30 pm Lockett 381

Tomasz Przebinda, University of Oklahoma
Orbital Integrals and Howe's Correspondence

In this talk I shall explain the construction of the invariant eigendistributions in more detail. In particular, we’ll show how it relates Harish-Chandra’s orbital on the Lie algebras via and the moment maps.

Posted April 13, 2006

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett, 235

Anna Zemlyanova, Department of Mathematics, LSU
The problem on reinforcement and repair of a hole in a plate with a patch

It is known that holes in a thin plate create undesirable stress concentration and can lead to the formation of cracks from the edge of the hole. I will consider the mechanical problem of repair of the hole by a two-dimensional patch. This problem will be reduced to the system of three singular integral equations. Uniqueness of the solution of the system will be proved. Numerical results will be given for some particular cases.

Monday, May 1, 2006

Posted March 13, 2006
Last modified January 6, 2021

2:30 pm Locket 276

Edith Adan-Bante, University of Southern Mississippi Gulf Coast
On Characters and Finite Groups

Posted April 18, 2006

3:30 pm James Kiesler Lounge, 319 Lockett Hall

Spring Math Awards Ceremony

Tuesday, May 2, 2006

Posted April 16, 2006

4:40 pm – 5:30 pm Lockett 284

Alissa Crans, University of Chicago/Loyola Marymount University
Self-Distributivity in Coalgebras

Abstract: Self-distributive binary operations have appeared extensively in knot theory in recent years, specifically in algebraic structures called `quandles.\' A quandle is a set equipped with two binary operations satisfying axioms that capture the essential properties of the operations of conjugation in a group. The self-distributive axioms of a quandle correspond to the third Reidemeister move in knot theory. Thus, quandles give a solution to the Yang-Baxter equation, which is an algebraic distillation of the third Reidemeister move. We formulate analogues of self-distributivity in the categories of coalgebras and Hopf algebras and use these to construct additional solutions to the Yang-Baxter equation.

Thursday, May 4, 2006

Posted April 19, 2006
Last modified February 2, 2022

3:40 pm 284 Lockett

Franco Rampazzo, Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova
Commutators of Flows of Non-Smooth Vector Fields

My talk will concern the problem of finding a nonsmooth analogue of the notion of Lie bracket—the commutator—of two vector fields. The results I am presenting are contained in joint works with H. Sussmann. In particular, by means of a notion of set-valued Lie bracket introduced in [1], in [2] we have extended some classical results valid for smooth vector fields to the case when the vector fields are just Lipschitz. For instance, we have proved that the flows of two Lipschitz vector fields commute for small times if and only if their set-valued Lie bracket vanishes everywhere (or, equivalently, if their classical Lie bracket vanishes almost everywhere). We have also extended the asymptotic formula that gives an estimate of the lack of commutativity of two vector fields in terms of their Lie bracket, and we have proved a simultaneous flow box theorem for commuting families of Lipschitz vector fields. Finally, I shall mention the question of higher order Lie brackets. In particular, the extension of the concept of set-valued Lie bracket to an order greater than two requires some care, and it cannot be merely treated by inductively applying the notion of degree-two bracket. However, we are proposing a concept of higher degree bracket which, in particular, allows us to generalize the classical Chow’s Theorem.

[1] Rampazzo, F., and H. J. Sussmann, “Set-valued differentials and a nonsmooth version of Chow’s theorem,” in Proceedings of the 40th IEEE Conference on Decision and Control (Orlando, FL, December 2001), Vol. 3, pp. 2613-2618.

[2] Rampazzo, F., and H. J. Sussmann, “Commutators of flows of nonsmooth vector fields,” submitted for publication.

Professor Rampazzo's visit is sponsored by the Louisiana Board of Regents Grant "Enhancing Control Theory at LSU".

Monday, May 8, 2006

Posted May 3, 2006
Last modified September 17, 2021

CCT Computing the Future Lecture Series

1:30 pm 338 Johnston Hall

Walter Gander, Computational Science, ETH Zurich
Solving problems in scientific computing using Maple and Matlab

Refreshments follow the talk.

Tuesday, May 9, 2006

Posted April 18, 2006
Last modified May 1, 2006

1:30 pm 102 Allen
(Originally scheduled for Tuesday, May 2, 2006, 1:30 pm)

Faculty meeting with Dean Ferreyra

Posted May 1, 2006
Last modified October 1, 2021

Control and Optimization Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 284

Abhijit Champanerkar, University of South Alabama
On the Mahler measure of Jones polynomials

We show that the Mahler measure of the Jones polynomial and of the colored Jones polynomials converges under twisting for any link. In terms of Mahler measure convergence, the Jones polynomial behaves like hyperbolic volume under Dehn surgery. We also show that after sufficiently many twists, the coefficient vector of the Jones polynomial and of any colored Jones polynomial decomposes into fixed blocks according to the number of strands twisted. We will also discuss recent results about links with cyclotomic Jones polynomials.

Thursday, May 11, 2006

Posted April 19, 2006
Last modified February 2, 2022

3:40 pm 381 Lockett

Franco Rampazzo, Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova
Moving Constraints as Controls in Classical Mechanics

In most applications of control theory to mechanics the control is identified with a force, or with a torque. However, in some concrete situations, the forces are in fact unknown, whereas what one is actually controlling is the position of part of the system. More precisely, if the state space consists of the product $\mathcal{Q} \times \mathcal{C}$ of two manifolds $\mathcal{Q}$ and $\mathcal{C}$, one can regard $\mathcal{Q}$ as the actual (reduced) state space by identifying $\mathcal{C}$ with a set of controls. As an example, one can think of a mathematical pendulum whose pivot is constrained on a vertical line. In this case $\mathcal{Q} = S^1$ and $\mathcal{C} = \mathbf{R}$. (The title of the talk refers to the fact that a control function $\mathbf{c}(·)$ defined on a time-interval $I$ can be considered as a time dependent (i.e., moving) state-constraint acting on the original state space $\mathcal{Q} \times \mathcal{C}$.)

To begin with, we will illustrate some remarkable geometric aspects, which involve, in particular, the metric induced by the kinetic energy on the manifold $\mathcal{Q} \times \mathcal{C}$ and its relation with the foliation $\{\mathcal{Q} \times \{\mathbf{c}\} \,|\, \mathbf{c} \in \mathcal{C} \}$ .

Secondly, we will address the question of the closure of the set of solutions for unbounded control systems, and we will see how this issue is connected with our mechanical problems.

Finally, we will show how some well-known mechanical questions—including the vibrational stabilization of the so-called inverted pendulum—can actually be regarded as instances of problems involving moving constraints as controls.

Professor Rampazzo's visit is sponsored by the Louisiana Board of Regents Grant "Enhancing Control Theory at LSU".

Tuesday, May 16, 2006

Posted March 28, 2006
Last modified February 11, 2022

until Thursday, May 25, 2006 To be announced

Louisiana Workshop on Mathematical Control Theory

Please see the MCT'06 Website.

Monday, May 22, 2006

Posted May 2, 2006
Last modified March 2, 2022

3:40 pm Lockett 235

Gnana Bhaskar Tenali, Mathematics, Florida Institute of Technology
Fixed point theorems in partially ordered metric spaces and applications

I'll talk about some recent progress made on fixed point theorems in partially ordered metric spaces. In particular, I will discuss a fixed point theorem for a mixed monotone mapping in a metric space endowed with a partial order, using a weak contractivity type of assumption. Besides including several recent developments, such a theorem can be used to investigate a large class of problems. As an application we discuss the existence and uniqueness of solution for a periodic boundary value problem.

Thursday, July 13, 2006

Posted June 20, 2006
Last modified January 6, 2021

2:30 pm – 3:30 pm 277, Lockett Hall

Mathias Stolpe, Institut for Mathematik, Danmarks Tekniske Universitet
A method for global optimization of the stacking sequence in laminated composite shell structures

Monday, August 21, 2006

Posted July 7, 2006

1:30 pm – 4:00 pm 285 Lockett

Comprehensive/PhD Qualifying Exam: Core-1 Analysis Test

Tuesday, August 22, 2006

Posted July 7, 2006

1:30 pm – 4:00 pm 285 Lockett

Comprehensive/PhD Qualifying Exam: Core-1 Topology

Wednesday, August 23, 2006

Posted August 8, 2006

8:30 am – 2:00 pm LSU Student Union

Orientation Meeting for all New Graduate Students at LSU

This orientation meeting is for all new LSU Graduate Students. It is conducted by the Graduate School.

Thursday, August 24, 2006

Posted July 7, 2006

1:30 pm – 4:00 pm 285 Lockett

Comprehensive/PhD Qualifying Exam: Core-1 Algebra

Friday, August 25, 2006

Posted July 7, 2006

9:00 am – 11:00 am 235 Lockett followed by 3rd floor computer lab

Training Session for Math 1431 TAs

Please check with Dr. Cochran if you are unsure of your assistantship duties for fall 2006.

Posted August 22, 2006

11:00 am Computer Lab, 3rd floor Lockett

Orientation for Math 1022 Lab Assistants

All TAs assigned to serve as Lab Assistants in Math 1022 must attend this meeting, which is run by Ms. Karla Neal.

Posted July 7, 2006

12:30 pm – 4:00 pm 285 Lockett

PhD Qualifying Exam: All Core-2 Tests

Posted August 8, 2006

1:00 pm – 6:00 pm LSU Union, Cotillion Ballroom

Teaching at LSU

This meeting is intended for all new Teaching Assistants at LSU. It will include a special session from 2:45-4:00 PM in the Vieux Carre Room for Math & Science TAs, featuring Alumni Professor Oxley and also award winning Math Graduate Assistant Julius Esunge. New TAs in Math should be sure to attend.

Tuesday, August 29, 2006

Posted July 20, 2006
Last modified January 6, 2021

3:30 pm – 4:30 pm 235, Lockett Hall

Fernando Fraternali, California Institute of Technology and Università di Salerno
Free Discontinuity Approaches to Fracture and Folding

Wednesday, August 30, 2006

Posted August 15, 2006
Last modified October 4, 2021

3:40 pm Lockett 15

Meeting of the tenured and tenure-track faculty

Introduction of new faculty.
Amendment to the hiring plan.
Discussion of hiring including consideration of the joint hire.

Thursday, August 31, 2006

Posted August 31, 2006

Algebra and Number Theory Seminar Questions or comments?

1:40 pm – 2:30 pm Lockett 381

Dirk Llewellyn Vertigan, Mathematics Department, LSU
Integer Flows and Cycle Covers: Introductory Lecture

Tuesday, September 12, 2006

Posted September 5, 2006

3:40 pm Lockett 282

Seva Joukhovitski, Mathematics Department, LSU
Splitting varieties and Bloch-Kato Conjecture

Wednesday, September 13, 2006

Posted September 11, 2006
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 381

Hongyu He, Department of Mathematics, LSU
Complementary series of the Universal Covering of the Symplectic Group

Complementary series arise as perturbation of the (degenerate) principal series. I will first discuss Sahi's classification. I will then show that complementary series restricted to a symplectic subgroup "half" of its original size are unitarily equivalent to the corresponding restriction of the principal series. The equivalence is given by the "square" root of the intertwining operator expressed in terms of the mixed model, which I will define. This talk is closely related to G. Olafsson's talk last semester in which he discussed the intertwining operator expressed in terms of the compact model.

Thursday, September 14, 2006

Posted September 1, 2006
Last modified September 12, 2006

3:40 pm – 4:30 pm Locket 285

Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Hilbert Tensor Algebras and Stochastic Differential Equations

Saturday, September 16, 2006

Posted August 22, 2006
Last modified December 13, 2022

Algebra and Number Theory Seminar Questions or comments?

9:45 am – 2:00 pm Hilltop Arboretum, 11855 Highland Rd, Baton Rouge

Graduate Student Picnic and Orientation Conference

Talks by faculty members and senior graduate students. Recreational Activities and Picnic Lunch. Please see Complete Details including Schedule of Events.

Tuesday, September 19, 2006

Posted September 12, 2006

3:40 pm Lockett 282

Seva Joukhovitski, Mathematics Department, LSU
Splitting varieties and Bloch-Kato Conjecture II

Posted September 5, 2006
Last modified September 19, 2006

4:40 pm – 5:30 pm Lockett 285

Patrick Gilmer, Mathematics Department, LSU
Surgery of type-p and quantum invariants of 3-manifolds

Wednesday, September 20, 2006

Posted September 14, 2006
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 381

Hongyu He, Mathematics Department, LSU
Complementary series of the Universal Covering of the Symplectic Group II

Thursday, September 21, 2006

Posted September 13, 2006

3:40 pm – 4:30 pm Lockett 285

Michael Malisoff, LSU Roy P. Daniels Professor
Lyapunov Functions, Stabilization, and Engineering Applications

Tuesday, September 26, 2006

Posted September 6, 2006
Last modified September 19, 2006

4:40 pm – 5:30 pm Lockett 284

Neal Stoltzfus, Mathematics Department, LSU
Dessins in Knot Theory

Wednesday, September 27, 2006

Posted August 30, 2006

Control and Optimization Seminar Questions or comments?

3:40 pm Lockett 6

Meeting of the Tenured Faculty

Discuss a promotion to associate professor with tenure.

Thursday, September 28, 2006

Posted September 18, 2006
Last modified September 17, 2021

3:30 pm 285 Lockett

Martin Hjortso, Louisiana State University Chevron Professor of ChemE
Some Problems in Population Balance Modeling

Friday, September 29, 2006

Posted September 26, 2006

3:40 pm – 4:30 pm Lockett 282

Habib Ouerdiane, Faculte des Sciences de Tunis, Tunis
Introduction to Brownian Functionals, and Applications to Stochastic Differential Equations

Tuesday, October 3, 2006

Posted September 19, 2006
Last modified January 10, 2022

4:40 pm – 5:30 pm Lockett 284

David Cimasoni, UC Berkeley
Generalized Seifert surfaces and signatures of colored links

The Seifert surface is a well-known and very useful tool in link theory. For instance, it permits to study the Alexander invariants, the Conway polynomial, and the signature of an oriented link. In this talk, we shall introduce 'generalized Seifert surfaces' for colored links. They provide a geometric interpretation of the multivariable Alexander invariants and of the Conway potential function. They also make it possible to define (and compute easily) a multivariable signature that generalizes the Levine-Tristram signature. This multivariable signature turns out to be a slight generalization of invariants introduced by P. Gilmer and L. Smolinsky.

Tuesday, October 10, 2006

Posted October 4, 2006

4:40 pm – 5:30 pm Lockett 284

Neal Stoltzfus, Mathematics Department, LSU
Skein Modules of Cylinders and Quantum Cluster Algebras

Friday, October 13, 2006

Posted October 4, 2006
Last modified October 10, 2006

3:40 pm – 4:30 pm Lockett 284

Indira Lara Chatterji, Ohio State University
A characterization of hyperbolicity.

Tuesday, October 17, 2006

Posted October 10, 2006

3:40 pm – 4:30 pm Lockett 381

Andy Sinton, Hebrew University of Jerusalem
Direct and Inverse Limits in Geometry and Representation Theory

Abstract: Direct limits (i.e. unions) of finite-dimensional groups are a natural place to look for infinite-dimensional generalizations of the finite-dimensional representation theory and related geometry. In many situations, it turns out that the appropriate analog for the regular representation is a found by letting the direct limit group act on the inverse limit of a related (quotient) space. The first half of the talk will provide an overview of the results of Olshanski, Vershik, Borodin, and others in the cases of the symmetric group and compact symmetric spaces. In the second half I will discuss the state of the art for non-compact symmetric spaces, which I am working on with Gestur Olafsson. Only a basic background in representation theory and Lie groups will be assumed.

Wednesday, October 18, 2006

Posted October 13, 2006

3:10 pm Lockett 9

Meeting of the tenured and tenure-track faculty

Hiring proposals.
A vote will be taken at the meeting.

Thursday, October 19, 2006

Posted October 5, 2006

3:40 pm – 4:30 pm Lockett 285

Habib Ouerdiane, University of Tunis
Infinite Dimensional Complex Analysis and Application to Probability

There will be coffee and cookies in the lounge at 3:00.

Friday, October 20, 2006

Posted October 12, 2006
Last modified October 20, 2006

3:30 pm – 5:00 pm Lockett, Room 6 (Basement)

Graduate Student Meeting for Career Guidance from Faculty - Refreshments at 3PM in Lounge

This meeting is required of all graduate students who have passed the General Exam. Those who have PhD Qualified are strongly encouraged to attend. Students for whom Qualifying is in the future are warmly invited to attend. A Math Faculty panel will make presentations and answer your questions. Panel includes Profs. Baldridge, Brendle, Malisoff, Olafsson, Richardson and Smolinsky. Refreshments at 3PM in Lounge!

Tuesday, October 24, 2006

Posted October 17, 2006

4:40 pm – 5:30 pm Lockett 284

Brendan Owens, LSU
Knot surgeries and negative definite four manifolds

Thursday, October 26, 2006

Posted September 1, 2006

2:00 pm – 5:00 pm Room 301D, Lockett Hall.

Final Exam for the Non-Thesis MS

This is the concluding part of the Final Exam for the non-thesis MS, the principal parts of which are the three core-1 Comprehensive Exams given earlier. See the Graduate Director for details. The Examining Committee will be Profs. Adkins (Chair), Oporowski, and Sundar.

Posted October 4, 2006
Last modified January 27, 2022

3:40 pm – 4:30 pm Lockett 285

Sarada Rajeev, Department of Physics and Astronomy, University of Rochester
The Stochastic Geometry of Two Dimensional Turbulence

Fluid motion is notoriously hard to predict due to the growth of small instabilities (the “Butterfly Effect”). Arnold showed that these instabilities can be explained geometrically as due to the negative curvature of the group of diffeomorphisms: ideal fluid flow is the geodesic motion on this group. A detailed understanding of fluid flow is still out of reach in the three dimensional case. I will describe an approach to two dimensional turbulence based on a surprising connection to geodesic motion on unitary groups. Including dissipation and fluctuation leads to a stochastic differential equation for which a steady state solution can be obtained. The eventual goal (not yet realized) is to explain how stable structures such as hurricanes arise from such an unstable chaotic system.

Visit supported by National Science Foundation Grant DMS 0601141

Friday, October 27, 2006

Posted October 12, 2006
Last modified October 20, 2006

3:40 pm Lockett 282
(Originally scheduled for Friday, October 20, 2006, 3:40 pm)

Habib Ouerdiane, University of Tunis
Infinite Dimensional Complex Analysis, Holomorphy and Application to Gaussian and non Gaussian Analysis

Thursday, November 2, 2006

Posted September 26, 2006
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 285

Darren Crowdy, Imperial College London and MIT
Vortex motion in complex domains: new theoretical perspectives

There will be coffee and cookies in the lounge at 3:00.

Posted November 2, 2006
Last modified February 20, 2022

5:00 pm Keisler Lounge

Applications of Statistics to Public Health Issues

Professors Lynn R. LaMotte, Qingzhao Yu, and Julia Volaufova from the School of Public Health in the LSU Health Sciences Center will come to speak.

Friday, November 3, 2006

Posted October 31, 2006

3:40 pm Lockett 282

Habib Ouerdiane, University of Tunis
Infinite Dimensional Complex Analysis, Holomorphy and Application to Gaussian and non Gaussian Analysis Part II

Tuesday, November 7, 2006

Posted October 25, 2006

4:40 pm – 5:30 pm Lockett 284

Matilde Lalin, University of British Columbia
Functional equations for the Mahler measure of genus 1 curves

Thursday, November 9, 2006

Posted November 3, 2006

11:00 am – 12:00 pm Johnston 338

Ronald Fintushel, Michigan State University
Surgery on Nullhomologous Tori

Virtual Seminar together with Rice University

Posted October 5, 2006
Last modified November 1, 2006

3:40 pm – 4:30 pm Lockett 285

Paul Kirk, Indiana University
The geography of 4-manifolds with specified fundamental group

There will be coffee and cookies in the lounge at 3:00.

Friday, November 10, 2006

Posted November 6, 2006

3:40 pm 282, Lockett

Suat Namli, Louisiana State University Graduate Student
A White Noise Analysis Approach to Orthogonal Polynomials

Monday, November 13, 2006

Posted November 1, 2006
Last modified March 3, 2021

3:30 pm – 4:30 pm 284 Lockett Hall

Blaise Bourdin, Department of Mathematics and Center for Computation & Technology, LSU
Numerical implementation of a variational model of brittle fracture

Fracture mechanics is a very active area of research, with vital applications. In recent years, the unexpected collapse of terminal 2F at Charles de Gaulle airport in France or the Columbia space shuttle disintegration upon re-entry illustrate the importance of a better understanding and numerical simulation of the mechanism of fracture.

In the area of brittle fracture, the most widely accepted theories are based on Griffith?s criterion and limited to the propagation of an isolated, pre-existing crack along a given path. Extending Griffith?s theory into a global minimization principle, while preserving its essence, the concept of energy restitution in between surface and bulk terms, G. Francfort and J.-J. Marigo proposed a new formulation for the brittle fracture problem. The basis of their model is the minimization of a total energy with respect to any admissible displacement and crack field. The main advantage of this approach is to be capable of predicting the initiation of new cracks, computing their path, and accounting the interactions between several cracks, in two and three space dimensions. Of course, this has a price both theoretically and numerically. In particular, in order to achieve global minimization with respect to any crack set, one has to devise special numerical methods.

After briefly reviewing the issues of brittle fracture mechanics, I will present the Francfort-Marigo model. I will rapidly describe some elements of its analysis, and present a numerical approximation based on the properties of Gamma-convergence. I will derive necessary optimality conditions with respect to the global time evolution, and show how to use them in a minimization algorithm. Then, I will present some extensions of the original model, accounting for body forces (under some restrictions) or thermal loads, and describe how to adapt the numerical implementation. I will illustrate my talk with several large scale two and three dimensional experiments.

Posted November 3, 2006
Last modified January 10, 2022

4:40 pm – 5:30 pm Lockett 284

Matthew Hedden, Michigan State University
The meaning and comparison of smooth concordance invariants

In the past three years, several new invariants of smooth knot concordance have been discovered. This lecture will focus on two of these invariants, denoted $\tau(K)$ and $s(K)$, respectively. Here $K$ denotes a knot in the three-sphere. The former invariant was discovered by Ozsváth and Szabó and independently by Rasmussen and is defined using the Floer homology theory for knots introduced by the aforementioned authors. $s(K)$ was introduced by Rasmussen and is defined in the context of Khovanov knot homology. The invariants share several formal properties and agree for many knots. In particular, each invariant is a homomorphism from the smooth knot concordance group to the integers, and each bounds the smooth four-genus, $g_4(K)$. Moreover, each invariant can be used to determine the smooth four-genera of torus knots and provide new proofs of Milnor's famous conjecture on the four-genera and unknotting numbers of these knots. It was conjectured by Rasmussen that $2\tau$ and $s$ agree for all knots. If confirmed, this conjecture would point to a surprising connection between the analytically defined Ozsváth-Szabó homology theory and the combinatorially defined Khovanov homology. Moreover, it would seem to indicate a relationship between the gauge theory of three and four-manifolds and the quantum framework underlying the Jones polynomial.

This lecture will explore Rasmussen's conjecture by discussing evidence for its validity and families of knots for which the conjecture holds. In this pursuit, it will be appropriate to briefly comment on the geometry contained by the $\tau$ invariant—in particular I'll discuss a theorem which indicates that $tau$ can be used to detect when a knot arises as the intersection of a complex curve in $C^2$ with the three-sphere. This connection partially arises with the $s$ invariant. The main purpose, however, will be to present the first counterexamples to Rasmussen's conjecture, discovered last year by myself and Philip Ording. The examples come from the Whitehead double construction. I will try to say some words about how Rasmussen's conjecture, though false, could be interpreted in the context of a larger conjecture connecting Floer homology to Khovanov homology, also due to Rasmussen.

Tuesday, November 14, 2006

Posted October 4, 2006
Last modified January 27, 2022

3:40 pm – 4:30 pm Lockett 285

Thierry Lévy, École normale supérieure and CNRS
Combinatorial aspects of the heat kernel measure on the unitary group

Computing asymptotic quantities related to the heat kernel measure on the unitary group U(N) as N tends to infinity is one of the basic questions of large N Yang-Mills theory, and a natural problem in the framework of large random matrices. P. Biane (1995) and F. Xu (1997) have independently computed limiting distributions and proved asymptotic freeness results. Recently, A. Sengupta has reformulated Xu’s computation of the limiting distribution in a very clear and attractive way. In this talk, I will explain how physical ideas related to “string theories” developed in the context of two-dimensional Yang-Mills theory by D. Gross and W. Taylor (1993) shed some light on the approach of Xu and Sengupta, in particular on its combinatorial aspects. More concretely, I will explain how elementary computations related to the Schur-Weyl duality allow one to relate the Brownian motion on the unitary group and the most natural random walk on the symmetric group. Then I will derive and discuss convergent series expansions for expectations of products of traces of unitary matrices under the heat kernel measure. This discussion will involve paths in the Cayley graph of the symmetric group and the lattice of non-crossing partitions.

Refreshments will be served in the lounge at 3pm

Visit supported by National Science Foundation Grant DMS 0601141

Wednesday, November 15, 2006

Posted November 6, 2006

3:40 pm – 4:30 pm Lockett 381

Jens Christensen, Mathematics Department, LSU
Time-Frequency analysis and Gelfand triples

In the 80\'s Feichtinger and Groechenig found a general class of Banach spaces tied to integrable group representations. These are called coorbit spaces and they are spaces for which the representation coefficients give isometric isomorphisms into other Banach spaces (for example weighted L_p spaces). A well known example is the class of modulation spaces, but also Besov spaces are coorbit spaces (this is rather loosely claimed by Feichtinger and Groechenig). I try to generalize the concept of coorbit spaces to make this construction easier and also possible for non-integrable square integrable representations. This work has been carried out together with Prof. Olafsson.

Thursday, November 16, 2006

Posted October 20, 2006
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 285

Larry Gerstein, University of California at Santa Barbara
Quadratic forms: classification and other problems

There will be coffee and cookies in the lounge at 3:00.

Friday, November 17, 2006

Posted November 2, 2006
Last modified January 27, 2022

3:40 pm – 4:30 pm 109 Nicholson

John Baez, Univeristy of California at Riverside
Higher Gauge Theory

Gauge theory describes the parallel transport of point particles using the formalism of connections on bundles. In both string theory and loop quantum gravity, point particles are replaced by 1-dimensional extended objects: paths or loops in space. This suggests that we seek some sort of “higher gauge theory” that describes parallel transport as we move a path through space, tracing out a surface. To find the right mathematical language for this, we must “categorify” concepts from topology and geometry, replacing smooth manifolds by smooth categories, Lie groups by Lie 2-groups, bundles by 2-bundles, and so on. Some interesting examples of these concepts show up in the mathematics of topological quantum field theory, string theory and 11-dimensional supergravity.

This is a joint Mathematics and Physics & Astronomy Event.

Monday, November 20, 2006

Posted November 1, 2006
Last modified March 2, 2022

3:30 pm – 4:30 pm 284 Lockett Hall

Jung-Han Kimn, Mathematics Department, LSU
Parallel Implementation of Domain Decomposition Methods

Many important problems from current industrial and academic research, including the numerical solution of partial differential equations, generate extremely large data sets beyond the capacity of single-processor computers. Parallel computation on multiple-processor super computers is therefore the key to increasing performance but efficient parallel algorithms for multiple-processor super computers with huge number of processors are still needed. Domain Decomposition methods comprise an important class of parallel algorithms that are naturally parallel and flexible in their application to a sweeping range of scientific and engineering problems. This talk gives a brief discussion of some issues when we implement parallel domain decomposition methods. We will present some of our recent theoretical and numerical results for parallel domain decomposition methods for elliptic and hyperbolic partial differential equations.

Monday, November 27, 2006

Posted November 21, 2006
Last modified September 17, 2021

CCT Distinguished Guest Lecture

11:00 am Life Sciences Building Annex A101

Ian Foster, The Computation Institute Argonne National Laboratory and the University Of Chicago Director of the Computation Institute Argonne National Laboratory
Scaling EScience Impact

Wednesday, November 29, 2006

Posted October 5, 2006
Last modified November 20, 2006

3:40 pm – 4:30 pm Lockett 235

Samuel M. Rankin, Director, American Mathematical Society Washington Office
Activities of the American Mathematical Society's Washington Office

There will be coffee and cookies in the lounge at 3:00.

Thursday, November 30, 2006

Posted September 29, 2006
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 285

Phuc Nguyen, Purdue University
Nonlinear equations with power source terms and measure data

There will be coffee and cookies in the lounge at 3:00.

Posted October 11, 2006
Last modified March 2, 2022

4:40 pm – 5:30 pm Room 284 Lockett Hall

Michael Mascagni, Department of Computer Science, Florida State University
Using Simple SDEs (Stochastic Differential Equations) to Solve Complicated PDEs (Partial Differential Equations)

This talk begins with an overview of methods to solve PDEs based on the representation of point solutions of the PDEs as expected values of functionals of stochastic processes defined by the Feynman–Kac formula. The particular stochastic processes that arise in the Feynman–Kac formula are solutions to specific SDEs defined by the characteristics of the differential operator in the PDE. The Feynman–Kac formula is applicable to wide class of linear initial and initial-boundary value problems for elliptic and parabolic PDEs. We then concentrate our attention on elliptic boundary value problems that arise in applications in materials science and biochemistry. These problems are similar in that the PDEs to be solved are rather simple, and hence the associated SDEs that arise in the Feynman–Kac formula are likewise simple. However, the geometry of the problem is often complicated and amenable to several acceleration approaches particular to these simple SDEs. We will specifically describe the walk on spheres, Greens function first passage, last passage, walk on the boundary, and walk on subdomains methods in this context. These methods will be presented in the setting of several applications studied by the author and his research collaborators.

Friday, December 1, 2006

Posted November 28, 2006

3:40 pm Lockett 282

Suat Namli, Louisiana State University Graduate Student
Orthogonal Polynomials of Exponential and Fractional Types and Beyond

Monday, December 4, 2006

Posted November 1, 2006
Last modified December 3, 2006

3:30 pm – 4:30 pm Lockett 284

Robert Lipton, Mathematics Department, LSU
Homogenization and Field Concentrations in Heterogeneous Media

Wednesday, December 6, 2006

Posted November 13, 2006
Last modified November 27, 2006

3:40 pm – 4:30 pm Lockett 381

Suat Namli, Louisiana State University Graduate Student
A white noise analysis idea applied to orthogonal polynomials

Friday, December 8, 2006

Posted December 4, 2006

3:40 pm Lockett 282

Hong Yin, Department of Mathematics, LSU Graduate Student
Backward Stochastic Differential Equations

Monday, December 11, 2006

Posted November 1, 2006
Last modified December 11, 2006

3:30 pm – 4:30 pm 284 Lockett Hall

Michael Stuebner, Louisiana State University
An inverse homogenization approach to stress constrained structural design

The presentation addresses the problem of optimal design of microstructure in composite materials. A computational method for grading the microstructure for the control of local stress in the vicinity of stress concentrations is developed. The method is based upon new rigorous multiscale stress criteria connecting the macroscopic or homogenized stress to local stress fluctuations at the scale of the microstructure. The approach is applied to different type of design problems.

Tuesday, January 9, 2007

Posted January 4, 2007

1:30 pm – 4:00 pm 285 Lockett

Comprehensive / PhD Qualifying Exam: Core-1 Topology

This exam is based on the subject matter of Math 7510.

Wednesday, January 10, 2007

Posted January 4, 2007

1:30 pm – 4:00 pm 285 Lockett
(Originally scheduled for Monday, January 8, 2007, 1:30 pm)

Core-1 Comprehensive / Phd Qualifying Exam: Core-1 Analysis

This exam is based on the subject matter of Math 7311.

Thursday, January 11, 2007

Posted January 4, 2007

1:30 pm – 4:00 pm 285 Lockett

Comprehensive / PhD Qualifying Exam: Core-1 Algebra

This exam is based on the subject matter of Math 7200.

Friday, January 12, 2007

Posted January 4, 2007

12:30 pm – 4:00 pm 285 Lockett

Comprehensive / PhD Qualifying Exams: Core-2

All Core-2 Exams which have been requested by students will be offered at this time and place. NOTICE THE EARLIER STARTING TIME! Core-2 Exams last 3 and 1/2 hours.

Sunday, January 14, 2007

Posted December 17, 2007

Academic Excellence Visiting Scholar

3:30 pm tba

tba

Monday, January 15, 2007

Posted January 28, 2007

3:40 pm Lockett 285

Meeting of the Tenured Faculty

Third year review cases. A vote will follow and continue through Mardi Gras break.

Tuesday, January 16, 2007

Posted December 17, 2007

Academic Excellence Visiting Scholar

3:30 pm tba

Paul Rabinowitz, University of Wisconsin E.B. Van Vleck Professor of Mathematics; National Academy Member; 1998 George David Birkhoff Prize in Applied Mathematics
tba

Thursday, January 18, 2007

Posted January 14, 2007
Last modified January 16, 2007

3:40 pm – 4:30 pm Lockett 277

Carlos A. Berenstein, University of Maryland
Internet Tomography

Abstract: The problem to be discussed is how to detect as early as possible an attack on a network by saturation. There will be coffee and cookies in the lounge at 3:00.

Tuesday, January 23, 2007

Posted December 11, 2006
Last modified December 18, 2006

3:10 pm LOCKETT 10

Meeting with the LSU CIO

Brian Voss, the Chief Information Officer at LSU and Randy Hall, IT Faculty Liaison will visit the department and hold an open meeting to give mathematics faculty the opportunity to raise and discuss any needs or concerns about information technology at LSU.

Thursday, January 25, 2007

Posted January 15, 2007
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 277

Jan Dijkstra, Vrije Universiteit Amsterdam
On sets with convex shadows

There will be coffee and cookies in the lounge at 3:00.

Monday, January 29, 2007

Posted January 16, 2007

A joint Algebra and Harmonic Analysis Seminar

3:40 pm – 4:30 pm Lockett 285

Anne-Marie Aubert, CNRS and Institut de Mathematiques de Jussieu
Geometric structure in the representation theory of $p$-adic groups

Abstract: We will recall the Bernstein decomposition of the category of smooth representations of reductive $p$-adic groups. Then we will associate to each Bernstein component a (complex) affine variety. We conjecture that the periodic cyclic homology of the corresponding ideal in the Hecke algebra of the $p$-adic group is isomorphic to the cohomology (with complex coefficients) of this affine variety. In addition, we conjecture that there is a bijection between the points of the affine variety and the corresponding Bernstein component. This bijection (conjecturally) has a number of properties which relate to the representation theory of $G$. We will illustrate some properties of our conjecture on the exceptional group $G_2$.

Tuesday, January 30, 2007

Posted January 10, 2007
Last modified January 21, 2007

Control and Optimization Seminar Questions or comments?

4:40 pm – 5:30 pm Lockett 276

Emille K. Davie, University of Georgia
Characterizing Right-Veering Surface Diffeomorphisms Via the Burau Representation

Wednesday, January 31, 2007

Posted January 30, 2007
Last modified January 31, 2007

11:30 am – 12:30 pm Lockett 301D (Conference Room)

Michael Malisoff, LSU Roy P. Daniels Professor
On the Stability of Periodic Solutions in the Perturbed Chemostat

We study the chemostat model for one species competing for one nutrient using a Lyapunov-type analysis. We design the dilution rate function so that all solutions of the chemostat converge to a prescribed periodic solution. In terms of chemostat biology, this means that no matter what positive initial levels for the species concentration and nutrient are selected, the long-term species concentration and substrate levels closely approximate a prescribed oscillatory behavior. This is significant because it reproduces the realistic ecological
situation where the species and substrate concentrations oscillate. We show that the stability is maintained when the model is augmented by additional species that are being driven to extinction. We also give an input-to-state stability result for the chemostat-tracking equations for cases where there are small perturbations acting on the dilution rate and initial concentration. This means that the long-term species concentration and substrate behavior enjoys a
highly desirable robustness property, since it continues to approximate the prescribed oscillation up to a small error when there are small unexpected changes in the dilution rate function. This talk is based on the speaker\'s joint work with Frederic Mazenc and Patrick De Leenheer.

Posted January 30, 2007

A^1 homotopy theory seminar

2:00 pm Lockett 381

Organizational meeting

Posted January 18, 2007
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 285

Kariane Calta, Cornell University Candidate for Assistant Professor Position
Billiards, translation surfaces and associated dynamical systems

In this talk I will discuss some of the basic notions relevant to the study of translation surfaces and provide several interesting examples of such surfaces, including those that arise from billiard tables. I will focus on the dynamics of the geodesic flow on an individual surface and the related dynamics of the action of SL(2,R) on the moduli space of translation surfaces. I will also discuss recent advances in this field, including some of my own results and their relationship to the work of a number of other authors.

Friday, February 2, 2007

Posted January 30, 2007
Last modified September 17, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

11:00 am 338 Johnston Hall

Thomas J.R. Hughes, The University Of Texas At Austin Professor of Aerospace Engineering and Engineering Mechanics
Computational Geometry And Computational Mechanics

Posted January 30, 2007

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm 338 Johnston Hall

Thomas J.R. Hughes, The University Of Texas At Austin Professor of Aerospace Engineering and Engineering Mechanics
Variational Multiscale Methods in Computational Fluid Dynamics

The talk is a part of the CCT Colloquium Series.

Posted January 26, 2007

3:40 pm – 4:30 pm Lockett 285

Ioan Bejenaru, University of California, Los Angeles Candidate for Assistant Professor Position
Local and global solutions for Schroedinger Maps

Abstract: We introduce the Schroedinger Maps which can be thought as free solutions of the geometric Schroedinger equation. More exactly, while the classical Schroedinger equation is written for functions taking values in $\\mathhb{C}$ (complex plane), the range of a Schroedinger Map is a manifold (with a special structure). We explain the importance of these Maps and what are the fundamental aspects one would like to understand about them. Then we focus on the particular case when the target manifold is $\\mathbb{S}^2$ (the two dimensional sphere) and review the most recent results along with our contribution to the field.

Saturday, February 3, 2007

Posted January 26, 2007
Last modified February 11, 2022

10:00 am – 12:00 pm Sunday, February 4, 2007 Lockett 237

Second Louisiana-Texas Topology Retreat

Together with Rice University; Schedule

Monday, February 5, 2007

Posted January 25, 2007

CCT Lecture Events organized by the LSU Center for Computation and Technology

10:00 am 338 Johnston Hall

Hae-Won Choi, National Center for Atmospheric Research Scientific Computing Division
Scientific Computing Technologies Devising High-Order Methods

Posted January 29, 2007
Last modified March 2, 2022

2:40 pm – 3:30 pm 338 Johnston Hall

Paul Saylor, University of Illinois
Stanford's Foresight and Forsythe's Stanford

What Stanford Was Like
What the Time Was Like
Over A Four Year Period
Starting with the Arrival of This New Man
Professor George Forsythe, In 1957
Plus A Bonus Look-Ahead to the Future

Posted January 29, 2007
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 285

Mahta Khosravi, Institute for Advanced Study, Princeton, NJ Candidate for Assistant Professor Position
Spectral Asymptotics on Heisenberg Manifolds

Let $R(t)$ be the error term in Weyl's law for $(2n+1)$-dimensional Heisenberg manifolds. Based on the Petridis-Toth conjecture $R(t)=O_\delta(t^{n-1/4+\delta})$. We discuss new pointwise and moment results that provide evidence for this conjecture in three dimensions and a proof for it in higher dimensions. The methods used also allow a proof of a new fifth moment result in the case of the Dirichlet Divisor problem.

Tuesday, February 6, 2007

Posted January 28, 2007

Control and Optimization Seminar Questions or comments?

4:00 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial Exams

Organizational meeting for preparation for spring exams. Math 4050 no longer will cover the entire FM exam. Supplementary lectures will be offered by Matthew Arnold. Refreshments will be served.

Wednesday, February 7, 2007

Posted February 4, 2007

11:30 am – 12:30 pm 239 Lockett

Michael Malisoff, LSU Roy P. Daniels Professor
Further Results on Lyapunov Functions for Slowly Time-Varying Systems

We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily exponentially stable. This complements our previous Lyapunov function constructions for rapidly time-varying dynamics. We also explicitly construct input-to-state stable Lyapunov functions for slowly time-varying control systems. We illustrate our findings by constructing explicit Lyapunov functions for a pendulum model, an example from identification theory, and a perturbed friction model. This talk is based on the speaker\'s joint work with Frederic Mazenc.

Thursday, February 8, 2007

Posted February 2, 2007

A^1-homotopy theory seminar

1:00 pm – 3:00 pm Lockett 381

Girja Shanker Tripathi, LSU
Closed model categories

Monday, February 12, 2007

Posted January 22, 2007

3:40 pm – 4:30 pm Lockett 285

Milen Yakimov, University of California, Santa Barbara
Poisson structures on flag varieties

Abstract: The geometry of Poisson structures originating from Lie theory found numerous applications in representation theory, ring theory, and dynamical systems. The linear Poisson structure on the dual of a Lie algebra provides the setting for the orbit method of Kirillov, Kostant, and Dixmier for the study of the unitary duals of Lie groups and the spectra of universal enveloping algebras. In this talk we will describe in detail the geometry of a class of Poisson structures on complex flag varieties and some of their relations to combinatorics (Schubert cells and their Deodhar partitions, cluster algebras, total positivity, the Springer and the Lusztig partitions of wonderful compactifications), ring theory (spectra of algebras of quantum matrices and other quantized algebras), integrable systems (Kogan-Zelevinsky systems). In the special case of hermitian symmetric spaces of compact type, these Poisson structures further elucidate the works of Wolf, Richardson, R\\\"ohrhle, and Steinberg on the structure of the orbits of certain Levi factors.

Tuesday, February 13, 2007

Posted January 25, 2007
Last modified January 26, 2007

Control and Optimization Seminar Questions or comments?

3:10 pm Lockett B10

Meeting of the Tenured and Tenure-track Faculty

Discussion and vote on a candidate for associate professor with tenure.

Wednesday, February 14, 2007

Posted February 9, 2007

11:40 am – 12:30 pm Lockett 239

Jimmie Lawson, Mathematics Department, LSU
The Symplectic Group and Semigroup and Riccati Differential

Abstract: We develop close connections between important control-theoretic matrix Riccati differential equation and the symplectic matrix group and its symplectic subsemigroup. We use this example as a case study to demonstrate how the Lie theory of the subsemigroups of a matrix group can be applied to problems in geometric control theory. As an application we derive from this viewpoint the existence of a solution for the Riccati equation for all $t\\geq 0$ under quite general hypotheses.

Posted January 29, 2007
Last modified February 7, 2007

3:40 pm – 4:30 pm Lockett 285

Christian Haesemeyer, University of Illinois at Urbana-Champaign Candidate for Assistant Professor Position
On the algebraic K-theory of singularities

Abstract: Algebraic K-theory is a highly complicated invariant of algebraic varieties and rings, encoding arithmetic, geometric and algebraic information. In this talk, I will try to explain these different notions and give some idea as to how to isolate geometric from algebraic information in the case of singularities.

Thursday, February 15, 2007

Posted February 8, 2007

A^1-homotopy theory seminar

1:00 pm – 3:00 pm Lockett 381

Girja Shanker Tripathi, LSU
Closed model categories II

Posted January 28, 2007

3:40 pm Lockett 285

Meeting of the Tenured Faculty

Third year year cases. A vote will follow and continue through Mardi Gras break.

Friday, February 16, 2007

Posted February 12, 2007
Last modified February 20, 2022

2:40 pm – 3:30 pm Keisler Lounge (Room 321 of Lockett)

Presentations about Research Experience For Undergraduates (REUs)

This will include presentations by Professors Lawrence Smolinsky and William Hoffman about possible paid summer research jobs.

Posted January 25, 2007
Last modified February 14, 2007

Special Lecture

3:40 pm – 4:30 pm 285 Lockett Hall

John Perry, University of Southern Mississippi
From Gauss to Groebner Bases

Abstract:
Gaussian elimination of linear systems into echelon form allows us to analyze the solution set of the linear system. What about systems of non-linear polynomials? In 1965, Bruno Buchberger discovered an algorithm that \"triangularizes\" such systems into Groebner bases. Using a Groebner basis, one can analyze the solutions much as one might analyze the echelon form of a linear system.
This talk introduces Groebner bases and Buchberger\'s algorithm; we present them as a generalization of Gaussian elimination and echelon form. We indicate some applications, describe some challenges in their computation, and conclude with some recent advances.
The talk will be accessible to undergraduates, graduate students, and faculty.

Monday, February 19, 2007

Posted January 29, 2007

11:00 am – 12:00 pm Johnston Hall Room 338

Fengyan Li, Rensselaer Polytechnic Institute
Recent development in nonconforming methods for Maxwell equations

In this talk, I will discuss some recent developments in computational electromagnetism. Two schemes are formulated for the reduced time-harmonic Maxwell equations. One is using the classical nonconforming finite elements, the other is based on the interior penalty type discontinuous Galerkin methods. The operators in these schemes naturally define two Maxwell eigensolvers which are spurious free. Theoretical and numerical results will be presented to demonstrate the performance of these methods. This is joint work with Susanne Brenner and Li-yeng Sung (LSU).

Posted February 12, 2007

CCT Lecture Events organized by the LSU Center for Computation and Technology

11:00 am 338 Johnston Hall

Fengyan Li, Rensselaer Polytechnic Institute
Sound and Sense; Beyond SenSurround

Thursday, February 22, 2007

Posted February 8, 2007
Last modified February 9, 2007

A^1-homotopy theory seminar

1:00 pm – 3:00 pm Lockett 381

Seva Joukhovitski, Mathematics Department, LSU
Etale and Nisnevich topology

Posted February 13, 2007
Last modified February 20, 2022

3:40 pm Keisler Lounge (Room 321 of Lockett Hall)

More Presentations about Research Experience For Undergraduates (REUs)

This will include presentations by Cecil Taylor Alumni Professor Robert Perlis and possibly other professors about possible paid summer research jobs.

Friday, February 23, 2007

Posted February 14, 2007

3:40 pm – 4:30 pm Lockett 285

Milen Yakimov, University of California, Santa Barbara
Poisson structures on flag varieties

Monday, February 26, 2007

Posted January 17, 2007
Last modified February 15, 2007

3:40 pm – 4:30 pm 284 Lockett Hall

Itai Shafrir, Department of Mathematics, Technion - Israel Institute of Technology
On a minimization problem with a mass constraint involving a potential vanishing on two curves

We study a singular perturbation type minimization problem with a mass constraint over a domain or a manifold, involving a potential vanishing on two curves in the plane. We describe the asymptotic behavior of the energy as the parameter epsilon goes to zero, and in particular, how it depends on the geometry of the domain. In the case of the problem on the sphere we give a precise description of the limiting behavior of both the minimizers and their energies. This is a joint work with Nelly Andre (Tours).

Posted January 5, 2007
Last modified January 27, 2022

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 277

Max Karoubi, University of Paris 7
Twisted K-theory, old and new

Twisted K-theory has its origins in the author's PhD thesis [K1] and in the paper of P. Donovan and the author about 37 years ago. The objective of the lecture is to revisit the subject in the light of new developments inspired by Mathematical Physics. See for instance E. Witten ArXiv hep-th/9810188, J. Rosenberg and M.F. Atiyah-G. Segal ArXiv math/0407054. The unifying theme is the notion of K-theory of graded Banach algebras, already present in [K1], from which most of the new theorems in twisted K-theory are derived. Some explicit computations are also given in the equivariant case, related to previous known results. (See https://webusers.imj-prg.fr/~max.karoubi/ or ArXiv mathKT/0701789 for more details.)

There will be coffee and cookies in the lounge at 3:00.

Tuesday, February 27, 2007

Posted February 6, 2007
Last modified February 7, 2007

3:40 pm – 4:30 pm Lockett 243

Max Karoubi, University of Paris 7
K-theory and characteristic classes in number theory

ABSTRACT: Let A be an arbitrary ring. We introduce a Dennis trace map mod n, from K_1(A;Z/n) to the Hochschild homology group with coefficients HH_1(A;Z/n). If A is the ring of integers in a number field, explicit elements of K_1(A,Z/n) are constructed and the values of their Dennis trace mod n are computed. If F is a quadratic field, we obtain this way non trivial elements of the ideal class group of A. If F is a cyclotomic field, this trace is closely related to Kummer logarithmic derivatives; this trace leads to an unexpected relationship between the first case of Fermat's last theorem, K-theory and the number of roots of Mirimanoff polynomials. This is joint work with Thierry Lambre, see ArXiv math.NT/0006237 for more details.

Wednesday, February 28, 2007

Posted February 22, 2007

Control and Optimization Seminar Questions or comments?

11:40 am – 12:30 pm Lockett 239

Jimmie Lawson, Mathematics Department, LSU
The Symplectic Group and Semigroup and Riccati Differential (Part II)

Thursday, March 1, 2007

Posted February 27, 2007

A^1 homotopy theory seminar

1:00 pm – 3:00 pm Lockett 381

Martin Laubinger, LSU Graduate Student
Homotopy theory on a Grothendieck Topos

Monday, March 5, 2007

Posted January 29, 2007
Last modified March 2, 2022

3:40 pm – 4:30 pm 284 Lockett Hall

Alexander Pankov, College of William and Mary
Gap solitons, periodic NLS, and critical point theory

Here a gap soliton means a spatially exponentially localized standing wave solution of periodic nonlinear Maxwell equations, having a carrier frequency in a spectral gap. There is an enormous literature devoted to study of what should be gap solitons by means of approximate methods, e.g., envelope function approach, and numerical simulations (basically, in one dimension). These results provide a lot of information about such solutions, say, their shape. However, the existence of gap solitons is not a clear issue. In this talk we discuss the existence problem in the case of periodic Akhmediev-Kerr medium. We consider two-dimensional case and look for (TM) polarized solutions. Then the problem reduces to a (two-dimensional) periodic stationary NLS with cubic nonlinearity. To study this equation we employ critical point theory (specifically, the linking theorem) together with the so-called periodic approximations. This leads to the existence of TM gap solitons and provides an estimate for the rate of exponential decay. Finally, we discuss certain open mathematical problems.

Tuesday, March 6, 2007

Posted March 2, 2007

Control and Optimization Seminar Questions or comments?

4:00 pm Lockett 240

Hong Yin, Department of Mathematics, LSU Graduate Student
Backward Stochastic Differential Equations

Wednesday, March 7, 2007

Posted March 5, 2007

11:40 am – 12:30 pm Lockett 239

Jimmie Lawson, Mathematics Department, LSU
The Symplectic Group and Semigroup and Riccati Differential Equations (Part III)

Posted February 28, 2007

3:40 pm – 4:30 pm Lockett 381

Michael Otto, University of Arizona
Poisson geometry and symmetric spaces

Abstract: Methods from Poisson/symplectic geometry can be used to study properties of Lie groups and associated symmetric spaces. A prominent example is provided by the classical symplectic convexity theorem of Atiyah and Guillemin-Sternberg and its connection with Kostant\'s convexity theorem for semisimple Lie groups. We will introduce several interesting Poisson structures on a symmetric space and discuss applications.

Thursday, March 8, 2007

Posted March 5, 2007

A^1-homotopy theory seminar

1:00 pm – 3:00 pm Lockett 381

Martin Laubinger, LSU Graduate Student
Definition of the A^1-homotopy category

Posted February 14, 2007
Last modified February 15, 2007

3:40 pm – 4:30 pm Lockett 285

Michael Otto, University of Arizona
The moment map in symplectic geometry and elsewhere

Abstract: The moment map is a central object of study in symplectic geometry. It also appears (in disguise) in several other branches of mathematics, such as linear algebra, classical mechanics, representation theory of Lie groups etc. This talk is intended to give an overview over some of its most interesting properties, most notably several convexity results and formulas of Duistermaat-Heckman type.

There will be coffee and cookies in the lounge at 3:00.

Posted March 8, 2007
Last modified March 2, 2021

5:00 pm James E. Keisler Mathematics Lounge (321 Lockett)

Charles Neal Delzell, Mathematics Department, LSU
On Hilbert's 17th Problem

Friday, March 9, 2007

Posted February 12, 2007

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm 338 Johnston Hall

Isiah M. Warner, Department of Chemistry, Louisiana State University Boyd Professor, Louisiana State University
Models for Creating and Sustaining Diversity among Undergraduate Students in Science

Tuesday, March 13, 2007

Posted March 7, 2007
Last modified March 12, 2007

Junior Topology Seminar

3:10 pm – 4:00 pm Lockett 276

Seminar on knot homology theories and related topics

Moshe Cohen (LSU): On Viro\'s description of Khovanov\'s knot homology

Wednesday, March 14, 2007

Posted March 13, 2007
Last modified May 20, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

11:00 am 338 Johnston Hall

Pavel Bochev, Sandia National Laboratories
Mimetic Discretizations And What They Can Do For You

Recent advances in compatible discretizations enabled impressive gains in computational science and affirmed the key role of homological principles in numerical PDEs. Thanks to homological ideas and tools, we now have a much better understanding of why some discretization methods work so well and why other methods fail spectacularly. More importantly, homological ideas can be used to develop stable and physically consistent discretizations, such as mimetic methods, which replace PDEs by algebraic equations that inherit their fundamental structural properties.

We provide a common framework for mimetic methods using algebraic topology to guide our analysis. The key concept in our approach is the natural inner product on co-chains. This inner product is sufficient to generate a combinatorial Hodge theory on co-chains but avoids complications attendant in the construction of robust discrete Hodge-star operators. In particular, using a reduction and a reconstruction maps between differential forms and co-chains we define mutually consistent sets of natural and derived discrete operations that preserve the invariants of the De Rham homology groups and obey a discrete Stokes theorem. By choosing a specific reconstruction operator we obtain well-known mixed FE, mimetic FD and covolume methods and explain when they are equivalent.

The second half of the talk will discuss several applications of the mimetic framework. We will start with a new interpretation of a certain class of compatible least-squares methods, as discrete realizations of a Hodge-star operator, obtained from weakly enforced material laws. Among other things, we will show that least-squares, Galerkin and mixed Galerkin methods, for a class of second order elliptic problems, can be derived from a common constrained optimization problem. Our second example will use the mimetic framework to reformulate the discrete Maxwell's equations into a system that is dominated by discrete Hodge-Laplace operators. As a result, the reformulated system can be solved by standard “black-box” AMG solvers for the Poisson equation. Time permitting, we will conclude with an example that explains how mimetic discretizations can be used to remap divergence free fields without advection algorithms.

This talk is based on joint work with M. Gunzburger (CSIT, Florida State University), M. Shashkov and M. Hyman (Theoretical Division, Los Alamos National Laboratory).

Thursday, March 15, 2007

Posted March 9, 2007

A^1-homotopy theory seminar

1:00 pm – 3:00 pm Lockett 381

Marco Schlichting, Louisiana State University
Brown-Gersten property and Realization functors

Posted March 14, 2007

Analysis/PDE Seminar

1:40 pm – 3:00 pm 203 Prescott Hall

Delio Mugnolo , Institute for Applied Analysis, University of Ulm, Germany
Evolution Equations on Networks - Interaction is Complexity (Part II)

Simplified versions of many complex systems can be modeled as networks: the Internet, an animal\'s brain, electrical circuits, a highway system, a social community... Although the descriptions of ongoing phenomena (transmission of potential, mechanical vibrations, spread of information...) as well as other relevant issues are specific for each model, they all lead to the consideration of partial differential equations on 1-d structures. Begun in the 1950\'s in the framework of chemical physics, interest in investigations of differential models for network-shaped structures has been revived in the last 20 years. Ever since, networks and their pervasiveness in everyday life have made their way even to the mainstream press. The aim of this lecture series is to present an abstract approach to differential problems on networks that is based on an interplay of functional analysis and graph theory. While pursuing our mathematical targets, we will often be motivated by, think of, and even speak the language of theoretical neurobiological problems. Having applications in mind, we will formulate and prove theoretical results (well-posedness, maximum principles, asymptotic, qualitative properties...) so that they can be promptly interpreted as soon as specific models are considered. Some basic knowledge (e.g., what is a Sobolev space, the spectrum of an unbounded operator, or an incidence matrix) in operator theory, partial differential equations, and graph theory will prove useful, but is no strict prerequisite. To demonstrate the usefulness of the results, some time will be devoted to the mathematical analysis of a few neurobiological systems (preceded by a crash course in neuronal modeling).

Posted March 14, 2007
Last modified February 20, 2022

5:00 pm James E. Keisler Mathematics Lounge (321 Lockett)

Pramod Achar, Mathematics Department, LSU
Regular Complex Polytopes

This talk will be understandable to undergraduates.

Friday, March 16, 2007

Posted March 13, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm 338 Johnston Hall

David Skinner, Lawrence Berkeley Lab
Integrated Performance Monitoring: HPC Workload Characterization

Monday, March 19, 2007

Posted March 17, 2007

Analysis/PDE Seminar

1:40 pm – 3:00 pm 203 Prescott Hall

Delio Mugnolo , Institute for Applied Analysis, University of Ulm, Germany
Evolution Equations on Networks - Interaction is Complexity (Part III)

Simplified versions of many complex systems can be modeled as networks: the Internet, an animal\'s brain, electrical circuits, a highway system, a social community... Although the descriptions of ongoing phenomena (transmission of potential, mechanical vibrations, spread of information...) as well as other relevant issues are specific for each model, they all lead to the consideration of partial differential equations on 1-d structures. Begun in the 1950\'s in the framework of chemical physics, interest in investigations of differential models for network-shaped structures has been revived in the last 20 years. Ever since, networks and their pervasiveness in everyday life have made their way even to the mainstream press. The aim of this lecture series is to present an abstract approach to differential problems on networks that is based on an interplay of functional analysis and graph theory. While pursuing our mathematical targets, we will often be motivated by, think of, and even speak the language of theoretical neurobiological problems. Having applications in mind, we will formulate and prove theoretical results (well-posedness, maximum principles, asysmptotics, qualitative properties...) so that they can be promptly interpreted as soon as specific models are considered. Some basic knowledge (e.g., what is a Sobolev space, the spectrum of an unbounded operator, or an incidence matrix) in operator theory, partial differential equations, and graph theory will prove useful, but is no strict prerequisite. To demonstrate the usefulness of the results, some time will be devoted to the mathematical analysis of a few neurobiological systems (preceded by a crash course in neuronal modeling).

Tuesday, March 20, 2007

Posted March 14, 2007

Junior Topology Seminar

3:10 pm – 4:00 pm Lockett 276

Seminar on knot homology theories and related topics

Adam Lowrance (LSU) on the combinatorial description of Oszvath-Szabo Heegaard Floer knot homology by Manolescu-O.-S.-Thurston

Thursday, March 22, 2007

Posted March 20, 2007

A^1-homotopy theory seminar

1:00 pm – 3:00 pm Lockett 381

Marco Schlichting, Louisiana State University
Homotopy invariant cohomology theories and the Brown Gersten property

Posted March 20, 2007

Junior Topology Seminar

3:10 pm – 4:00 pm Lockett 276

Seminar on knot homology theories and related topics

Adam Lowrance (LSU) on the combinatorial description of Oszvath-Szabo Heegaard Floer knot homology by Manolescu-O.-S.-Thurston, Part II

Posted March 20, 2007

5:00 pm Keisler Lounge (321 Lockett)

Padmanabhan Sundar, Mathematics Department, LSU
Large Deviations and Rare Events

Friday, March 23, 2007

Posted January 17, 2007

1:00 pm – 4:00 pm Conference Room: 301D Lockett
(Originally scheduled for 1:00 pm)

Concluding part of Final Exam for Non-Thesis MS

Posted March 13, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm 338 Johnston Hall

Chokchai "Box" Leangsuksun, Louisiana Tech University Associate Professor in Computer Science and the Center for Entrepreneurship and Information Technology (CEnIT).
Reliability-aware runtime system research for HPC

Tuesday, March 27, 2007

Posted March 20, 2007

3:10 pm B 10 Locket Hall

Graduate student meeting

We will discuss additions to the graduate school program.

Posted March 26, 2007

4:00 pm 240 Lockett

Suat Namli, Louisiana State University Graduate Student
Orthogonal polynomials of the exponential and fractional type

Posted March 7, 2007

Control and Optimization Seminar Questions or comments?

4:40 pm – 5:00 pm Lockett 276

Kathy Zhong, Cal State Sacramento
Calculate Kauffman Polynomials of some Knots Using Kauffman Skeins

Wednesday, March 28, 2007

Posted March 26, 2007

11:40 am – 12:30 pm 239 Lockett

Feng Gao, LSU Department of Mechanical Engineering
A Generalized Approach for the Control of MEM Relays

Abstract: We show that voltage-controlled, electrostatic and electromagnetic micro-relays have a common dynamic structure. As a result, both types of microelectromechanical (MEM) relays are subject to the nonlinear phenomenon known as pull-in, which is usually associated with the electrostatic case. We show that open-loop control of MEM relays naturally leads to pull-in during the relay closing. Two control schemes - a Lyapunov design and a feedback linearization design - are presented with the objectives of avoiding pull-in during the micro-relay closing and improving the transient response during the micro-relay opening. Simulations illustrate the performance of the two control schemes in comparison to the typical open-loop operation of the MEM relay.

Posted March 23, 2007

3:00 pm

277 Lockett Hall

At 3:00 - Rank III promotion case for Ameziane Harhad

At 3:30 - Instructors meeting, mandatory for instructors

Posted March 14, 2007
Last modified March 15, 2007

3:40 pm – 4:30 pm Lockett 381
(Originally scheduled for Wednesday, March 21, 2007, 3:40 pm)

Hongyu He, Mathematics Department, LSU
Introduction to Theta Correspondence

In this talk, I will introduce Howe\'s dual reductive pair. I will then discuss
the basic theory of theta correspondence and its application in representation
theory. The talk will be accessible to graduate students.

Thursday, March 29, 2007

Posted March 21, 2007
Last modified March 28, 2007

11:00 am Lockett 381
(Originally scheduled for Wednesday, March 28, 2007, 4:40 pm)

Stephen Bigelow, UC Santa Barbara
Representations of Planar Algebras

Time/Date Changed

Posted March 29, 2007

A^1-homotopy theory seminar

1:00 pm – 3:00 pm Lockett 381

Jerome W. Hoffman, Mathematics Department, LSU
Some calculations in A^1-homotopy theory

Posted March 28, 2007
Last modified February 20, 2022

Pasquale Porcelli Lecture Series Special Lecture Series

5:00 pm 321 Lockett (Keisler Lounge)

Rick Barnard, LSU Department of Mathematics Graduate Student
What Is A Control System?!

Friday, March 30, 2007

Posted March 13, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm 338 Johnston Hall

Guan Qin, Texas A&M University Institute for Scientific Computation
Mathematical Challenges and Hot Topics in Oil Reservoir Simulation

Tuesday, April 10, 2007

Posted March 30, 2007
Last modified April 7, 2007

3:40 pm – 4:30 pm Room 130, Howe-Russell Geoscience Complex

Richard Kadison, University of Pennsylvania Member of the National Academy of Sciences
The Pythagorean Theorem: A Closer Look

Extensions and variants of the Pythagorean theorem are presented, first from the point of view of finite-dimensional, linear algebra and, later, in the framework of infinite-dimensional Hilbert space. The results discussed make contact with the work of Kostant, Atiyah, and Guillemin-Sternberg in the convex geometry of symmetric spaces, the work of Horn and Schur on spectral theory, matrix inequalities, majorization, and convex polytopes, and semi-commutative, metric geometry from the point of view of conditional expectations. The first of the two Pythagoras lectures will be relatively elementary, the second will be slightly more advanced, relying somewhat on the operator-algebra, survey lecture that follows the first lecture. There will be coffee and cookies in the Atrium, Howe-Russell E, at 3:00.

Wednesday, April 11, 2007

Posted March 30, 2007
Last modified April 7, 2007

Pasquale Porcelli Lecture Series Special Lecture Series

3:40 pm – 4:30 pm 130 Howe-Russell Geoscience Complex.

Richard Kadison, University of Pennsylvania Member of the National Academy of Sciences
Operator Algebras: A Sampler

There will be coffee and cookies in the Atrium, Howe-Russell E, at 3:00.

Thursday, April 12, 2007

Posted March 30, 2007

A^1-homotopy theory seminar

1:00 pm – 3:00 pm Lockett 381

Jerome W. Hoffman, Mathematics Department, LSU
Projective n-space in A^1-homotopy and other calculations

Posted March 30, 2007
Last modified April 7, 2007

Pasquale Porcelli Lecture Series Special Lecture Series

3:40 pm – 4:30 pm 130 Howe-Russell Geoscience Complex

Richard Kadison, University of Pennsylvania Member of the National Academy of Sciences
The Pythagorean Theorem: An Advanced View

There will be coffee and cookies in the Atrium, Howe-Russell E, at 3:00.

Monday, April 16, 2007

Posted March 30, 2007
Last modified April 9, 2007

Calculus Textbook and Webwork Presentation

3:40 pm – 4:30 pm Lockett 285
(Originally scheduled for Tuesday, April 17, 2007, 3:40 pm)

University Calculus

An Addison Wesley representative will present their integration of Webworks with their book \'University Calculus\' by Haas, Wier, and Thomas.

Tuesday, April 17, 2007

Posted April 10, 2007

Junior Topology Seminar

3:10 pm – 4:00 pm Lockett 276

Seminar on knot homology theories and related topics

Godi Pruidze (LSU): Topology of robot motion planning

Posted April 9, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:30 pm Life Sciences Building Annex A101 Auditorium

Alfred Z. Spector, Independent Consultant Former CTO and Vice President of Strategy & Technology for IBM's Software Group
Towards a Software Science of Design

Reception starting at 3:00 p.m. in lobby.

Posted April 10, 2007

3:40 pm – 4:30 pm Lockett 285

Hongyu He, Mathematics Department, LSU
Introduction to Theta Correspondence II

In this talk, I will introduce Howe\'s dual reductive pair. I will then discuss the basic theory of theta correspondence and its application in representation theory. The talk will be accessible to graduate students.

Posted March 30, 2007

4:00 pm Lockett 240

Wojbor Woyczynski , Case Western Reserve University Center for Stochastic and Chaotic Processes in Sciences and Technology
Nonlinear evolution equations driven by Levy diffusions

Abstract: Nonlinear evolution equations, such as conservation laws, KPZ Hamilton Jacobi equations develop surprising critical behavior when driven by Levy diffusions with infinitesimal generators with different asymptotic behavior of their symbols. A study of this type of formalism is motivated by physical problems related to deposition of thin semiconductor films and flows in random media.

Posted April 9, 2007

Control and Optimization Seminar Questions or comments?

4:30 pm James E. Keisler Lounge (room 321 Lockett)

Material on Interest Theory Exam

Matthew Arnold will conduct the session.

Wednesday, April 18, 2007

Posted April 16, 2007

11:40 am – 12:30 pm Room 239 Lockett

Peter Wolenski, LSU Department of Mathematics Russell B. Long Professor
The role of convexity in optimization and control theory.

Abstract: This talk will broadly survey the role of convexity in optimization theory, and outline its special place in optimal control. Roughly speaking, convexity plays the role in optimization analogous to that enjoyed by linearity in dynamical system theory. We shall illustrate this by discussing the features of local vs. global statements, generalized differentiation, duality, and representation formulas.

Posted April 15, 2007

1:40 pm – 2:30 pm 276 Lockett Hall

Chris Rodger, Auburn University
Hamilton decompositions in complete multipartite graphs

Posted March 30, 2007

Calculus Textbook and Webwork Presentation

3:40 pm – 4:30 pm Lockett 285

Calculus, Early Transcendentals

A Hoffman-Mifflin representative will present their integration of Webworks with their book \'Calculus, Early Transcendentals\' by Larson, Hostedler, and Edwards.

Thursday, April 19, 2007

Posted April 15, 2007

A^1-homotopy theory seminar

1:00 pm – 3:00 pm Lockett 381

Seva Joukhovitski, Mathematics Department, LSU
The category of spectra

Posted April 11, 2007
Last modified January 27, 2022

3:40 pm – 4:30 pm Lockett 277

Kevin Knudson, Mississippi State University
Algorithms in discrete Morse theory

Discrete Morse theory was developed by Robin Forman to provide a combinatorial analogue, for simplicial complexes, of classical smooth Morse theory on manifolds. Constructing efficient discrete Morse functions is a nontrivial task. In this talk, I will present an algorithm that begins with a function h defined on the vertices of a complex K and extends it to a discrete Morse function on the entire complex so that the resulting discrete gradient field mirrors the large scale behavior of h. This has applications to the analysis of point cloud data sets and several examples will be given. No prior knowledge of Morse theory (discrete or smooth) will be assumed.

There will be coffee and cookies in the lounge at 3:00.

Posted March 30, 2007

Calculus Textbook and Webwork Presentation

3:40 pm – 4:30 pm Lockett 285

Calculus, Early Transcendentals

A W. H. Freeman representative will present their integration of Webworks with their book \'Calculus, Early Transcendentals\' by Rogowski.

Posted April 14, 2007
Last modified February 20, 2022

Special Math Club Lecture

5:00 pm 237 Lockett Hall

Paul Saylor, LSU Center for Computation and Technology
Numerical Analysis: Do Computers Really Compute? Who Knows? Google? YouTube? Math Knows.

Come one, come all. See the amazing powers and wondrous skills of numerical analysis. See before you (1) a math problem discover sensitivity on a railroad bayou; (2) proof that it’s smart to approximate; (3) a computer compute an uncommon conundrum; and (4) a mighty matrix meet its match when it fails to resist relentless recursion.

Paul Saylor was visiting Professor of Mathematics from 2004-2006 at LSU and also a member of the Center for Computation and Technology (CCT). Association with CCT is continuing in the areas of computational mathematics and the numerical analysis of merry math madness. Saylor is Professor Emeritus of Computer Science at the University of Illinois Urbana-Champaign which is somewhere north of Baton Rouge and south of a recently discovered, vast underground pool of floating point numbers.

Friday, April 20, 2007

Posted April 9, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm 338 Johnston Hall

Bruce N. Walker, Georgia Institute of Technology Sonification Lab
Anditory Displays, Anditory Graphs, and Sonifications: Research and Design

Monday, April 23, 2007

Posted March 8, 2007
Last modified March 13, 2007

Control and Optimization Seminar Questions or comments?

3:40 pm – 4:30 pm 284 Lockett Hall

Hong Zhang, Dept. of Computer Science, Illinois Institute of Technology and Mathematics and Computer Science Division, Argonne National Laboratory
Eigenvalue Problems in Nanoscale Material Modeling

Together with a group of material scientist, we intend to calculate the atomic and electronic structure of nanoparticles on a quantum-mechanical level. The mathematical core of this modeling is a sequence of large and sparse eigenvalue problems. In this talk, I will present the special requirements of the solutions, the challenges on the computational method, our algorithmic approach and software development. Numerical implementation on the advanced distributed computers will be demonstrated.

This work also demonstrates how to efficiently develop special-purpose application code on the top of available parallel software packages. By the end of the talk, as a PETSc developer, I will give a demo on using PETSc (Portable, Extensible Toolkit for Scientific Computation) as a tool for large scale numerical simulation.

Tuesday, April 24, 2007

Posted April 23, 2007

Junior Topology Seminar

3:10 pm – 4:00 pm Lockett 276

Seminar on knot homology theories and related topics

Cody Armond (LSU) : On Rasmussen\'s relation between Khovanov homology and sliceness

Wednesday, April 25, 2007

Posted April 23, 2007

11:40 am – 12:30 pm Room 239 Lockett

Peter Wolenski, LSU Department of Mathematics Russell B. Long Professor
The role of convexity in optimization and control theory (Part II)

Posted April 24, 2007
Last modified September 17, 2021

3:40 pm – 4:30 pm Lockett 381

Hongyu He, Department of Mathematics, LSU
Introduction to Theta Correspondence III

In this talk, I will introduce Howe's dual reductive pair. I will then discuss the basic theory of theta correspondence and its application in representation theory. The talk will be accessible to graduate students.

Thursday, April 26, 2007

Posted April 25, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

9:00 am 338 Johnston Hall

Larry Bergman, California Institute of Technology, Jet Propulsion Laboratory Manager of the Mission Computing and Autonomous Systems Research Program Office at the Jet Propulsion Laboratory (JPL)
The Role of Information Technology in Robotic Space Exploration

Posted April 19, 2007

4:00 pm Lockett 240

Walfredo Javier, Department of Mathematics, Southern University
Mutual information of certain multivariate distributions

Posted April 23, 2007
Last modified February 20, 2022

5:00 pm 237 Lockett Hall

Sharon Besson, Cain Center Geaux Teach Program Manager
Geaux Teach: LSU's Secondary Teacher Preparation Program

The Geaux Teach program was modeled after the UTeach program developed at the University of Texas at Austin. This new model is based on apprenticeship, much like that found in other professions such as the medical profession. Prospective teachers get their undergraduate degree in their content areas with a secondary education concentration. In the Geaux Teach program, the teaching of teacher candidates has become a collaborative effort between content area researchers, education professors, and practicing mentor teachers. The heart of the apprenticeship program is the step courses: three of the four education classes are paired with a 1 hour lab run by a content area research professor; the course + lab includes 40 hours in a high/middle school classroom observing, tutoring, teaching and being mentored by a high/middle school teacher. These classes are taken in the three semesters leading up to student teaching, and step up the level of teaching each semester. In their education class students learn theory and pedagogy, including how to appropriately use technology and how to teach in culturally diverse settings. Further information will be available at Besson’s lecture.

Friday, April 27, 2007

Posted April 25, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm 338 Johnston Hall

H. J. Siegel, Colorado State Univ., Dept. of Electrical and Comp. Engr. and Dept. of Comp. Sci.
An Intro to Research Issues in Heterogeneous Parallel & Distributed Computing

Posted April 25, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

4:10 pm 338 Johnston Hall

H. J. Siegel, Colorado State Univ., Dept. of Electrical and Comp. Engr. and Dept. of Comp. Sci.
Colorado State's Information Science & Technology Center (ISTeC)

Monday, April 30, 2007

Posted April 7, 2007

3:30 pm The James Kiesler Lounge 319 Lockett Hall

Spring Math Awards Ceremony

The Porcelli Award for Academic Excellence, the Porcelli Scholarships, the Betti and Robert Giles Senior Mathematics Award, the David Oxley Memorial Graduate Student Teaching Award, and Certificates of Teaching Excellence (for graduate assistants) will be awarded. Refreshments will be provided.

Posted February 12, 2007
Last modified April 23, 2007

3:40 pm – 4:30 pm 284 Lockett Hall

Lia Bronsard, McMaster University
Ginzburg-Landau vortices concentrating on curves.

We study the two-dimensional Ginzburg-Landau functional for superconductivity and the related Gross-Pitaevskii functional for Bose-Einstein Condensate. In a convex simply-connected domain, Serfaty has shown that the vortices accumulate around a single point in the domain as the Ginzburg--Landau parameter $\kappa\to\infty$. Our previous papers (with Aftalion and Alama) on multiply connected domains show that vortices may instead accumulate on an appropriate curve as $\kappa\to\infty$. In our recent result with S. Alama and V. Millot, we study the number and distribution of these vortices along the curve of concentration. Their distribution is determined by a classical problem from potential theory.

Tuesday, May 1, 2007

Posted April 25, 2007
Last modified September 17, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

1:30 pm 338 Johnston Hall

Mary Fanett Wheller, University of Texas at Austin Center for Subsurface Modeling, Institute for Computational Engineering and Sciences
Multiscale Discretizations for Flow, Transport and Mechanics in Porous Media.

There will be a reception at 1:00.

Posted April 17, 2007

Algebra and Number Theory Seminar Questions or comments?

2:30 pm Lockett 16

Meeting with the Dean

The Dean's annual meeting with the mathematics faculty.

Posted April 24, 2007
Last modified April 27, 2007

3:40 pm Lockett 136

Jens Hornbostel, University of Regensburg, Germany
Rigidity theorems for A^1-representable theories

We prove that for a large class of A^1-representable theories including
all orientable theories it is possible to construct transfer maps and to
prove rigidity theorems similar to those of Gabber for algebraic
K-theory. This extends rigidity results
of Panin and Yagunov from algebraically closed fields to arbitrary
infinite ones.

Wednesday, May 2, 2007

Posted May 1, 2007

Control and Optimization Seminar Questions or comments?

11:40 am – 12:30 pm Room 239 Lockett

Peter Wolenski, LSU Department of Mathematics Russell B. Long Professor
The role of convexity in optimization and control theory (Part III)

Posted March 30, 2007
Last modified January 27, 2022

3:40 pm – 4:30 pm Lockett 285

William Velez, The University of Arizona
Increasing the number of mathematics majors

In the late 1980's I began my efforts to increase the success rate of minorities in first semester calculus. The interventions that I devised were very time consuming and as the number of minority students increased, I could not manage that kind of effort. I developed my Calculus Minority Advising Program in an effort to meet with scores of minority students each semester. This program consists of a twenty-minute meeting with each student at the beginning of each semester. These meetings with students eventually transformed my own attitude about the importance of mathematics in their undergraduate curriculum.

I took over the position of Associate Head for Undergraduate Affairs in the department four years ago. I set a very modest goal for myself: to double the number of mathematics majors. With almost 500 mathematics majors I have reached that goal. I think the next doubling is going to be much harder to achieve. My work with minority students provided me with the tools to accept this new challenge of working with all students.

This talk will describe my own efforts to encourage ALL of our students that a mathematics major, or adding mathematics as a second major, is a great career choice.

Thursday, May 3, 2007

Posted April 26, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

12:00 pm 338 Johnston Hall

Luisa T. Buchman, Univeristy of Texas at Austin Research Fellow
Improved outer boundary conditions for Einstein's field equations

Posted April 24, 2007

A^1-homotopy theory seminar

1:00 pm – 3:00 pm Lockett 381

Jens Hornbostel, University of Regensburg, Germany
Homotopy coniveau and slice filtration in stable A^1 homotopy theory (after Levine and Voevodsky)

Posted April 26, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm A101 Life Sciences Building Annex

Enterprise Transformation and the Future of Higher Education

During the 130 years between 1860 and 1990 higher education was transformed, evolving from a limited province fo the cultural elite to a great instrument of state material and martial strength.

Posted April 23, 2007
Last modified October 4, 2021

3:40 pm Lockett 285

Raul Quiroga, Centro de Investigacion en Matematicas (CIMAT)
Actions of Noncompact Simple Lie Groups on Pseudo Riemannian Manifolds

Let $G$ be a noncompact simple Lie group acting on a compact manifold $M$, and suppose that the $G$-action has a dense orbit and preserves a pseudo-Riemannian metric. A general conjecture of R. Zimmer states that, for this geometric/dynamical setup, $M$ is essentially a coset space of a semisimple Lie group $H$ containing $G$. In this talk we will discuss some geometric conditions on the $G$-action on $M$ that ensure the conclusion of Zimmer's conjecture.

Friday, May 4, 2007

Posted April 26, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm 338 Johnston Hall

Q. Jim Chen, Louisiana State University Associate Professor of Civil and Environmental Engineering
Multi-scale modeling of storm surges and water waves

More than 50% of the U.S. population lives within 50 miles of the shoreline and the coastal population continues to grow.

Tuesday, May 8, 2007

Posted May 4, 2007
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 381

Raul Quiroga, Centro de Investigacion en Matematicas (CIMAT)
Rigidity results for pseudo-Riemannian manifolds

We will continue our discussion of compact pseudo-Riemannian manifolds with a noncompact simple Lie group of isometries. It will be seen that such pseudo-Riemannian manifolds have two very remarkable properties: 1) they carry large local isotropy groups, 2) they are locally homogeneous on an open dense subset. These will allow us to describe some structure results for the pseudo-Riemannian manifolds considered. As a consequence, we will prove that if $M$ is an irreducible pseudo-Riemannian manifold with an isometric action of $SO(p,q)$ and $dim(M) \leq dim(SO(p,q)) + p + q$, then the universal covering space of $M$ is a noncompact simple Lie group.

Wednesday, May 9, 2007

Posted May 3, 2007

3:40 pm – 4:30 pm Lockett 381

Hongyu He, Department of Mathematics, LSU
Introduction to Theta Correspondence IV

In this talk, I will introduce Howe\'s dual reductive pair. I will then discuss the basic theory of theta correspondence and its application in representation theory. The talk will be accessible to graduate students.

Friday, May 11, 2007

Posted May 3, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

11:00 am 218 Johnston Hall

Joel de Guzman, Boost Consulting
A cookbook approach to parsing and output generation with Spirit2

Spirit2 will debut at the Boost conference. It will be a complete parsing and output generation system that attempts to cover the whole spectrum from lexing to output generation.

Posted May 3, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

2:00 pm Design Building Room Auditorium

Turner Whitted, Microsoft Research Pioneer in three-dimensional computer graphics
Procedural Graphics

The re-introduction of programmability into graphics hardware has produced a tremendously flexible imaging platform.

Tuesday, May 15, 2007

Posted May 9, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm 338 Johnston Hall

Robert Moorhead, Mississippi State University Director of Visualizarion Analysis and Imaging Lab Professor of Electrical and Computer Engineering Associate Director of GeoResources Institute
The High Performance Computing Collaboratory at MSU

The High Performance Computing Collaboratory (HPC2) at Mississippi State University is a federation of 5 entities, all focused on HPC applications.

Posted May 9, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:30 pm 338 Johnston Hall

Song Zhang, Mississippi State University Assistant Professor in the Department of Computer Science and Engineering
Tensor Visualization For Finding Structures in Brain and Nematic Liquid Crystal

Matrix-valued datasets (so-called tensor field) have become more common in various disciplines of science. Compared to scalar dataset or vector field, tensor field incorporates more information at any one data point.

Tuesday, May 22, 2007

Posted May 21, 2007
Last modified March 2, 2021

8:30 am – 6:00 pm Thursday, May 31, 2007 237 Lockett Hall

Louisiana Workshop on Mathematical Control Theory (MCT'07)

See this link.

Wednesday, May 30, 2007

Posted May 9, 2007
Last modified February 11, 2022

until Sunday, June 3, 2007 tba

A second time around the Volume conjecture

Friday, June 1, 2007

Posted May 22, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

1:30 pm 152 Coates Hall

James Demmel, University of California - Berkeley Richard Carl Dehmel Distinguished Professor of Computer Science and Mathematics
The Future of High Performance Linear Algebra

Linear algebra is at the core of much scientific and engineering computing problem, so faster and more accurate algorithms and software are always welcome. We survey three areas of recent progress.

Tuesday, June 5, 2007

Posted May 25, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm 145 Coates Hall

Michael Lesk, Rutgers University Professor of Library and Information Science
Scientific Data Libraries: Changing Research

Reception at 2:30 p.m. in 145 Coates Hall. Abstract: The traditional paradigm of scientific research is being changed by our ability to gather enormous quantities of data with sensors and store them online.

Thursday, July 26, 2007

Posted July 19, 2007
Last modified February 11, 2022

8:30 am Location TBA

Workshop on Control Theory and Mathematical Biology (Day 1 of 2)

Note: This is a TWO-DAY WORKSHOP, starting on Thursday July 26th at 8:30AM, and ending on Friday July 27th at 4:30PM. See https://www.math.lsu.edu/~malisoff/MCTMB.html for updated information.

Friday, July 27, 2007

Posted July 20, 2007
Last modified February 11, 2022

8:30 am Location TBA

Workshop on Control Theory and Mathematical Biology (Day 2 of 2)

Note: This is a TWO-DAY WORKSHOP, starting on Thursday July 26th at 8:30AM, and ending on Friday July 27th at 4:30PM. See https://www.math.lsu.edu/~malisoff/MCTMB.html for updated information.

Monday, August 13, 2007

Posted August 7, 2007
Last modified July 25, 2021

until Saturday, August 25, 2007 Room 244 Lockett: other locations for special activities

GEAUX

This is the Graduate Education and Acclimation to the University eXperience. Current graduate students conduct orientation activities for all the new Mathematics graduate students.

Thursday, August 16, 2007

Posted August 7, 2007

7:45 am – 12:00 pm Friday, August 17, 2007 Campbell Auditorium, Cox Communication Building

Required Orientation for All New International Graduate Students at LSU

Bring ID such as passport. This is where an international student receives an appointment for the required written English test and the required spoken English interview.

Monday, August 20, 2007

Posted August 7, 2007
Last modified July 25, 2021

1:30 pm – 4:00 pm Room 285 Lockett

Comprehensive / PhD Qualifying Exam in Core-1 Topology

Tuesday, August 21, 2007

Posted August 7, 2007
Last modified July 25, 2021

1:30 pm – 4:00 pm Room 285 Lockett
(Originally scheduled for 1:00 pm)

Comprehensive / PhD Qualifying Exam in Core-1 Analysis

Thursday, August 23, 2007

Posted August 7, 2007
Last modified July 25, 2021

1:30 pm – 4:00 pm Room 285 Lockett Hall

Comprehensive / PhD Qualifying Exam in Core-1 Algebra

Friday, August 24, 2007

Posted August 7, 2007
Last modified July 25, 2021

12:30 pm – 4:00 pm 285 Lockett

Comprehensive / PhD Qualifying Exams: All Core-2 Tests

Posted August 16, 2007
Last modified March 2, 2022

3:40 pm – 4:40 pm 285 Lockett Hall

Shinnosuke Oharu, Chuo University, Japan
Ecological models of red tide plankton in the coastal ocean.

This talk will be concerned with a mathematical model consisting of an ecological model for a specific species of plankton and an ocean model, numerical models consistent with the PDE models, and computer simulations by means of new CFD methods.

Thursday, August 30, 2007

Posted August 20, 2007
Last modified August 22, 2007

3:10 pm Lockett 6

Meeting of Research Faculty

Visitors for the academic year and other miscellaneous topics.

Tuesday, September 4, 2007

Posted August 27, 2007
Last modified August 31, 2007

5:10 pm – 6:00 pm Lockett 276

Adam Lowrance, Department of Mathematics, Vassar College
On Knot Floer Width and Turaev Genus

Monday, September 10, 2007

Posted September 5, 2007

Control and Optimization Seminar Questions or comments?

4:30 pm – 5:30 pm Lockett 276

Steve Wallace, LSU
Surgery untying of knots

Tuesday, September 11, 2007

Posted September 5, 2007

Seminar on Algebraic K-theory and Grothendieck-Witt groups

1:40 pm – 3:30 pm Lockett 381

Marco Schlichting, Louisiana State University
Overview and Motivation

Wednesday, September 12, 2007

Posted September 9, 2007

2:30 pm – 3:30 pm Prescott 205

Alvaro Guevara, Dept of Mathematics, LSU
Student Seminar on Control Theory and Optimization

Introduction to Convex Analysis II

Posted August 17, 2007

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm A101 Auditorium Life Sciences Building Annex

Tinsley Oden, University of Texas at Austin Director, Institute for Computational Engineering and Sciences
Adaptive Multiscale Modeling of Large-Scale Molecular Systems

Frontiers of Scientific Computing Lecture Series There will be a reception at 4:00 pm. More info

Posted September 7, 2007

3:40 pm – 4:30 pm Biological Sciences Annex Building - A663

Moshe Cohen, Department of Mathematics, Bar-Ilan University, Israel
Introductory remarks on Khovanov homology

This is a virtual topology seminar together with U Iowa

Friday, September 14, 2007

Posted September 11, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

2:00 pm 338 Johnston Hall

Philip Maechling, University of Southern California Information Technology Architect, Southern California Earthquake Center
Seismic Hazard Modeling using Heterogeneous Scientific Workflows

As a part of the Southern California Earthquake Center (SCEC) program of seismic hazard research, we are using scientific workflow technologies to run large-scale high performance and high throughput scientific applications.

Monday, September 17, 2007

Posted September 13, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm 338 Johnston Hall

Poojitha Yapa, Clarkson University Porfessor, Department of Civil and Environmental Engineering
Modeling Oil and Gas Discharges from Deepwater Blowouts

A computer model (CDOG) developed to simulate the behavior of oil and gas accidentally released from deepwater is presented. Deepwater is considered to be water depths in excess of 800 m.

Posted September 7, 2007

4:40 pm – 5:30 pm Lockett 276

Hee Jung Kim, Department of Mathematics, LSU
Topological triviality of smoothly knotted surfaces in 4-manifolds

Tuesday, September 18, 2007

Posted September 18, 2007
Last modified March 2, 2021

Seminar on Algebraic K-theory and Grothendieck-Witt groups

1:40 pm – 3:00 pm

Marco Schlichting, Louisiana State University
Exact categories and Quillen's Q-construction

Posted August 20, 2007

3:10 pm Lockett 6

Meeting of the tenured faculty

Promotion and tenure cases will be reviewed.

Wednesday, September 19, 2007

Posted September 16, 2007

Student Seminar

2:40 pm – 3:30 pm 203 Prescott

Silvia Jimenez, Dept of Mathematics, LSU
Student Seminar on Control Theory and Optimization

Lower Bounds on Field Concentrations

Posted September 13, 2007
Last modified September 18, 2007

3:40 pm – 4:30 pm Biological Sciences Annex Building - A663

Neal Stoltzfus, Mathematics Department, LSU
Quasi-Trees and Khovanov homology

Virtual Seminar together with U Iowa

Friday, September 21, 2007

Posted September 13, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

2:00 pm 338 Johnston Hall

Brygg Ullmer, Louisiana State University Assistant Professor Department of Computer Science Center for Computation and Technology
Tangible Interfaces for Visualization, Collaboration, and Education

Over the last decade, there has been rapidly growing interest in bridging human interaction between the physical and digital worlds.

Monday, September 24, 2007

Posted September 13, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

1:00 pm 338 Johnston Hall

Thomas Fahringer, University of Innsbruck-Austria Institute of Computer Science
Radu Prodan, University of Innsbruck, Austria Institute of Computer Science
ASKALON: An Application Development and Runtime Environment for the Grid

In this presentation we describe the ASKALON Grid application development and computing environment whose ultimate goal is to provide an invisible Grid to the application developer.

Posted September 14, 2007
Last modified March 2, 2022

3:40 pm – 4:30 pm Lockett 233

Édouard Oudet, Laboratoire de Mathématiques, Université de Savoie, France
Constant width bodies in dimension 3

A body (that is, a compact connected subset $K$ of $\mathbf{R}^n$) is said to be of constant width $\alpha$ if its projection on any straight line is a segment of length $\alpha>0$, the same value for all lines.

We present in this talk a complete analytic parametrization of constant width bodies in dimension 3 based on the median surface: more precisely, we define a bijection between some space of functions and constant width bodies. We compute simple geometrical quantities like the volume and the surface area in terms of those functions. As a corollary we give a new algebraic proof of Blaschke's formula. Finally, we present some numerical computations based on the preceding parametrization.

É. Oudet will be visiting the department this week (9/24 – 9/28). If you want to schedule a meeting with him, contact B. Bourdin.

Posted September 19, 2007

4:40 pm – 5:30 pm Lockett 276

Scott Baldridge, Louisiana State University
A symplectically aspherical manifold with b_1=1

Tuesday, September 25, 2007

Posted September 21, 2007
Last modified March 2, 2021

K-theory and Grothendieck-Witt groups

1:40 pm – 3:00 pm Lockett 381

Marco Schlichting, Louisiana State University
The fundamental group of Quillen's Q-construction

Wednesday, September 26, 2007

Posted September 26, 2007

2:40 pm – 3:30 pm Prescott 203

Rick Barnard, LSU Department of Mathematics Graduate Student
Student Seminar on Control and Optimization

Introduction to Differential Inclusions math.lsu.edu/dept/student_control_opt

Posted September 24, 2007
Last modified October 1, 2021

On knot Floer width and Turaev genus

3:40 pm – 4:30 pm Biological Sciences Annex Building - A663

Adam Lowrance, Department of Mathematics, Vassar College
On knot Floer width and Turaev genus, Part I

Monday, October 1, 2007

Posted September 24, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

11:00 am 338 Johnston Hall

Ravi Vadapalli, Texas Tech University Research Scientist, High Performance Computing Center, Applicant for CCT's CyD IT Analyst Position
Deploying Regional Cyberinfrastructure for Strategic Appl. Development & Support

Grid Computing is an emerging collaborative computing paradigm to extend institutional/organization specific high performance computing capabilities greatly beyond local resources.

Posted September 28, 2007
Last modified March 2, 2022

3:40 pm – 4:30 pm Lockett Hall 233

Burak Aksoylu, Department of Mathematics and CCT
Physics-based preconditioners for solving PDEs on highly heterogeneous media

Eigenvalues of smallest magnitude become a major bottleneck for iterative solvers especially when the underlying physical properties have severe contrasts. These contrasts are commonly found in many applications such as composite materials, geological rock properties and thermal and electrical conductivity.

The main objective of this work is to construct a method as algebraic as possible that could efficiently exploit the connectivity of highly heterogeneous media in the solution of diffusion operators. We propose an algebraic way of separating binary-like systems according to a given threshold into high- and low-conductivity regimes of coefficient size $O(m)$ and $O(1)$, respectively where $m >> 1$. The condition number of the linear system depends both on the mesh size $\Delta x$ and the coefficient size $m$. For our purposes, we address only the $m$ dependence since the condition number of the linear system is mainly governed by the high-conductivity subblock. Thus, the proposed strategy is inspired by capturing the relevant physics governing the problem. Based on the algebraic construction, a two-stage preconditioning strategy is developed as follows: (1) a first stage that comprises approximation to the components of the solution associated to small eigenvalues and, (2) a second stage that deals with the remaining solution components with a deflation strategy (if ever needed). The deflation strategies are based on computing near invariant subspaces corresponding to smallest and deflating them by the use of recycled the Krylov subspaces.

Due to its algebraic nature, the proposed approach can support a wide range of realistic geometries (e.g., layered and channelized media). Numerical examples show that the proposed class of physics-based preconditioners are more effective and robust compared to a class of Krylov-based deflation methods on highly heterogeneous media. We also report on singular perturbation analysis of the stiffness matrix and the impact of the number of high-conductive regions on various matrices.

Posted September 24, 2007

4:40 pm – 5:30 pm Lockett 276

Scott Baldridge, Louisiana State University
A symplectically aspherical manifold with b_1=1, Part II

Tuesday, October 2, 2007

Posted October 2, 2007
Last modified March 2, 2021

Seminar on algebraic K-theory and Grothendieck-Witt groups

1:40 pm – 3:00 pm Lockett 381

Marco Schlichting, Louisiana State University
Quillen's theorems A and B

Wednesday, October 3, 2007

Posted September 24, 2007
Last modified October 1, 2021

On knot Floer width and Turaev genus

3:40 pm – 4:30 pm Biological Sciences Annex Building - A663

Adam Lowrance, Department of Mathematics, Vassar College
On knot Floer width and Turaev genus, Part II

Posted September 28, 2007

3:40 pm – 4:30 pm Lockett 381

Jens Christensen, Mathematics Department, LSU
Bergman spaces and representations of SL_2

Graduate Students are encouraged to attend. Abstract: I will start by presenting a general framework for describing Banach spaces by use of representations. Next I will take a closer look at a specific representation leading to a characterization of Bergman spaces on the unit disc. The talk will most likely be split on two days.

Thursday, October 4, 2007

Posted October 1, 2007

3:40 pm Lockett 381

Ambar Sengupta, Mathematics Department, LSU
Gaussian Matrix Integrals

Posted October 1, 2007
Last modified February 20, 2022

4:30 pm Keisler Lounge, Lockett

Leonard F. Richardson, Mathematics Department, LSU
An Informal Presentation about Graduate Study in Mathematics

Friday, October 5, 2007

Posted September 24, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

2:00 pm 338 Johnston Hall

Barbara Chapman, University of Houston Department of Computer Science
OpenMP In The Multicore Era

Dual-core machines are actively marketed for destop and home computing. Sysems with a larger number of cores are deployed in the server market. Some cores are capable of executing multiple threads.

Tuesday, October 9, 2007

Posted October 9, 2007
Last modified March 2, 2021

K-theory and Grothendieck-Witt groups

1:40 pm – 3:00 pm Lockett 381

Marco Schlichting, Louisiana State University
Quillen's fundamental theorems

Wednesday, October 10, 2007

Posted October 1, 2007
Last modified October 1, 2021

3:40 pm – 4:30 pm Biological Sciences Annex Building - A663

Moshe Cohen, Department of Mathematics, Bar-Ilan University, Israel
On a result of Ozsvath and Manolescu

Virtual Seminar together with U Iowa

Monday, October 15, 2007

Posted September 19, 2007

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm Johnston Hall 338

Doug Arnold, Institute for Mathematics and its Applications, Minneapolis Director
Finite Element Exterior Calculus: A New Approach To The Stability Of Finite Elements

More information...

Posted October 2, 2007
Last modified January 10, 2022

4:40 pm – 5:30 pm Lockett 276

Neal Stoltzfus, Mathematics Department, LSU
The Bollobás-Riordan-Tutte polynomial as a tri-graded Poincaré-polynomial (due to N. Forman)

Tuesday, October 16, 2007

Posted September 19, 2007
Last modified October 1, 2007

10:00 am Johnston Hall 338

Doug Arnold, Institute for Mathematics and its Applications, Minneapolis Director
The Institute for Mathematics and its Applications

Abstract: The Institute for Mathematics and its Applications (IMA) in Minneapolis is a leading research center, founded by the National Science Foundation in 1982. The primary mission of the IMA is to increase the impact of mathematics by fostering interdisciplinary research linking mathematics with important scientific and technological problems from other disciplines, industry, and society. Through a variety of programs, it provides opportunities for scientists, mathematicians, and engineers from academia and government labs and industry to make contact and interact with each other, to learn about new developments, and to stimulate the study of interesting and relevant problems and their solution. In this informal presentation the director of the IMA will discuss IMA operations, upcoming programs, and outcomes, in order to promote participation and gather input from LSU researchers.

Posted October 14, 2007
Last modified October 16, 2007

Seminar on K-theory and Grothendieck-Witt groups

1:40 pm Lockett 381

Marco Schlichting, Louisiana State University
K(Z) and the Vandiver conjecture

Wednesday, October 17, 2007

Posted October 16, 2007

Student Semina

2:40 pm – 3:30 pm Prescott 203

Qinqxia Li, LSU Math Dept.
An Introduction to Multi-objective optimal control problem

Posted October 3, 2007
Last modified October 11, 2007

3:40 pm – 4:30 pm Biological Sciences Annex Building - A663

John Etnyre, Georgia Institute of Technology
A geometric reason for the non-sharpness of Bennequin's inequality for some fibered knots

Virtual Seminar together with U Iowa

Posted September 28, 2007

3:40 pm – 3:30 pm Lockett 381

Jens Christensen, Mathematics Department, LSU
Bergman spaces and representations of SL_2 II

Thursday, October 18, 2007

Posted October 15, 2007
Last modified February 20, 2022

1:40 pm 232 Lockett

John Etnyre, Georgia Institute of Technology
Knot Colorings—From Grade School to Grad School (and Back?) in One Hour

Knots in strings and ropes have fascinated people for millennia but have only been a subject of serious mathematical inquiry for the last century or so. Their study is now a fundamental and central part of low-dimensional topology and string theory indicates they might, in some subtle and deep way, be related to how the universe works! After a brief introduction to knots as mathematical objects, I will discuss one of the simplest ways to study them, that is by coloring them. Yes, that’s right, by pulling out your good old crayons and coloring (but of course we will need a few rules about how to color to make this useful). Once we see that this simple idea can be surprisingly powerful, I will discuss how it is in fact related to the fairly sophisticated notion of representations of the fundamental group of the knot complement. (I will define and discuss all these notions.) This is a great example of the common theme in low dimensional topology that one can frequently take fairly sophisticated things (like representations, group actions, holomorphic curves…) and turn them into a fairly simple (combinatorial) thing (like colorings, polynomials, convex polygons…). This interaction between the sophisticated and the simple is one of the beautiful and appealing things about low dimensional topology.

Posted September 28, 2007
Last modified October 8, 2007

3:40 pm – 4:30 pm Lockett 285

John Etnyre, Georgia Institute of Technology
Invariants of embeddings via contact geometry

Abstract: I will describe a method to define, hopefully new, invariants of any embedded submanifold of Euclidean space. To define this invariant we will need to take an excursion into the realm of contact geometry and a recent generalization of Floer homology called contact homology. More specifically, after recalling various notions from contact geometry, I will show how to associate a Lagrangian submanifold to any embedded submanifold of Euclidean space. The invariant of the embedding will be the contact homology of this Lagrangian. Though the definition of this invariant is somewhat complicated it is possible to compute it for knots in Euclidean 3-space. Lenny Ng has combinatorially studied this invariant for such knots and has shown that it does not seem to be determined by previously known invariants but non the less has some connections with the classical Alexander polynomial of a knot. I will concentrate on the more geometric aspects of the invariant and ongoing work of Tobias Ekholm, Lenny Ng, Michael Sullivan and myself aimed at a better understanding of the invariant (in particular, showing that it is well defined in some generality).
There will be coffee and cookies in the lounge at 3:00.

Monday, October 22, 2007

Posted October 9, 2007
Last modified March 2, 2022

3:30 pm – 4:30 pm Lockett 233

Michael Zabarankin, Stevens Institute of Technology
Generalized Analytic Functions in 3D Axially Symmetric Stokes Flows

A class of generalized analytic functions, defined by a special case of the Carleman system that arises from related potentials encountered in various areas of applied mathematics has been considered. Hilbert formulas, establishing relationships between the real and imaginary parts of a generalized analytic function from this class, have been derived for the domains exterior to the contour of spindle, lens, bi-spheres and torus in the meridional cross-section plane. In bi-spherical and toroidal coordinates, this special case of the Carleman system has been reduced to a second-order difference equation with respect to either the coefficients in series or densities in integral representations of the real and imaginary parts. For spindle and lens, the equation has been solved in the framework of Riemann boundary-value problems in the class of meromorphic functions. For torus, the equation has been solved by means of the Fourier transform, while for bi-spheres, it has been solved by an algebraic method. As examples, analytical expressions for the pressure in the problems of the 3D axially symmetric Stokes flows about rigid spindle, biconvex lens, bi-spheres and torus have been derived based on the corresponding Hilbert formulas.

Posted October 22, 2007
Last modified January 10, 2022

4:40 pm – 5:30 pm Lockett 276

Neal Stoltzfus, Mathematics Department, LSU
The Bollobás-Riordan-Tutte polynomial as a tri-graded Poincaré-polynomial (due to N. Forman), Part II

Tuesday, October 23, 2007

Posted October 18, 2007

Seminar on K-theory and Grothendieck-Witt groups

1:40 pm Lockett 381

Jerome W. Hoffman, Mathematics Department, LSU
Algebraic cycles

Posted October 8, 2007

4:00 pm – 5:30 pm Room 9, Lockett Hall

Career Guidance for Graduate Students - a Faculty Panel Discussion with Questions

A faculty panel--Drs. Cohen, Dasbach, Sengupta and Shipman will join the Chair and the Graduate Director in providing career guidance for students. This meeting is required of all graduate students who have passed the General Exam. Others are very warmly encouraged to attend as well--it being never too early to plan ones career. Refreshments will be served first at 3:30 in the Lounge.

Wednesday, October 24, 2007

Posted October 17, 2007

3:40 pm – 4:30 pm Lockett 381

Jens Christensen, Mathematics Department, LSU
Bergman spaces and representations of SL_2 III

Posted October 22, 2007
Last modified March 2, 2021

3:40 pm – 4:30 pm Biological Sciences Annex Building - A663

Charles Frohman, University of Iowa
On Bar-Natan's skein module

Virtual Seminar together with U Iowa (talk this week is from Iowa)

Thursday, October 25, 2007

Posted September 14, 2007
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 285
(Originally scheduled for Thursday, September 20, 2007)

Alex Iosevich , University of Missouri–Columbia
Some examples of interaction between harmonic analysis, geometric measure theory, combinatorics and number theory

Many problems stated in analytic terms often turn out to be, in essence, problem in combinatorics or number theory. The opposite phenomenon, where number theoretic or combinatorial problems are fundamentally analytic in nature is equally ubiquitous. We shall discuss this phenomenon from a systematic point of view and will outline mechanisms that allow one to transfer techniques and ideas from area to another.

There will be coffee and cookies in the lounge at 3:00.

Posted October 22, 2007
Last modified February 20, 2022

5:00 pm 232 Lockett

Alex Iosevich , University of Missouri–Columbia
The Cauchy–Schwarz inequality or… if the Elephant is fat, then there must be a way to place a mirror to make this obvious…

We use the Cauchy–Schwarz inequality to see that if the set occupied by the elephant in three dimensions has large volume, then at least one of its projections onto the coordinate planes has a large area. We then explore a similar question in higher dimensions, encountering fascinating analytic and combinatorial objects along the way.

The speaker got his B.S. in mathematics at the University of Chicago in 1989 and a Ph.D. from UCLA in 1993 under the direction of Chris Sogge. He held a postdoctoral position at McMaster from 1993–95, a tenure track position at Wright State University from 1995–1998, and a tenure track and then a tenured position at Georgetown from 1998–2000. He then moved to the University of Missouri where he is now a Professor of Mathematics. In addition to math, the speaker spends way too much of his time reading about the history of medieval Europe.

Friday, October 26, 2007

Posted September 19, 2007
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 381
(Originally scheduled for Monday, September 24, 2007)

Alex Iosevich , University of Missouri–Columbia
Bounds for discrete Radon transforms and application to problems in geometric combinatorics and additive number theory

Monday, October 29, 2007

Posted September 5, 2007
Last modified September 7, 2007

3:30 pm – 4:30 pm 301D Lockett

Non-Thesis MS Final Exam, concluding event.

The Committee will be Profs. Richardson (chair), Adkins, and Dasbach. This is the concluding event of the Comprehensive Final Exam for the non-thesis MS.

Posted October 4, 2007

3:40 pm – 4:30 pm Lockett 233

Thirupathi Gudi, CCT, LSU
Local Discontinuous Galerkin Methods for Elliptic Problems

Posted October 24, 2007

4:40 pm – 5:30 pm Lockett 276

Ambar Sengupta, Mathematics Department, LSU
Gaussian Matrix Integrals

Abstract: The talk of the same title given in the probability seminar concluded with a definition of a who a topologist is. In this talk we will strive to define a probabilist. Along the way we shall examine the representation of Gaussian integrals of matrix-trace functions in terms of sums over surfaces of varying genus. This is an illustration of a broader phenomenon of integrals arising from physical theories having topological interpretations.

Tuesday, October 30, 2007

Posted October 29, 2007

Seminar on K-theory and Grothendieck-Witt groups

1:40 pm Lockett 381

Jerome W. Hoffman, Mathematics Department, LSU
Algebraic cycles II

Wednesday, October 31, 2007

Posted October 25, 2007

3:40 pm – 4:30 pm Biological Sciences Annex Building - A663

Jeff Boerner (U Iowa): On the Asaeda-Przytycki-Sikora homology

Virtual Seminar together with U Iowa (talk this week is from Iowa)

Posted October 5, 2007
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 381

Martin Laubinger, LSU Graduate Student
Complex Structures on Principal Bundles

Holomorphic principal G-bundles over a complex manifold M can be studied using non-abelian cohomology groups $H1(M,G)$. On the other hand, if $M=\Sigma$ is a closed Riemann surface, there is a correspondence between holomorphic principal $G$-bundles over $\Sigma$ and coadjoint orbits in the dual of a central extension of the Lie algebra $C^\infty(\Sigma, \g)$. We review some of these results and use a Theorem of A. Borel to give more detail in the case of $\Sigma$ having genus one.

The talk is based on my diplom thesis, a short version of which is available on the ArXiv: arXiv:0708.3261v1

Thursday, November 1, 2007

Posted October 25, 2007
Last modified October 1, 2021

12:40 pm – 1:30 pm tba

Junior Topology Seminar

This is a reading seminar.

Posted November 1, 2007
Last modified February 20, 2022

4:30 pm 232 Lockett

An Overview of Spring 2008 Math Course Offerings Followed by Elections

Friday, November 2, 2007

Posted October 26, 2007

11:40 am – 12:30 pm 113 Lockett Hall

Deborah Chun, LSU Graduate student
Deletion-contraction to form a polymatroid

All welcome

Posted October 30, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

2:00 pm 338 Johnston Hall

Valerie Taylor, Department of Computer Science, Texas A&M University Department Head and Royce E. Weisenbaker Professorship II
Performance Analysis and Optimization of Large-scale Scientific Applications

The current trend in high performance computing systems is shifting towards cluster systems with CMPs (chip multiprocessors).

Saturday, November 3, 2007

Posted September 19, 2007
Last modified July 25, 2021

Algebra and Number Theory Seminar Questions or comments?

9:00 am – 2:00 pm Burden Conference Center

Burak Aksoylu, Department of Mathematics and CCT
Jimmie Lawson, Mathematics Department, LSU
Richard A. Litherland, Mathematics Department, LSU
Marco Schlichting, Louisiana State University
Graduate Student Picnic/Orientation Conference

Monday, November 5, 2007

Posted October 10, 2007
Last modified November 4, 2007

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm – 4:00 pm 338, Johnston Hall

Qiang Du, Department of Mathematics, Pennsylvania State University
Phase Field Models and Simulations of Some Interface Problems

Part of the Frontiers of Scientific Computing Lecture Series

Abstract: In this talk, Dr. Du will report some recent works on the phase field modeling and simulation of interface problems in materials science and biology.

Tuesday, November 6, 2007

Posted November 4, 2007
Last modified November 5, 2007

Seminar on K-theory and Grothendieck-Witt groups

1:30 pm – 3:00 pm Lockett 381

Jerome W. Hoffman, Mathematics Department, LSU
Mumford's counter-example

for more information, see the seminar webpage

Posted November 2, 2007
Last modified November 4, 2007

3:40 pm – 4:30 pm Lockett 277

Daniel Sage, Mathematics Department, LSU
Perverse coherent sheaves and special pieces in the unipotent variety

Wednesday, November 7, 2007

Posted November 4, 2007
Last modified March 2, 2021

3:40 pm – 4:30 pm Biological Sciences Annex Building - A663

Heather Russell, University of Iowa
Embedded Khovanov homology of $S^1\times D^2$ and the homology of the $(n,n)$-Springer Fiber

Virtual Seminar together with U Iowa (talk this week is from Iowa)

Posted November 5, 2007

3:40 pm Lockett 9

Faculty Meeting about VIGRE

The meeting to discuss the VIGRE grant proposal and the upcoming site visit, which is scheduled for December 6th.

Thursday, November 8, 2007

Posted November 6, 2007
Last modified September 17, 2021

12:40 pm – 1:30 pm Lockett 119

Junior Topology Seminar

Reading seminar.

Posted September 14, 2007
Last modified November 5, 2007

3:40 pm – 4:30 pm Lockett 285

Clint Dawson, University of Texas at Austin
Simulation of Coupled Ground Water/Surface Water Flow

Abstract: There is strong evidence that the supply and quality of water are influenced by interactions between water stored at the surface and water stored in the subsurface. There have been a few efforts at modeling this interaction, but a number of outstanding questions still remain. In this talk we will address the mathematical modeling and numerical simulation of coupled ground water/surface water flow. Mathematical modeling issues include determining the appropriate models of flow within each subdomain, and determining the interface or boundary conditions to couple the models. Given a model, the next question is how to solve it. Here we will discuss an approach based on the discontinuous Galerkin (DG) method. A priori error analysis for a DG formulation for a shallow water model coupled with saturated ground water flow will be presented. Numerical results will also be discussed for several practical scenarios. We will also discuss recent analysis and results for a simplified surface water flow model, the diffusive wave approximation.

There will be coffee and cookies in the lounge at 3:00.

Posted November 5, 2007
Last modified February 20, 2022

5:00 pm 232 Lockett

James Madden, Mathematics Department, LSU
Conservation of Momentum: Euclid, Newton and Noether

The key idea of Euclid’s proof that triangles with equal bases and equal heights have the same area was used by Newton to prove the conservation of angular momentum. At a deeper level, both proofs are about symmetry. This talk tells the story of all of this—and more.

Friday, November 9, 2007

Posted November 7, 2007

11:40 am – 12:30 pm 113 Lockett Hall

Moshe Cohen, Department of Mathematics, Bar-Ilan University, Israel
Ribbon Graphs and Quasi-trees

Posted October 30, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

2:00 pm 338 Johnston Hall

Quantum Technologies --- The Second Quantum Revolution!

We are currently in the midst of a second quantum revolution. The first quantum revolution gave us new rules that govern physical reality. The second quantum revolution will take these rules and use them to develop new technologies.

Posted November 7, 2007

3:40 pm Lockett 9

Meeting of the Tenured and Tenure-track Faculty

Hiring discussion.

Monday, November 12, 2007

Posted November 6, 2007

Algebra and Number Theory Seminar Questions or comments?

4:40 pm – 5:30 pm Lockett 276

Patrick Gilmer, Mathematics Department, LSU
Congruence and quantum invariants

Tuesday, November 13, 2007

Posted November 9, 2007

Seminar on K-theory and Grothendieck-Witt groups

1:30 pm – 3:00 pm Lockett 381

Martin Laubinger, LSU Graduate Student
Bott periodicity via Gamma spaces

for further information, see the seminar webpage

Posted September 12, 2007
Last modified January 6, 2021

3:40 pm – 4:30 pm Lockett 240

Zhaohu Nie, Texas A&M Department of Mathematics
Singularities of admissible normal functions

The first proof of the Lefschetz (1,1) theorem was given by Poincare and Lefschetz using normal functions for a Lefschetz pencil. The hope to generalize this method to higher codimensional Hodge conjecture was blocked by the failure of Jacobian inversion. In another direction, one can hope for an inductive proof of the Hodge conjecture if for any primitive Hodge class one can find a, necessarily singular hypersurface to "capture part of it". Recently Green and Griffiths introduced the notion of extended normal functions over higher dimensional bases such that their singular loci corresponds to such hypersurfaces. In this talk, we will present how to understand singularities using the viewpoint of admissible normal functions, and how the Hodge conjecture is then equivalent to the existence of singularities. This is joint work with P. Brosnan, H. Fang and G. Pearlstein.

Wednesday, November 14, 2007

Posted November 7, 2007

Student Seminar

2:40 pm – 3:30 pm Prescott 203

Jasson Vindas, LSU Department of Mathematics, LSU
Student Seminar on Control Theory and Optimization

Some asymptotic notions for Schwartz distributions

Posted November 6, 2007

3:40 pm – 4:30 pm Biological Sciences Annex Building - A663

Steve Wallace, LSU
Surgery equivalence invariants of colored knots

Virtual Seminar together with U Iowa

Thursday, November 15, 2007

Posted November 6, 2007
Last modified September 17, 2021

12:40 pm – 1:30 pm Lockett 119

Junior Topology Seminar

Reading Seminar.

Posted November 12, 2007

3:30 pm Lockett 381

P. Sundar, Department of Mathematics, LSU
Fractional Gaussian integrals

Posted November 11, 2007
Last modified February 20, 2022

3:40 pm 285 Lockett

Bin Li, LSU Department of Experimental Statistics
Introduction to Data Mining

Recently, data mining has been attracting more and more attention in statistics and mathematics. This presentation will start with some motivating examples from real applications. Then I will introduce some of the latest data mining methods and illustrate them in the examples. Finally, I will discuss some challenges and opportunities specifically for mathematicians and statisticians to dive into this area.

The speaker received his B.S. in biophysics at Fudan University in 1998 and his Ph.D. in Statistics from The Ohio State University in 2006. He is currently an assistant professor in the Department of Experimental Statistics, LSU. His research has mainly focused on the interdisciplinary area between statistics and machine learning.

Friday, November 16, 2007

Posted November 12, 2007

Algebra and Number Theory Seminar Questions or comments?

11:40 am – 12:30 pm 113 Lockett Hall

Stan Dziobiak, Department of Mathematics, LSU Graduate Student
Coloring Graphs within a Constant Error in Polynomial Time

Monday, November 19, 2007

Posted November 14, 2007
Last modified November 19, 2007

11:40 am – 12:30 pm Lockett 241

Daniel Sage, Mathematics Department, LSU
Perverse coherent sheaves and special pieces in the unipotent variety, part 2

Posted November 8, 2007

3:40 pm Lockett 9

Meeting of the Tenured and Tenure-track Faculty

We will discuss hiring plan for math/cct and mhi hiring. There may have been a change in the department\'s original agreement and understanding.

Tuesday, November 20, 2007

Posted November 12, 2007

3:00 pm – 4:00 am Lockett B9

Site Visit Information for Graduate Students

This is an important meeting for all math graduate students to find out from Profs. Olafsson and Smolinsky about the National Science Foundation site visit to our department on December 6.

Wednesday, November 21, 2007

Posted November 6, 2007

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm

NO VIRTUAL SEMINAR (THANKSGIVING)

Tuesday, November 27, 2007

Posted November 19, 2007
Last modified March 2, 2021

Seminar on K-theory and Grothendieck-Witt groups

1:30 pm – 3:00 pm Lockett 381

Girja Shanker Tripathi, LSU
Gersten's conjecture and Bloch's formula

Posted September 14, 2007
Last modified November 20, 2007

3:40 pm – 4:30 pm Lockett 239

Pramod Achar, Mathematics Department, LSU
Staggered t-structures and equivariant coherent sheaves

Wednesday, November 28, 2007

Posted November 26, 2007

Student Seminar on Control Theory and Optimization

2:40 pm – 3:30 pm Prescott 203

Patricio Jara, LSU Math Department
Rational approximation of Semigroups

Posted November 12, 2007

3:40 pm – 4:30 pm Lockett 381
(Originally scheduled for Wednesday, November 21, 2007, 3:40 pm)

Boris Rubin, Louisiana State University
Spherical Means in Odd Dimensions and EPD equations.

I am planning to present a simple proof of the
Finch-Patch-Rakesh inversion formula for the spherical mean Radon
transform in odd dimensions. This transform arises in thermoacoustic
tomography. Applications will be given to the Cauchy problem for the
Euler-Poisson-Darboux equation with initial data on the cylindrical surface.
The argument relies on the idea of analytic continuation and properties of
the Erdelyi-Kober fractional integrals. Some open problem will be discussed.

Posted November 6, 2007

Informal Geometry and Topology Seminar Questions or comments?

3:40 pm – 4:30 pm Biological Sciences Annex Building - A663

Adam Lowrance, Department of Mathematics, Vassar College
On a paper by Ozsvath, Rasmussen and Szabo on the odd Khovanov homology

Virtual Seminar together with U Iowa

Thursday, November 29, 2007

Posted November 28, 2007
Last modified July 25, 2018

12:40 pm – 1:30 pm 143 Lockett Hall

Framed knot contact homology

Posted November 12, 2007

3:40 pm – 4:30 pm Lockett 285

Michael Lacey, Georgia Institute of Technology
Pointwise convergence of Fourier series

Abstract: Lennart Carleson\'s celebrated theorem on the pointwise convergence of Fourier series was one of three results cited by the Abel Prize committee, in making their award to him. This result states that any square integrable function on the unit circle is the limit, almost everywhere, of the Fourier partial sums. We will recall the theorem, explain why it is worthy of an Abel prize, and give a brief description of a proof. The theorem is related, even required, for a range of related questions, a much more recent development investigated by the speaker and Christoph Thiele, among many others. We close with a very recent new result of Victor Lie on the Quadratic Carleson Theorem.

There will be coffee and cookies in the lounge at 3:00.

Posted November 13, 2007
Last modified February 20, 2022

5:00 pm 232 Lockett

How to Apply for REUs

The United States National Science Foundation (NSF) funds many research opportunities for undergraduates through its REU Sites program. An REU Site consists of a group of ten or so undergraduates who work in the research programs of the host institution. Each student is associated with a specific project, where he/she works closely with faculty and other researchers. Students are granted stipends and, in many cases, assistance with housing and travel. Undergraduates supported with NSF funds must be citizens or permanent residents of the United States or its possessions. The speaker will give advice on how to apply for REU jobs.

The speaker is the Cecil Taylor Alumni Professor of Mathematics at LSU. He is a noted scholar in the area of algebraic number theory, and is one of three LSU professors who organize the LSU mathematics REU.

Friday, November 30, 2007

Posted November 28, 2007

11:40 am – 12:30 pm 113 Lockett Hall

Evan Morgan, LSU Mathematics Department Graduate student
Tree-width and contraction

All welcome.

Posted November 26, 2007
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

2:00 pm Life Sciences Building Annex Room A101 Auditorium

Daniel Huttenlocher, Cornell University Neafsey Professor of Computing, Information Science and Business
Computational Soc. Sci.: Large-Scale Studies of Wikis, Blogs, Soc. Networking Sites

Many social interactions that are ephemeral in the physical world are recorded and accessible in the online world.

Monday, December 3, 2007

Posted October 17, 2007
Last modified November 27, 2007

Informal Geometry and Topology Seminar Questions or comments?

3:40 pm – 4:30 pm 233 Lockett

Itai Shafrir, Department of Mathematics, Technion - Israel Institute of Technology
Global minimizers for a p-Ginzburg-Landau energy.

We study the problem of existence of global minimizers for a p-Ginzburg-Landau type energy on the plane and on the half-plane, for p>2, under a degree condition at infinity. We prove existence of a minimizer when the degree equals 1. This is joint work with Yaniv Almog, Leonid Berlyand and Dmitry Golovaty.

Tuesday, December 4, 2007

Posted December 3, 2007
Last modified July 25, 2018

12:40 pm Lockett 119

Reading Seminar

Posted November 30, 2007
Last modified March 2, 2021

Seminar on K-theory and Grothendieck-Witt groups

1:40 pm – 3:00 pm Lockett 381

Girja Shanker Tripathi, LSU
The proof of Gersten's conjecture in the geometric case

Wednesday, December 5, 2007

Posted November 7, 2007

Student Seminar

2:40 pm – 3:30 pm Prescott 203

Bacim Alali, Department of Mathematics
Student Seminar on Control Theory and Optimization

Optimal Lower Bounds on the Stress and Strain Fields Concentrations in Random Media

Wednesday, December 12, 2007

Posted December 10, 2007

Holiday Party

12:00 pm Keisler Lounge

Holiday Party

Everyone is invited to share in the Season\'s Spirit. Please bring a dish to share.

Monday, January 14, 2008

Posted December 17, 2007
Last modified January 12, 2008

An abstract is available here.

3:30 pm Howe/Russell room 130

Paul Rabinowitz, University of Wisconsin E.B. Van Vleck Professor of Mathematics; National Academy Member; 1998 George David Birkhoff Prize in Applied Mathematics
Towards an Aubry - Mather type theory for PDE's

Posted January 29, 2008

3:40 pm Lockett 285

Meeting of the Tenured Faculty

Third year review cases. A vote will follow.

Tuesday, January 15, 2008

Posted December 18, 2007
Last modified January 8, 2008

3:40 pm – 4:30 pm Johnston 338

Hongchao Zhang, University of Minnesota Candidate for Assistant Professor Position
TBA

http://www.cct.lsu.edu/events/talks/307

Wednesday, January 16, 2008

Posted December 17, 2007
Last modified January 12, 2008

An abstract is available here.

3:30 pm Howe/Russell room 130

Thursday, January 17, 2008

Posted December 18, 2007
Last modified January 10, 2008

3:40 pm – 4:30 pm Johnston 338

Johnny Guzman, University of Minnesota Candidate for Assistant Professor Postion
TBA

http://www.cct.lsu.edu/events/talks/308

Friday, January 18, 2008

Posted December 17, 2007
Last modified January 12, 2008

An abstract is available here.

3:30 pm Howe/Russell room 130

Tuesday, January 22, 2008

Posted January 17, 2008

Seminar on Algebraic Cycles

1:30 pm – 3:00 pm Lockett 381

Seva Joukhovitski, Mathematics Department, LSU
Sums of squares formulas via motivic cohomology

Posted December 18, 2007
Last modified August 29, 2023

3:40 pm – 4:30 pm Johnston 338

Clayton Webster, Sandia National Laboratories Candidate for Assistant Professor Position
A Dimension-Adaptive Sparse Grid Stochastic Collocation Technique for Partial Differential Equations with High-Dimensional Random Input Data

https://www.cct.lsu.edu/events/talks/313

Wednesday, January 23, 2008

Posted January 21, 2008

3:30 pm – 4:30 pm Bio. Sciences Annex, A663

Charles Frohman, University of Iowa
An introduction to Frobenius extensions and TQFT over rings

Virtual Seminar together with UIowa

Posted January 15, 2008
Last modified January 22, 2008

Applied Analysis Graduate Student Seminar

3:40 pm – 4:30 pm Prescott 205

Laurentiu Marinovici, Louisiana State University
Survey on Estimation Algorithms for Networked Control Systems using UDP-like Communication

Thursday, January 24, 2008

Posted January 24, 2008

Control Research Seminar

10:00 am EE117, Electrical and Computer Engineering

Robert Bitmead, University of California at San Diego Fellow of the Institute of Electrical and Electronics Engineers
Experimental Certification of Jet Engine Controllers

Posted December 18, 2007
Last modified January 21, 2008

3:40 pm – 4:30 pm Johnston 338

Jianlin Xia, University of CA at Los Angeles Candidate for Assistant Professor Position
Superfast Solvers For Some Large Structured Matrix Problems

http://www.cct.lsu.edu/events/talks/311

Friday, January 25, 2008

Posted January 7, 2008
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

11:30 am

Sangtae "Sang" Kim, Purdue University Donald W. Feddersen Distingusihed Professor Of Mechanical Engineering And Distinguished Professor Of Chemical Engineering
Fluidic Self Assembly And The Network Of Things

Fluidic Self Assembly (FSA) is now a microhydrodynamic, particulate process for the integration of Electrical, optical and mechanical devices.

Tuesday, January 29, 2008

Posted January 22, 2008

Seminar on Algebraic Cycles

1:30 pm – 3:00 pm Lockett 381

Seva Joukhovitski, Mathematics Department, LSU
Sums of squares formulas via motivic cohomology (cont.)

Posted December 18, 2007
Last modified January 24, 2008

3:40 pm – 4:30 pm Johnston 338

Wei Zhu, New York University Candidate for Assistant Professor Position
Modeling And Simulation Of Liquid Crystal Elastomers

http://www.cct.lsu.edu/events/talks/315

Posted January 24, 2008

Topics in Functional Analysis

4:40 pm – 6:00 pm Lockett 284

Richard Kadison, University of Pennsylvania Member of the National Academy of Sciences
A Survey of Operator Algebras I

Wednesday, January 30, 2008

Posted January 22, 2008
Last modified January 28, 2008

3:30 pm – 4:30 pm Bio. Sciences Annex, A663

Charles Frohman, University of Iowa
sl_3 Topological Quantum Field Theory after Khovanov

Virtual Seminar together with UIowa

Posted January 16, 2008
Last modified January 22, 2008

Applied Analysis Graduate Student Seminar

3:40 pm – 4:30 pm Prescott 203

Santiago Fortes, Department of Mathematics, LSU
A Proof of the Uniform Boundedness Principle using Continuous Functions

Thursday, January 31, 2008

Posted December 18, 2007
Last modified January 21, 2008

3:40 pm – 4:30 pm Johnston 338

Xiaoliang Wan Candidate for Assistant Professor Position
Polynomial Chaos And Uncertainty Quantification

http://www.cct.lsu.edu/events/talks/312

Friday, February 1, 2008

Posted January 23, 2008
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 277

Jan Dijkstra, Vrije Universiteit Amsterdam
Homeomorphism groups of manifolds and Erdős space

There will be coffee and cookies in the lounge at 3:00.

Monday, February 4, 2008

Posted December 28, 2007
Last modified March 3, 2022

3:40 pm – 4:40 pm 233 Lockett Hall

Peter Sternberg, Indiana University
Bifurcating solutions in a model for a superconducting wire subjected to an applied current

We study formally and rigorously the bifurcation to steady and time-periodic states in a model for a thin superconducting wire in the presence of an imposed current. Exploiting the PT-symmetry of the equations at both the linearized and nonlinear levels, and taking advantage of the collision of real eigenvalues leading to complex spectrum, we obtain explicit asymptotic formulas for the stationary solutions, for the amplitude and period of the bifurcating periodic solutions and for the location of their zeros or “phase slip centers” as they are known in the physics literature. In so doing, we construct a center manifold for the flow and give a complete description of the associated finite-dimensional dynamics. This is joint work with Jacob Rubinstein and Kevin Zumbrun.

Thursday, February 7, 2008

Posted January 30, 2008

1:40 pm – 2:30 pm Lockett 16

Pallavi Dani, Department of Mathematics, LSU
Filling invariants for groups

Abstract: For any loop in a simply-connected Riemannian manifold, one can look for a disk of minimal area whose boundary is that loop. More generally, one can consider fillings of $n$-spheres by $(n+1)$-balls. These notions have natural analogues in the realm of finitely presented groups, where one models the group using suitably defined geometric spaces. I will discuss Dehn functions of groups, which capture the difficulty of filling spheres with balls. A fundamental question in the area is that of determining which functions arise as Dehn functions of groups. I will give an overview of known results and describe recent progress in the $2$-dimensional case. This is joint work with Josh Barnard and Noel Brady.

Posted December 25, 2007
Last modified January 14, 2008

3:10 pm Lockett 6

Graduate Core II Curriculum

Please see:

https://www.math.lsu.edu/dept/node/649

For a proposal and response. We will discuss the matter and formulate a proposal for a vote.

Posted February 5, 2008
Last modified February 20, 2022

4:30 pm 232 Lockett

Pallavi Dani, Department of Mathematics, LSU
Wallpaper Groups

Anyone who has redecorated a room knows that choosing between the hundreds of wallpaper patterns in the store is a daunting task. In this talk I hope to convince you that the number of distinct wallpaper patterns is surprisingly small.

Friday, February 8, 2008

Posted February 7, 2008

3:40 pm Lockett 381

Gestur Olafsson, Mathematics Department, LSU
Analysis on Symmetric Spaces

This is a seminar class on homogeneous symmetric spaces G/K, where G is a linear Lie group. We study the basic structure theory for G non-compact. We will then discuss the representation theory related to G/K and harmonic analysis on G/K. In particular we hope to be able to introduce the Fourier transform and, in case G is non-compact, the Radon transform on G/K related to the principal series representations. There is a link to the lecture notes on our webpage http://www.math.lsu,edu/~olafsson/teaching.html

Posted February 7, 2008

3:40 pm

Gestur Olafsson, Mathematics Department, LSU
Analysis on Symmetric Spaces

Monday, February 11, 2008

Posted February 8, 2008

3:40 pm Lockett 9

Meeting of the Tenured and Tenure-track Faculty

Hiring and the hiring plan.

Tuesday, February 12, 2008

Posted January 29, 2008

Seminar on Algebraic Cycles

1:30 pm – 3:00 pm Lockett 381

Marco Schlichting, Louisiana State University
Sums-of-Squares formulas via K-theory

Posted January 24, 2008
Last modified January 29, 2008

Topics in Functional Analysis

3:40 pm – 5:00 pm Lockett 284
(Originally scheduled for Tuesday, February 5, 2008, 3:40 pm)

Richard Kadison, University of Pennsylvania Member of the National Academy of Sciences
A Survey of Operator Algebras II

Wednesday, February 13, 2008

Posted January 24, 2008
Last modified February 14, 2008

3:30 pm – 4:30 pm Bio. Sciences Annex, A663

A diagramless link homology

Adam McDougall (Virtual Seminar together with UIowa)

Posted February 12, 2008

Applied Analysis Graduate Student Seminar

3:40 pm – 4:30 pm Prescott 205

Lingyan Huang, LSU Math Dept
Introduction to Nonsmooth Analysis and Control Theory I

Posted February 12, 2008

Applied Analysis Graduate Student Seminar

3:40 pm – 4:30 pm Prescott 205

Jacob Blanton, Mathematics Department, LSU
Introduction to Nonsmooth Analysis and Control Theory II

Thursday, February 14, 2008

Posted January 29, 2008

3:40 pm Lockett 285

Meeting of the Tenured Faculty

Third year review cases. A vote will follow.

Posted February 12, 2008
Last modified February 20, 2022

4:30 pm 232 Lockett

Peggy Wang, Baton Rouge Transition To Teaching Program Project Director
Alternative Paths to Teacher Certification in Secondary Math and Science

Baton Rouge Transition to Teaching (BRTTT) is looking for math students who are passionate about math and who want to make a difference in their communities. Funded by the US Department of Education, BRTTT provides an alternative path to teacher certification in secondary math and science. We are looking for nontraditional candidates including graduating seniors who are not majoring in education to help address the critical teacher shortage in math and science. Through our intensive seven-week Summer Institute, we add educational theory and instructional strategies to candidates’ content knowledge. Upon successful completion of our Summer Institute, candidates can begin teaching full-time in August. Support is a cornerstone of our program; we provide specialized training to principals and mentor teachers so that they can effectively support new teachers in their first years of teaching. We also have Robert Noyce Scholarships ranging in value from \$12,600 to \$15,000 for graduating seniors who go through our program and teach in one of our partner districts for at least two years.

Friday, February 15, 2008

Posted February 15, 2008
Last modified March 3, 2021

3:40 pm Lockett 381

Gestur Olafsson, Mathematics Department, LSU
Seminar on Symmetric Spaces

Monday, February 18, 2008

Posted February 6, 2008

CCT Lecture Events organized by the LSU Center for Computation and Technology

10:40 am – 11:30 am Johnston Hall 338

David E. Keyes, Columbia University And Lawrence Livermore National Lab
A Nonlinearly Implicit Manifesto

Frontiers of Scientific Computing Lecture Series. More info.

Posted February 6, 2008

SIAM Student Chapter Talk

1:40 pm 338 Johnston Hall

David E. Keyes, Columbia University And Lawrence Livermore National Lab
Scalable Solver Infrastructure for Multirate, Multiscale PDE Applications

Followed by refreshments and a short discussion of careers and a Q&A session.

Tuesday, February 19, 2008

Posted February 17, 2008

Seminar on Algebraic Cycles

1:30 pm – 2:30 pm Lockett 381

Daniel Isaksen, Wayne State University
Motivic homological algebra

I will describe some preliminary explicit computations in motivic homotopy theory. Over arbitrary ground fields, we just don\'t know enough to compute much. But over the complex numbers, we have explicit descriptions (due to Voevodsky) of the cohomology of a point and of the Steenrod algebra of all cohomology operations. I will describe some computations of Ext groups over the motivic Steenrod algebra (over the complex numbers). Via the motivic Adams spectral sequence, these computations say something about motivic stable homotopy groups. Over the real numbers, the cohomology of a point and the Steenrod algebra are also explicitly known (again due to Voevodsky). Similar Ext computations are possible over the real numbers, but the homological algebra is trickier. I believe that these calculations will be an important guide for further research in motivic homotopy theory.

Posted February 13, 2008

Topics in Functional Analysis

3:40 pm – 5:00 pm Lockett 284

Frank Hansen, Department of Economics, University of Copenhage
Quantum information inequalities.

Abstract: The Wigner-Yanase-Dyson informations are examples of measures of (pure) quantum information. They satisfy all but one of the desired properties, proposed by Wigner and Yanase, to a good measure of quantum information. We introduced a much wider class of information measures, the so called metric adjusted skew informations. They are constructed from monotone metrics on the state space of a quantum system and labeled by a special class of operator monotone functions. We develop inequalities for measures of quantum information and derive the so called dynamical uncertainty principle.

Wednesday, February 20, 2008

Posted February 17, 2008

Applied Analysis Graduate Student Seminar

2:40 pm – 3:30 pm Prescott 203

Jacob Blanton, Mathematics Department, LSU
Introduction to Nonsmooth Analysis and Control Theory II

Posted January 24, 2008
Last modified February 15, 2008

3:30 pm – 4:30 pm Bio. Sciences Annex, A663

Hee Jung Kim, Department of Mathematics, LSU
Embeddings of Surfaces in 4-manifolds

(Virtual Seminar together with UIowa)

Thursday, February 21, 2008

Posted February 18, 2008
Last modified February 26, 2008

10:40 am – 11:30 am Lockett 381

Hongyu He, Mathematics Department, LSU
Associated Varieties of Irreducible Unitary Representation

Abstract: I will discuss algebraic invariants associated with Irreducible
unitary representations. These invariants will then be used to study the
restrictions of a unitary representation to its subgroups.

Posted February 12, 2008
Last modified February 20, 2022

4:30 pm 232 Lockett

Peter Wolenski, LSU Department of Mathematics Russell B. Long Professor
Nonsmooth Analysis: The Mathematics of Optimization

Nonsmooth analysis is the study of generalized notions of derivatives for functions that are not necessarily differentiable in the usual sense. It is an important area of mathematical analysis that undergirds much of modern optimization theory. The theory of nonsmooth analysis was developed by Francis Clarke and his school in the 1970s, and has since been employed in economics, engineering, finance, and other areas. This talk will provide a nontechnical overview of this theory and a glimpse at some of the many applications in which nonsmooth analysis has had a major impact.

Professor Wolenski received his Ph.D. in Mathematics in 1988. He held positions at Imperial College of Science and Technology in London and the University of Montreal and has lectured extensively throughout the US and Europe. He came to LSU in 1990 and is now the Russell B. Long Professor of Mathematics. He has more than 50 publications including many in leading mathematics journals.

Friday, February 22, 2008

Posted February 11, 2008
Last modified February 17, 2008

11:30 am – 12:30 pm Johnston 338

William Gropp, Mathematics and Computer Science Division, Argone National Laboratory
Challenges For The Message-Passing Interface In The PetaFLOPS Era

There will be a reception at 11:00AM. More info.

Posted February 22, 2008

3:40 pm Lockett 381

Gestur Olafsson, Mathematics Department, LSU
Analysis on Symmetric Spaces

This is the third lecture in the series. We will discuss the Iwasawa decomposition of the Lie algebra and the group.

Monday, February 25, 2008

Posted January 30, 2008
Last modified February 25, 2008

3:40 pm – 4:30 pm Lockett 276

Gregor Masbaum, University Paris 7
TQFT and the Nielsen-Thurston classification of surface homeomorphisms

Tuesday, February 26, 2008

Posted February 22, 2008

Seminar on Algebraic Cycles

1:40 pm – 3:00 pm Lockett 381

Jerome W. Hoffman, Mathematics Department, LSU
Motives and Algebraic Cycles

Posted January 31, 2008
Last modified February 9, 2008

3:40 pm HOWE/RUSSELL E130

Richard A. Askey, University of Wisconsin Member of the National Academy of Sciences
Binomial theorem, gamma and beta functions and extensions

The binomial theorem goes back centuries, yet there are
still interesting things one can do with it and extensions which
were found not that long ago which are very important. The gamma
and beta functions are not as old, a bit under 300 years.
There are important extension of them which have been found
much more recently, both in one and in several variables. Some of
these results will be described, proven, and/or used.

Wednesday, February 27, 2008

Posted January 31, 2008
Last modified March 2, 2021

3:40 pm HOWE/RUSSELL 130

Richard A. Askey, University of Wisconsin Member of the National Academy of Sciences
What is Ptolemy's theorem and why is it useful to know a few different ways to prove it?

This talk will be accessible to all undergraduate math majors and any students who had a good high school geometry course.

Ptolemy was best known for his astronomy work, but his book on this contains an important theorem in geometry which is still of interest. The theorem deals with quadrilaterals inscribed in a circle, and was important to Ptolemy as a tool to construct what we would call tables of values of trigonometric functions. We know better ways to do that now, but Ptolemy's theorem is still important, both as a way of learning important ways of attacking some geometry problems, and because of other uses of it. A number of proofs will be given, including Ptolemy's geometric proof, Euler's proof using the law of cosines, a combination of these two proofs to extend Ptolemy's theorem to general quadrilaterals, and ways to reduce this problem to a simple problem on a line.

Thursday, February 28, 2008

Posted February 25, 2008

10:40 am – 11:30 am Lockett 381

Dan Barbasch, Cornell University
Spherical unitary spectrum for split real and p-adic groups.

Abstract: I will give a description of the parametrization of the spherical unitary dual for split groups, and discuss the techniques used to obtain it. The spherical unitary dual is important for problems in harmonic analysis on symmetric spaces and automorphic forms.

Posted January 22, 2008
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 285

Dan Barbasch, Cornell University
Unipotent representations and unitarity

There will be coffee and cookies in the lounge at 3:00.

Friday, February 29, 2008

Posted January 31, 2008
Last modified March 2, 2021

3:40 pm HOWE/RUSSELL 130

Richard A. Askey, University of Wisconsin Member of the National Academy of Sciences
Orthogonal polynomials — what are they and some of the things one can do with them

Most of you know the names of some of the important classical orthogonal polynomials, Hermite polynomials, Legendre polynomials, and Chebyshev polynomials, and may even know some places where these polynomials arise. There are a number of other classical type orthogonal polynomials which will be discussed. The problems they arise in range from stable distribution of charges on an interval, which is connected eventually with Selberg's multidimensional beta integral, to the Rogers-Ramanujan identities, which themselves show up in statistical mechanics and other unlikely places in addition to their interpretation as partition identities for special classes of integers.

Tuesday, March 4, 2008

Posted February 29, 2008

Seminar on Algebraic Cycles

1:40 pm – 3:00 pm Lockett 381

Jerome W. Hoffman, Mathematics Department, LSU
Motives and Algebraic Cycles II

Posted February 21, 2008

Topics in Functional Analysis

3:40 pm – 4:30 pm Lockett 284

Richard Kadison, University of Pennsylvania Member of the National Academy of Sciences
A Survey of Operator Algebras III

A survey of the theory of Operator Algebras - an approach to the spectral theory of bounded and unbounded operators on Hilbert space. I\'ll head for the basic density theorems of the subject (the von Neumann density, the Kaplansky density, and the transitivity theorems), and explain the approximation-theory aspects of the theory of operator algebras. Some more specifics: Factors, comparison theory of projections, and thence, the dimension function and \"factor type,\" the trace, and examples (von Neumann group algebras) of finite factors.

Wednesday, March 5, 2008

Posted February 20, 2008
Last modified February 27, 2008

3:30 pm – 4:30 pm Bio. Sciences Annex, A663

Alissa Crans, University of Chicago/Loyola Marymount University
2-groups: Categorified groups

(Virtual Seminar together with UIowa; the talk is broadcasted from Iowa)

Thursday, March 6, 2008

Posted March 5, 2008
Last modified March 3, 2021

10:40 am – 11:30 am Lockett 381

Joseph Wolf, University of California, Berkeley
Plancherel Formula for Commutative Spaces

Let $(G,K)$ be a Gelfand pair, in other words $G$ is a separable locally compact group, $K$ is a compact subgroup, and the convolution algebra $L^1(K\backslash G/K)$ is commutative. Examples include Riemannian symmetric spaces, locally compact abelian groups and homogeneous graphs. Then the natural representation of $G$ on $L^2(G/K)$ is multiplicity-free and there is a very simple analog of the Euclidean space Fourier transform. I'll describe that transform and the corresponding analog of the Fourier inversion formula.

Posted January 29, 2008
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 285

Joseph Wolf, University of California, Berkeley
Limits of nilpotent commutative spaces

There will be coffee and cookies in the lounge at 3:00.

Monday, March 10, 2008

Posted February 25, 2008
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

2:30 pm 155 Coates Hall

Randal E. Bryant, Carnegie Mellon University Dean, School of Computer Science
Data-Intensive Super Comp.: Taking Google-Style Comp. Beyond Web Search

Web Search engines have become fixtures in our society, but few people realize that they are actually publicly accessible supercomputing systems, where a single query can unleach the power of several hundred processors operating on a date set of over 200 terabytes.

Posted February 26, 2008
Last modified March 3, 2008

3:30 pm – 4:30 pm Lockett Hall 233

Razvan Teodorescu, Los Alamos National Laboratory
Harmonic Growth in 2D via Biorthogonal Polynomials

Evolution of planar domains (representing physical clusters) under harmonic forces is representative for many problems in mathematical physics. In certain situations, the evolution leads to finite-time singularities. I will discuss a regularization of this evolution inspired by the equilibrium distribution of eigenvalues of large random normal matrices. Connections to operator theory will also be discussed.

Tuesday, March 11, 2008

Posted March 10, 2008

Seminar on Algebraic Cycles

1:40 pm – 3:00 pm Lockett 381

Jerome W. Hoffman, Mathematics Department, LSU
Motives and Algebraic Cycles III

Posted February 25, 2008
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:00 pm 338 Johnston Hall

Roman Beck, Institute of Information, Johann Wolfgang Goethe University, Frankfurt, Germany E-Finance and Services Science Chair
A Cost-based Multi-Unit Resource Auction for Service-oriented Grid Computing

The Application of Grid technology is finally spreading from engineering and natural science related industrial sectors to other industries with a high demand for computing applications. However, the diffusion of Grid technology within these sectors is often hindered by a lack of the incentive to share the computational reserches across departments or branches even within the same enterprise.

Posted March 10, 2008
Last modified March 11, 2008

Topics in Functional Analysis

3:40 pm – 5:00 pm Lockett 285

Richard Kadison, University of Pennsylvania Member of the National Academy of Sciences
A Survey of Operator Algebras IV

Wednesday, March 12, 2008

Posted March 6, 2008

Applied Analysis Graduate Student Seminar

3:40 pm – 4:30 pm Prescott 205

Jasson Vindas, LSU Department of Mathematics, LSU
Local boundary behavior of harmonic and analytic functions: Abelian theorems for quasiasymptotics of distributions

Thursday, March 13, 2008

Posted March 10, 2008
Last modified February 20, 2022

4:30 pm 232 Lockett

Guoli Ding, Mathematics Department, LSU
Solving Linear Inequalities, with Applications to Geometry, Optimization, and Combinatorics

Since every equation $A = B$ can be equivalently expressed as two inequalities $A ≤ B$ and $B ≤ A$, solving inequalities can be considered a generalization of solving equations. In this talk, beginning with a very simple algorithm, we develop a general theory on solving linear inequalities. Then we will discuss applications of this theory in different areas of mathematics, including polyhedral theory, linear programming, and combinatorics.

Monday, March 24, 2008

Posted January 22, 2008

1:45 pm – 3:00 pm 301D Lockett Hall

Non-Thesis MS Final Exam, concluding event.

The Committee will be Profs. Richardson (chair), Adkins, and Dasbach. This is the concluding event of the Comprehensive Final Exam for the non-thesis MS.

Tuesday, March 25, 2008

Posted March 23, 2008

Seminar on Algebraic Cycles

1:40 pm – 3:00 pm Lockett 381

Marco Schlichting, Louisiana State University
Semi-simplicity of the category of numerical motives

Posted March 25, 2008

Topics in Functional Analysis

3:40 pm – 5:00 pm Lockett 285

Richard Kadison, University of Pennsylvania Member of the National Academy of Sciences
A Survey of Operator Algebras V

Wednesday, March 26, 2008

Posted February 20, 2008
Last modified March 20, 2008

3:30 pm – 4:30 pm Bio. Sciences Annex, A663

Hee Jung Kim, Department of Mathematics, LSU
Knotting Surfaces in 4-manifolds, Part II

(Virtual Seminar together with UIowa)

Posted March 25, 2008
Last modified March 2, 2021

Applied Analysis Graduate Student Seminar

3:30 pm – 4:30 pm Prescott 205

Cristina Tugurlan, LSU Math Dept
Distributed Fast Marching Methods

Seminar Website. Fast Marching Methods are efficient algorithms for solving problems of front evolution where the front speed is monotonic. They are theoretically optimal in terms of operation count. They are also highly sequential and hence not straightforward to parallelize. I will present several parallel implementations of the Fast Marching Method. In these implementations one combines fast sweeping with fast marching, in such a way that allows fast convergence. I will illustrate the power of these approaches on some numerical examples, show the monotonicity and stability properties of the algorithms, and study the convergence and the error estimates.

Posted March 25, 2008

Applied Analysis Graduate Student Seminar

3:40 pm – 4:30 pm Prescott 205

Cristina Tugurlan, LSU Math Dept
Distributed Fast Marching Methods

math.lsu.edu/dept/student_app_analysis

Thursday, March 27, 2008

Posted March 17, 2008

3:40 pm – 4:30 pm Lockett 285

Toshiyuki Kobayashi, Harvard and University of Tokyo
Existence Problem of Compact Locally Symmetric Spaces.

Abstract: The local to global study of geometries was a major trend of 20th
century geometry, with remarkable developments achieved particularly in
Riemannian geometry. In contrast, in areas such as Lorentz geometry,
familiar to us as the space-time of relativity theory, and more generally
in pseudo-Riemannian geometry, as well as in various other kinds of
geometry (symplectic, complex geometry, ...), surprising little is known
about global properties of the geometry even if we impose a locally
homogeneous structure.

I will give a survey on the recent developments regarding the question
about how the local geometric structure affects the global nature of
non-Riemannian manifolds, with emphasis on the existence problem of compact
forms, rigidity and deformation.

There will be coffee and cookies in the lounge at 3:00.

Friday, March 28, 2008

Posted February 25, 2008
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

11:30 am 338 Johnston Hall

Rudolf Eigenmann, School of Electrical and Computer Engineering, Purdue University
High Performance Computing Going Mainstream

HPC (High Performance Computing) has progressed far beyond the niche technology it was in the 1980s and 1990s.

Posted January 22, 2008

until Sunday, March 30, 2008

2008 Spring Southeastern AMS Meeting

Monday, March 31, 2008

Posted January 24, 2008
Last modified March 31, 2008

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 276

Charles Livingston, Indiana University
Twisted Alexander polynomials, metabelian representations, and the knot slicing problem

Tuesday, April 1, 2008

Posted February 14, 2008
Last modified March 31, 2008

1:40 pm – 2:30 pm Lockett 111

David Treumann, Northwestern University
Staggered t-structures on toric varieties

Achar has introduced a family of t-structures, called staggered t-structures, on the derived category of equivariant coherent sheaves on a G-scheme. These generalize the perverse coherent t-structures of Bezrukavnikov and Deligne, their main point of interest being that they are more often self-dual. We will discuss the example of torus-equivariant sheaves on a toric variety. We will also indicate a similarity between the main new ingredient of Achar’s t-structures – what are called s-structures – and the weight-truncation formalism of Morel.

Posted April 1, 2008

Topics in Functional Analysis

3:40 pm – 5:00 pm Lockett 285

Richard Kadison, University of Pennsylvania Member of the National Academy of Sciences
A Survey of Operator Algebras VI

Wednesday, April 2, 2008

Posted March 25, 2008
Last modified March 2, 2021

1:30 pm 338 Johnston Hall

Alex Pothen, Old Dominion University Professor, Computer Science Department and Center for Computational Science
Combinatorial Algorithms Enabling Computational Science and Engineering

Combinatorial problems arise as critical subproblems in many computational simulations in science and engineering. Combinatorial scientific computing (CSC) is a multi-disciplinary area in which such problems are formulated and solved. The CSCAPES Institute has been established with funding from the problems and thereby enable high performance computing for breakthrough science.

Posted February 20, 2008
Last modified April 1, 2008

3:30 pm – 4:30 pm Bio. Sciences Annex, A663

Models for evaluating the Homfly polynomial

Anna Meyers (UIowa) (Virtual Seminar together with UIowa)

Thursday, April 3, 2008

Posted April 1, 2008

10:40 am – 11:30 am Lockett 381

Hongyu He, Department of Mathematics, LSU
Associated Varieties of Irreducible Unitary Representation II

Abstract: I will discuss algebraic invariants associated with Irreducible unitary representations. These invariants will then be used to study the restrictions of a unitary representation to its subgroups.

Posted March 25, 2008
Last modified March 2, 2021

3:30 pm 338 Johnston Hall

Claes Eskilsson, Department of Civil and Environmental Engineering Visiting Assistant Professor, Louisiana State University
Modeling of Shallow Water Flows: Applications of DG Methods

There are many examples of water flows where the characteristic length scale is large compared to the vertical scale. The resulting depth-integrated shallow water equations (SWE) is a model equation of great importance since it is used in hydraulic and coastal engineering to model river flooding as well as storm surges and tsunamis.

Posted February 17, 2008

3:40 pm – 4:30 pm Lockett 285

Ron Goldman, Department of Computer Science, Rice University
Three Problems in Search of a Graduate Student

Abstract: Three unsolved problems that originated from research in
Computer Graphics and Geometric Modeling will be presented. The first
problem involves understanding the notion oscillation for Bezier
surfaces, the freeform surfaces most common in Computer Graphics and
Geometric Modeling. The second problem is related to Bezier curves and
univariate Bernstein polynomials, and concerns the combinatorics of
symmetrizing multiaffine functions. The third problem pertains to
fractals and asks if there is an algorithm to determine whether two
arbitrary sets of contractive affine transformations generate the same
fractal.

There will be coffee and cookies in the lounge at 3:00.

Monday, April 7, 2008

Posted April 7, 2008

3:40 pm Lockett 381

P. Sundar, Department of Mathematics, LSU
On the Martingale Problem

Tuesday, April 8, 2008

Posted March 27, 2008

Seminar on Algebraic Cycles

1:40 pm – 3:00 pm Lockett 381

Marco Schlichting, Louisiana State University
Chow motives and the triangulated category of mixed motives

Posted April 4, 2008

Topics in Functional Analysis

3:40 pm – 5:00 pm Lockett 285

Richard Kadison, University of Pennsylvania Member of the National Academy of Sciences
A Survey of Operator Algebras VII

Wednesday, April 9, 2008

Posted April 7, 2008
Last modified April 8, 2008

3:30 pm – 4:30 pm Bio. Sciences Annex, A663

Cody Armond, Department of Mathematics, LSU
On the Huynh-Le Quantum Determinant for the Colored Jones Polynomial

(Virtual Seminar together with UIowa)

Thursday, April 10, 2008

Posted April 4, 2008

10:40 am – 11:30 am Lockett 381

Hongyu He, Mathematics Department, LSU
Associated Varieties of Irreducible Unitary Representation III

Abstract: I will discuss algebraic invariants associated with Irreducible unitary representations. These invariants will then be used to study the restrictions of a unitary representation to its subgroups.

Posted January 22, 2008
Last modified April 4, 2008

3:40 pm – 4:30 pm Lockett 285

Oleg Viro, SUNY Stony Brook
Compliments to bad spaces

Abstract: Could Mathematics be made any better by a different choice of basic definitions? Definitions in some mathematical theories exclude any mentioning of objects, which are believed to be nasty. We will consider few examples of such "political correctness". Speaking on differential manifolds, we usually pretend that they have no singular siblings. This causes lots of inconveniences. Another example is finite topological spaces. Most of mathematicians believe that all finite topological spaces are either trivial or nasty. Topology appears to be the only mathematical field that feels ashamed of its finite objects.

There will be coffee and cookies in the lounge at 3:00.

Friday, April 11, 2008

Posted April 3, 2008
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

11:30 am 338 Johnston Hall

Wolfgang Gentzsch, Duke University RENCI Renaissance Computing Institute at UNC Chapel Hill and D-Grid Initiative
Building and Operating Grid Infrastructures for e-Science

After almost a decade of research and development in the field of grid technology, it is still challenging to design, build, and operate large-scale grid infrastructures for science and industry.

Posted February 18, 2008
Last modified April 4, 2008

3:40 pm – 4:30 pm Lockett 276

Oleg Viro, SUNY Stony Brook
Twisted acyclicity of circle and link signatures

Monday, April 14, 2008

Posted March 1, 2008
Last modified March 3, 2008

2:00 pm HOWE/RUSSELL E137

Hyman Bass, University of Michigan National Medal of Science Laureate (2006)
Improving U.S. Mathematics Education: Myths and Realities

Professor Bass has chaired the Mathematical Sciences Education Board at the National Academy of Sciences and the Committee on Education of the American Mathematical Society. Abstract of the talk: Although there is widespread dissatisfaction with U.S. students\' mathematical performance, there is little agreement on the roots of the problem or its solutions. This presentation will argue that teacher capacity and teaching quality are key to the improvement of mathematics education, and will analyze the levers that could make a difference for their effectiveness.

Posted February 29, 2008
Last modified March 3, 2008

3:30 pm HOWE/RUSSELL E130

Hyman Bass, University of Michigan National Medal of Science Laureate (2006)
Revisiting an approach to the two-dimensional Jacobian Conjecture

This is about an approach I tried many years ago using the Weyl Algebra. While I wasn\'t able to push it all the way through, it did make some interesting contact with diophantine geometry and classical function theory. Since no significant recent progress has been made on the Jacobian Conjecture, I thought that I might try to revive awareness of this approach. The Jacobian Conjecture is of broad mathematical interest.

Posted March 24, 2008
Last modified March 2, 2022

3:40 pm – 4:30 pm 233 Lockett Hall

Yuliya Gorb, Department of Mathematics Texas A&M University
Fictitious Fluid Approach for Justification of Asymptotics of Effective Properties of Highly Concentrated Suspensions

The method of the discrete network approximation has been used for determining effective properties of high contrast disordered composites with particles close to touching. It is illustrated by considering a highly packed suspension of rigid particles in a Newtonian fluid. The effective viscous dissipation rate of such a suspension exhibits a singular behavior, and the goal is to derive and justify its asymptotic formula as a characteristic interparticle distance tends to zero. The main idea of the presented approach is a reduction of the original continuum problem described by partial differential equations with rough coefficients to a discrete network. This reduction is done in two steps which constitute the \"fictitious fluid\" approach. While previously developed techniques based on a direct discretization allowed to obtain only the leading singular term of asymptotics for special symmetric boundary conditions, we are able to capture all singular terms in the asymptotic formula of the dissipation rate for generic boundary conditions. The fictitious fluid approach also allows for a complete qualitative description of microflow in a thin gap between neighboring particles in the suspension.

Tuesday, April 15, 2008

Posted April 11, 2008
Last modified March 2, 2021

Seminar on Algebraic Cycles

1:40 pm – 3:00 pm Lockett 381

Ben Dribus, LSU
Griffiths's Famous Example: Homological and Algebraic Equivalence are Different

Posted February 29, 2008
Last modified March 2, 2021

3:40 pm HOWE/RUSSELL E130

Hyman Bass, University of Michigan National Medal of Science Laureate (2006)
Cake sharing, Euclidean algorithm, and square tiling of rectangles

This talk will be accessible to all undergraduate math majors.
This talk answers the question: If you want to equally share c cakes among s students, what is the smallest number of cake pieces required? It makes interesting connections with all the topics in the title.

Friday, April 18, 2008

Posted April 7, 2008

11:30 am – 12:30 pm

Tim Warburton, Rice University Assistant Professor, Department of Computational and Applied Math
Advances In Wave Propagation With The Discontinuous Galerkin Method

More informations

Posted April 3, 2008
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

1:00 pm 143 Coates Hall

Anita K. Jones, University of Virginia University Professor and Professor of Computer Science in the School of Engineering and Applied Science
CyberSecurity - Serving Society Badly

During the latter half of the 20th century the world created a new infrastructure, the cyber, or information, infrastructure. It underpins many of the processes and activities of society. Usefulness of the cyber infrastructure depends on many aspects, and notable among them is security. Fundementally, today\'s perimeter defense model on which most cyber security relies does not work.

Monday, April 21, 2008

Posted February 25, 2008
Last modified March 2, 2022

3:30 pm – 4:30 pm 237 Lockett Hall

Mikhail Stepanov, Department of Mathematics, The University of Arizona
Instantons in hydrodynamics

We consider the hydrodynamic type system (Navier–Stokes or Burgers equation) with random forcing. The untypical events of high vorticity or large velocity gradients are due to extreme realizations of the forcing. To generate such an event one can increase the forcing amplitude or to optimize its shape (without sacrificing the probability of such forcing to happen). The tails of the velocity field probability distribution function can be obtained by finding an optimal shape of forcing, which corresponds to saddle point (instanton) approximation in the path integral describing the velocity statistics. It will be shown how to find the instantons in hydrodynamic systems numerically.

Tuesday, April 22, 2008

Posted April 21, 2008

Topics in Functional Analysis

3:40 pm – 5:00 pm Lockett 285

Richard Kadison, University of Pennsylvania Member of the National Academy of Sciences
A Survey of Operator Algebras VIII

Posted April 8, 2008
Last modified February 20, 2022

3:40 pm 239 Lockett

Tara Brendle, Department of Mathematics, LSU
Braids and Cryptography

In the late 1990s Anshel, Anshel, and Goldfeld proposed a new cryptosystem based on Dehn’s famous “Decision Problems” in combinatorial group theory. Their paper sparked a great debate about the effectiveness of such a cryptosystem which continues today. In this talk, we will take no sides in this debate! We will describe the particular group which Anshel, Anshel, and Goldfeld suggested for use in their cryptosystem, known as the braid group. This group is widely studied by topologists because of its close connections with knots and surfaces. We will also show how to implement the Anshel–Anshel–Goldfeld cryptoscheme using braid groups.

Posted March 31, 2008
Last modified March 2, 2022

3:40 pm – 4:30 pm 240 Lockett Hall

John W. Cain, Virginia Commonwealth University
A Kinematic Model for Propagation of Cardiac Action Potentials

Propagation of cardiac action potentials is usually modeled with a reaction-diffusion equation known as the cable equation. However, when studying the initiation of arrhythmias, one is primarily interested in the progress of action potential wavefronts without regard to the complete wave profile. In this talk, I will explain how to derive a purely kinematic model of action potential propagation in cardiac tissue. I will reduce a standard PDE model (the cable equation) to an infinite sequence of ODEs which govern the progress of wave fronts in a repeatedly stimulated fiber of cardiac tissue. The linearization of the sequence of ODEs admits an exact solution, expressible in terms of generalized Laguerre polynomials. Analyzing the solutions yields valuable insight regarding nonlinear wave propagation in an excitable medium, providing interesting physiological implications.

Wednesday, April 23, 2008

Posted April 18, 2008

Pasquale Porcelli Lecture Series Special Lecture Series

1:30 pm – 2:30 pm Room 134, Prescott Hall

Student Career Talk by Dr. John Aiken (LSU Math PhD 1972) of the MITRE Corp.

Dr. John Aiken earned his PhD in Math at LSU in 1972. He was a student of Profs. Ernest Griffin and Prof. Pasquale Porcelli. Dr. Aiken is a member of the technical staff at MITRE (MIT Research Engineering) in Fairfax, VA. He is visiting to attend the Porcelli Talks this week, and he has accepted our invitation to give a talk for Graduate Students in Mathematics about non-academic careers in Mathematics.

Posted January 25, 2008
Last modified February 21, 2008

3:40 pm – 4:30 pm Howe-Russell E 130

Don Zagier, Max Planck Institut, Bonn and College de France
The "q" in "q-series"

There will be refreshments before the lecture at 3pm in the Howe-Russell Atrium.

Thursday, April 24, 2008

Posted April 23, 2008

SIAM Student Chapter Talk

12:30 pm Prescott 205

Boris Baeumer, University of Otago, New Zealand
A Random Walk to Fractal Calculus

We use a basic random walk model to derive fractional PDE\'s as governing equations to parsimoniously model dispersion. Dispersion of course happens all over science and thus we derive a set of governing equations that made impacts in Physics, Hydrology, Finance, Chemistry, and Ecology. We then use a fractional reaction-dispersion equation to model the spread of Hawthorn at Porters Pass in New Zealand.

Posted January 25, 2008
Last modified February 21, 2008

Pasquale Porcelli Lecture Series Special Lecture Series

3:40 pm – 4:30 pm Howe-Russell E 130

Don Zagier, Max Planck Institut, Bonn and College de France
The "q" in "quadratic"

There will be refreshments before the lecture at 3pm in the Howe-Russell Atrium.

Friday, April 25, 2008

Posted January 25, 2008
Last modified February 21, 2008

Pasquale Porcelli Lecture Series Special Lecture Series

3:40 pm – 4:30 pm Howe-Russell E 134 (note the room change)

Don Zagier, Max Planck Institut, Bonn and College de France
The "q" in "quantum"

There will be refreshments before the lecture at 3pm in the Howe-Russell Atrium.

Monday, April 28, 2008

Posted February 27, 2008
Last modified April 21, 2008

3:40 pm – 4:30 pm Lockett 276

Joan Birman, Barnard College, Columbia University Recipient of the Chauvenet Prize
Twisted torus knots and Lorenz knots

Posted April 25, 2008

3:40 pm Lockett 381

Julius Esunge, Department of Mathematics, LSU Graduate Student
Anticipating Linear SDEs

Posted March 26, 2008

3:40 pm – 4:30 pm 233 Lockett Hall

Bogdan Vernescu, Worcester Polytechnic Institute
TBA

Posted April 11, 2008
Last modified April 23, 2008

3:40 pm – 4:30 pm Lockett 284

Milen Yakimov, University of California, Santa Barbara
Reality of representations of rational Cherednik algebras

The Calogero-Moser spaces are the phase spaces of the complexified CM
hamiltonian systems. Recently they also appeared in several different
contexts in representation theory. We will describe a
criterion for reality of representations of rational Cherednik algebras
of type A, which is a class of related algebras. We will then
apply it to study the real locus of a Calogero-Moser space and its
relation to the symplectic geometry of the space. We will finish with
applications to Schubert calculus. (Joint work with Iain Gordon
and Emil Horozov).

Tuesday, April 29, 2008

Posted April 7, 2008

SIAM Student Chapter Talk

3:30 pm Johnston Hall 338

Mihaly Kovacs , Chalmers University
TBA

Wednesday, April 30, 2008

Posted March 11, 2008
Last modified April 17, 2008

3:30 pm Old President’s House (across Highland Rd from the Union)

Spring Math Awards Ceremony

The Porcelli Academic Excellence Award, The Porcelli Scholarships, The Betti and Robert Giles Senior Mathematics Award, The David Oxley Memorial Graduate Student Teaching Award, and Certificates of Teaching Excellence (for graduate assistants) will be awarded. Refreshments will be provided.

Friday, May 2, 2008

Posted April 15, 2008
Last modified March 3, 2021

Informal Geometry and Topology Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 284

Phuc Nguyen, Purdue University
Singular quasilinear and Hessian equations and inequalities

We give complete characterizations for the solvability of the following quasilinear and Hessian equations: $$-\Delta_p u = \sigma u^q + \omega, \qquad F_k[-u] = \sigma u^q + \omega, \qquad u \ge 0$$ on a domain $\Omega\subset\mathbb{R}^n$. Here $\Delta_p$ is the $p$-Laplacian, $F_k[u]$ is the $k$-Hessian, and $\sigma$, $\omega$ are given nonnegative measurable functions (or measures) on $\Omega$. Our results give a complete answer to a problem posed by Bidaut-Véron in the case $\sigma\equiv 1$, and extend earlier results due to Kalton and Verbitsky, Brezis and Cabré for general $\sigma$ to nonlinear operators. This talk is based on joint work with Igor E. Verbitsky.

Tuesday, May 6, 2008

Posted May 5, 2008
Last modified March 2, 2021

Seminar on Algebraic cycles (and derived categories)

1:40 pm – 3:00 pm Lockett 113

Pramod Achar, Mathematics Department, LSU
Equivariant derived categories d'apres Bernstein-Lunts

Following Verdier and Grothendieck, we know that the derived category of sheaves on a space is the correct setting in which to talk about various operations on sheaves, adjointness theorems, and duality. But if the space is equipped with a group action, and we want to work with equivariant sheaves, it turns out that the derived category of the category of equivariant sheaves often does not behave the way we want it to. Bernstein and Lunts have shown how to construct another triangulated category, the \"equivariant derived category,\" in which all the usual theorems about sheaves hold. I will discuss the problems with the \"naive\" derived category and explain the Bernstein-Lunts construction.

Thursday, May 8, 2008

Posted May 6, 2008
Last modified July 25, 2018

12:30 pm – 1:30 pm Lockett 112

Reading Seminar

Friday, May 9, 2008

Posted May 8, 2008

Student Seminar on Algebraic Geometry and Representation Theory

10:00 am Lockett 112

Jared Culbertson, Mathematics Department, LSU
Introduction to triangulated categories and derived categories

Friday, June 6, 2008

Posted June 5, 2008

Joint ECE-Math-ME Control Systems Seminar

11:30 am 112 Lockett

Guoxiang Gu, LSU Department of ECE F. Hugh Coughlin/CLECO Professor
Michael Malisoff, LSU Roy P. Daniels Professor
Three ACC08 Talks

The speakers will present their 2008 American Control Conference papers. Here are the titles and abstracts.

Monday, August 11, 2008

Posted August 8, 2008
Last modified December 13, 2022

9:30 am – 9:21 am Friday, August 22, 2008

G.E.A.U.X.---Math Graduate Orientation Program for Incoming Students

The GEAUX team, comprised of current graduate students, will conduct orientation for two weeks for all the incoming graduate students in mathematics. See math.lsu.edu/geaux for daily schedule. This is required for all incoming graduate students in Mathematics.

Monday, August 18, 2008

Posted August 8, 2008

1:00 pm – 4:00 pm 285 Locket

PhD Qualifying/Comprehensive Exam for Topology

This is one part of the 3-part PhD Qualifying Exam/Comprehensive Exam in Mathematics.

Wednesday, August 20, 2008

Posted August 8, 2008
Last modified August 12, 2008

11:00 am – 12:00 pm 338 Johnston Hall

Jennifer Ryan, Delft University Of Technology
Local Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering For Discontinuous Galerkin Methods

Posted August 8, 2008

1:00 pm – 4:00 pm 285 Lockett

PhD Qualifying/Comprehensive Exam in Analysis

This is part of the PhD Qualifying/Comprehensive Exam in Mathematics.

Friday, August 22, 2008

Posted August 8, 2008

1:00 pm – 4:00 pm 285 Lockett

PhD Qualifying/Comprehensive Exam in Algebra

This is part of the 3-part PhD Qualifying/Comprehensive Exam in Mathematics.

Wednesday, August 27, 2008

Posted August 22, 2008

3:40 pm X-lab

Test run for Virtual Seminar

Participating Universities: LSU, U Iowa, GWU, U Miami

Thursday, August 28, 2008

Posted August 11, 2008
Last modified August 20, 2008

3:40 pm Lockett 15

Meeting of the tenured and tenure-track faculty

Possible impact hire.

Friday, August 29, 2008

Posted August 27, 2008

5:10 pm – 6:00 pm 381 Lockett Hall

James Shook, University of Mississippi Graduate Student
Some properties of k-trees

James will introduce a new parameter, branch number, that is useful for studying Hamiltonian properties of k-trees. The main result in his talk generalizes a recent result of Broersma et al.

Thursday, September 4, 2008

Posted August 28, 2008

12:12 pm – 12:12 pm Graduate School, David Boyd Hall
(Originally scheduled for 12:12 pm)

MS Degrees to be Awarded at December Commencement

Fully signed, printed Applications for the MS Degree for December, 2008, are due tomorrow, Sept. 5, at the Graduate Records Office in David Boyd Hall.

Friday, September 5, 2008

Posted August 29, 2008

2:30 pm – 3:30 pm 145 Coates Hall

Linda Petzold, UC Santa Barbara Member, National Academy of Engineering
Multiscale Simulation Of Biochemical Systems

Posted September 5, 2008

3:00 pm – 4:00 pm 285 Lockett Hall

Mareike Massow, Technische Universitat Berlin
Diametral Pairs of Linear Extensions

Abstract: Let a finite partially ordered set (or poset) P be given. We are interested in the family of its linear extensions (LEs). The distance between two LEs L_1 and L_2 of P is the number of incomparable pairs appearing in different orders in L_1 and L_2. A pair of LEs maximizing this distance among all pairs of LEs of P is called a diametral pair. This talk will be about properties of diametral pairs. It is based on joint work with Graham Brightwell.

Tuesday, September 9, 2008

Posted September 9, 2008

3:30 pm – 4:30 pm Monday, October 27, 2008 TBA

Dmitry Golovaty, University of Akron
TBA

Wednesday, September 10, 2008

Posted September 10, 2008

3:30 pm – 4:30 pm X-lab: Lockett 233

Heather Russell, USC
Virtual Seminar

Live from Iowa City

Thursday, September 11, 2008

Posted August 28, 2008

12:00 pm – 12:00 pm Graduate Records Office, David Boyd Hall

Application for MS Final Exam for December Degree

Be sure to file Application for the MS Final Exam by Sept. 12, tomorrow. Print forms from Graduate School website and get signatures in time to deliver to Graduate Records, David Boyd Hall.

Friday, September 12, 2008

Posted September 12, 2008

3:40 pm – 4:30 pm Lockett 381

Graduate Student Seminar in Harmonic Analysis

We will meet to discuss the subjects for the semester. Please bring articles to go with your suggestion.

Friday, September 19, 2008

Posted September 11, 2008

Joint Harmonic Analysis and Probability Seminar

2:40 pm Lockett 285

Maria Gordina, University of Connecticut
Gaussian type measures and Riemannian geometry in infinite dimensions

Abstract: we will talk about how curvature of an infinite-dimensional curved space effects the behaviour of Gaussian type measures. In particular, several settings for infinite-dimensional manifolds will be considered: Hilbert-Schmidt groups which are natural infinite-dimensional analogues of matrix groups, Heisenberg infinite-dimensional groups modelled over an abstract Wiener space, and the homogeneous space Diff(S1)/S1 associated with the Virasoro algebra. We will describe what is known about the Ricci curvature in each of the case, and how its boundness (or unboundness) is reflected in the heat kernel (Gaussian) measure behaviour. The work on the Heisenberg group is joint with Bruce Driver.

Posted September 15, 2008

3:40 pm – 4:30 pm Lockett 285

Service-Learning: What it is and why we do it

This is a talk/discussion about service-learning around the world, across campus, and in the department. Led by D. Kopcso, S. Kurtz and R. Perlis.

Posted September 16, 2008
Last modified March 2, 2021

5:00 pm – 6:00 pm Johnston 338

Panel Discussion on Students' Past Summer Activities

Pizza will be provided

Posted September 19, 2008

5:10 pm – 6:00 pm 285 Lockett Hall

Evan Morgan, LSU Mathematics Department Graduate student
1-switching in cubic graphs

Abstract: Most of the time we want what we don\'t have. Fortunately in the case of cubic graphs our desire need not go unrequited. I will present a small local operation we can perform repeatedly on a connected cubic graph with n vertices which will transform it into any other connected cubic graph on $n$ vertices. And if we want to start 3-connected and end 3-connected, we can even keep it 3-connected the whole way through. Some extensions to embedded graphs may be discussed.

Monday, September 22, 2008

Posted August 19, 2008
Last modified September 10, 2008

Algebra and Number Theory Seminar Questions or comments?

3:40 pm 285 Lockett

Meeting of the Tenured Faculty

Discussion of promotion/tenure case.

Tuesday, September 23, 2008

Posted September 15, 2008
Last modified September 19, 2008

3:40 pm Lockett 235

Christopher Bremer, Mathematics Department, LSU
Periods of Irregular Singular Connections

Let X be a nonsingular complex projective algebraic curve. Suppose that E is a vector bundle over X with meromorphic connection \nabla, where \nabla has poles along a divisor D. If \nabla has regular singularities along D, (E, \nabla) is uniquely determined by its sheaf of horizontal sections \scr(E) on the analytic points of X\D. The classification of irregular singular connections requires an additional piece of data: a Stokes filtration on \scr(E) defined on sectors around the singular points of \nabla.

A theorem of Malgrange (1991) states that there is a quasi-isomorphism between the algebraic de Rham complex associated to (E, \nabla), and the `moderate growth' cohomology of \scr(E) + Stokes. In this talk, I will describe a method for computing the matrix coefficients, or `periods', of this map. In a later talk, I will discuss the epsilon factorization for the determinant of the period map.

Wednesday, September 24, 2008

Posted September 23, 2008

3:40 pm – 4:30 pm X-lab: Lockett 233

Hee Jung Kim, Department of Mathematics, LSU
tba

Virtual Seminar together with UIowa and the University of Miami

Thursday, September 25, 2008

Posted September 16, 2008

3:40 pm – 4:30 pm Lockett 235

Ravi Rau, Department of Physics and Astronomy, LSU
Possible links between physics problems in quantum computing and fibre bundles, projective geometry and coding/design theory

Abstract:
Quantum Information, the field that embraces quantum computing,
cryptography and teleportation, involves as a central object an
entangled pair of spin-1/2 (or two-level) systems. I have been
interested in developing geometrical pictures for manipulating the
fifteen-operator su(4) algebra that describes such systems. For a
single spin, its su(2) algebra's fibre bundle of a two-sphere
(called Bloch sphere by physicists) and a u(1) phase plays a major
role throughout the field of magnetic resonance. I will present
analogous geometrical descriptions of fibre bundles for su(4) and
its sub-algebras (and also higher su(N)). One of these sub-algebras,
su(2) X su(2) X u(1), also "maps" onto octonions and the Fano Plane.
Other sub-algebras and the full su(4) can be similarly related to
Desargues's and other diagrams of projective geometry. These relate
to the subjects of coding and design theory, and Hadamard matrices.
I am looking for help from mathematical experts in each of these
areas to see how these connections may be exploited for application
in quantum information.

There will be coffee and cookies in the lounge at 3:00.

Friday, September 26, 2008

Posted September 23, 2008

2:00 pm – 3:00 pm Johnston 338

Hongchao Zhang, Louisiana State University
Introduction to Some Problems in Nonlinear Optimization

Professor Zhang will talk about his PostDoc experiences at the Institute for Mathematics and Optimization (IMA). Afterwards, he will also describe briefly his research interests in optimization.

Posted September 23, 2008
Last modified December 13, 2022

3:40 pm – 4:30 pm Lockett 381

Characters and Representations of U(N): An Introduction

Prof. Sengupta will start a series of talks in the Graduate Student Harmonic Analysis Seminar on "Characters and Representations of U(N)".

Abstract: The unitary group U(N) is the basic symmetry group arising in quantum theory. In these talks, we will follow Hermann Weyl's approach to determining the representations of U(N). A few basic facts about U(N) will be stated, and the theory will be developed from these in a self-contained way. Key (buzz) words include Schur's Orthogonality Relations and Vandermonde determinants.

Posted November 25, 2008

5:10 pm – 6:00 pm 285 Lockett Hall

Mark Bilinski, LSU, Mathematics
Bounding the circumference of 3-connected claw-free graphs

Abstract: The circumference of a graph is the length of its longest cycle. A result of Jackson and Wormald implies that the circumference of a 3-connected claw-free graph is at least $\\frac 12 n^{\\log_{150}2}$. In this paper we improve this lower bound to $\\Omega(n^{\\log_3 2})$, and our proof implies a polynomial time algorithm for finding a cycle of such length. Bondy and Simonovits showed that the best lower bound one can hope for is $\\Omega(n^{\\log_98})$.

Monday, September 29, 2008

Posted September 18, 2008
Last modified September 19, 2008

3:40 pm – 4:30 pm Lockett 381

Hui-Hsiung Kuo, Mathematics Department, LSU
The MRM for Orthogonal Polynomials

Wednesday, October 1, 2008

Posted October 1, 2008

3:40 pm – 4:30 pm X-lab: Lockett 233

Virtual Seminar with UIowa/UMiami

Adam McDougall (U Iowa): On the diagramless link homology
Talk is broadcasted from Iowa

Thursday, October 2, 2008

Posted August 4, 2008
Last modified March 2, 2021

3:40 pm Lockett 15

Dean's meeting with math faculty

Discussion of the chair's evaluation from last year.

Friday, October 3, 2008

Posted September 25, 2008

11:30 am – 12:30 pm 338 Johnston Hall

George Karniadakis, Brown University
Multiscale Modeling of the Human Arterial Tree on the Teragrid

http://www.cct.lsu.edu/events/talks/423

Posted September 29, 2008

2:40 pm Locket 285

Discussion of Dual Enrollment

Dual Enrollment programs are programs where high school teachers teach a class for college credit. The meeting is to discuss the possibility of this program being offered through the state\'s EarlyStart initiative.

The provost is asking for our views and I will send her a short report.

Monday, October 6, 2008

Posted September 18, 2008

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 381

Rahul Roy, Indian Statistical Institute, Delhi
Coverage of space by random sets

Tuesday, October 7, 2008

Posted September 24, 2008
Last modified October 3, 2008

2:40 pm Lockett 235
(Originally scheduled for Monday, September 29, 2008)

Christopher Bremer, Mathematics Department, LSU
Periods of Irregular Singular Connections, Part II

Continuation of the September 23 seminar.

Posted September 17, 2008
Last modified September 19, 2008

3:40 pm Lockett 5

Meeting of the faculty

Discussion about membership in the College of A&S / College of Basic Sciences.

Wednesday, October 8, 2008

Posted October 1, 2008

3:40 pm – 4:30 pm X-lab: Lockett 233

Virtual Seminar with UIowa/UMiami

Ken Baker (University of Miami)
(talk is broadcasted from Miami)

Monday, October 13, 2008

Posted October 10, 2008

Algebra and Number Theory Seminar Questions or comments?

5:00 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial Student Association Meeting

1. A visitor from Career Services will give a presentation and answer questions on internships and jobs.
2. Discussion of study groups for upcoming exams

Tuesday, October 14, 2008

Posted October 10, 2008

3:40 pm Lockett 235

Charles Neal Delzell, Mathematics Department, LSU
A new, simpler, finitary construction of the real closure of a discrete ordered field

Wednesday, October 15, 2008

Posted October 8, 2008
Last modified October 13, 2008

3:40 pm Lockett 15

Meeting with the deans

Dean Guillermo Ferreyra from A&S and Dean Kevin Carman from Basic Sciences will meet with the faculty to answer questions and discuss the possibility of moving the department.

Monday, October 20, 2008

Posted August 1, 2008
Last modified September 17, 2008

2:30 pm The Old President's House

Meeting with and Presentation to the Provost

The provost has and is conducting meetings with each foundation of excellence department. My instructions were
"Purpose:
This is an opportunity for you to showcase scholars in teaching, research and creative activity.
* This is an opportunity for all to share what is distinctive about the department and its intellectual assets.
Ground rules:
* No discussion of administrators or the budget."

Tuesday, October 21, 2008

Posted September 24, 2008
Last modified September 25, 2008

3:30 pm – 5:00 pm Lockett 5

Career Guidance for Graduate Students---a Faculty Panel Discussion with Questions

A faculty panel---Drs. Lipton, Litherland, Sage, and Sundar---will join the Chair and the Graduate Director in providing career guidance for doctoral students. This meeting is required of all doctoral students who have passed the General Exam. Others are very warmly encouraged to attend as well---it being never too early to plan ones career. Refreshments will be served first at 3:00 in the Lounge.

Thursday, October 23, 2008

Posted September 19, 2008
Last modified October 17, 2008

3:40 pm – 4:30 pm Lockett 235

Ricardo Cortez, Tulane University
Regularized Stokeslets and other elements with applications to biological flows

Biological flows, such as those surrounding swimming microorganisms or beating cilia, are often modeled using the Stokes equations due to the small length scales. The organism surfaces can be viewed as flexible interfaces imparting force on the fluid. I will present the Method of Regularized Stokeslets and other elements that are used to compute Stokes flows interacting with immersed flexible bodies or moving through obstacles. The method treats the flexible bodies as sources of force or torque in the equations and the resulting velocity is the superposition of flows due to all the elements. Exact flows are derived for forces that are smooth but supported in small spheres, rather than point forces. I will present the idea of the method, some of the known results and several examples from biological applications.

There will be coffee and cookies in the lounge at 3:00.

Monday, October 27, 2008

Posted September 13, 2008
Last modified March 2, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 285

Dmitry Golovaty, University of Akron
An effective model for ferronematic liquid crystals

I will discuss a nonlinear homogenization problem for ferronematics—colloidal suspensions of small ferromagnetic particles in a nematic liquid crystalline medium—in a regime when the volume fraction of weakly interacting particles is small. The energy of the suspension is given by a Ginzburg–Landau term supplemented by a Rapini–Papoular surface anchoring energy term and terms describing interaction between the suspension and the magnetic field. For a pure nematic, the energy density of interaction between the magnetic field and the nematic director is given by a quadratic term that is minimized when the director is parallel to the field. For a ferronematic, the additional indirect coupling between the nematic and the field is introduced into the energy via anchoring of nematic molecules on the surfaces of the particles.

Assuming that the particles are identical prolate spheroids with fixed positions but variable orientations, we use the method of quasisolutions to show that the influence of particles on the suspension can be accounted for by an effective nonlinear potential. For needle-like particles of large eccentricity, the model reduces to a known expression of Brochard and de Gennes. This is a joint work with C. Calderer, A. DeSimone, and A. Panchenko.

Tuesday, October 28, 2008

Posted October 14, 2008
Last modified October 24, 2008

3:40 pm Lockett 235

Jerome W. Hoffman, Mathematics Department, LSU
Motives, algebraic cycles, and Hodge theory

Wednesday, October 29, 2008

Posted August 28, 2008
Last modified July 25, 2021

1:30 pm – 2:30 pm 301D Lockett Hall

MS Final Exam, final event

Exam Committee: Profs. Richardson (chair), Adkins, and Dasbach. Be sure to file Application for the MS degree by Sept. 5 and Application for the MS Final Exam by Sept. 12.

Posted October 12, 2008
Last modified October 27, 2008

3:30 pm – 4:30 pm Lockett 285

Itai Shafrir, Department of Mathematics, Technion - Israel Institute of Technology
On a minimization problem involving a potential vanishing on two curves

This talk is concerned with a vector-valued singular perturbation problem involving a potential vanishing on two curves. We study the limiting behaviour of the minimizers, and demonstrate how it depends on the geometry of the domain. This is a joint work with Nelly Andre (University of Tours).

Thursday, October 30, 2008

Posted October 21, 2008
Last modified February 20, 2022

1:40 pm 129 Allen

Mihai Putinar, University of California at Santa Barbara
Polynomial Approximation

A classical Positivstellensatz and a linearized form of it have made a lasting imprint in the field of polynomial optimization. A history of polynomial positivity, starting with Hilbert’s 17th problem and up to current research, will constitute the main body of the talk.

Professor Putinar earned his Ph.D. in Mathematics in 1984 and has lectured extensively throughout the world. He came to UC Santa Barbara in 1997 and is currently the Undergraduate Vice-Chair in mathematics. He has written two books and has more than 50 other publications including many in leading mathematics journals.

Posted August 28, 2008
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 235

Mihai Putinar, University of California at Santa Barbara
Poincaré's variational problem in potential theory

The simultaneous diagonalization of two quadratic forms naturally attached to a domain in the Euclidean space has guided Poincaré in his study of the Dirichlet problem. Put in modern setting, due to a pioneering work of Mark G. Krein, Poincaré's variational principle offers a deep understanding of modern aspects of function theory (quasiconformal mappings, Beurling-Schiffer transform) and provides the theoretical background of some recent studies of an inverse problem in electrostatics. Based on joint work with D. Khavinson and Harold S. Shapiro.

There will be coffee and cookies in the lounge at 3:00.

Monday, November 3, 2008

Posted October 7, 2008
Last modified October 21, 2008

Algebra and Number Theory Seminar Questions or comments?

11:00 am – 12:00 pm Johnston 338

Zhijun Wu, Iowa State University
Bioinformatics and Biocomputing

Tuesday, November 4, 2008

Posted October 10, 2008
Last modified November 3, 2008

3:40 pm Lockett 276

Alexander Prestel, Universität Konstanz
Representing polynomials positive on a semialgebraic set

Wednesday, November 5, 2008

Posted October 17, 2008
Last modified February 20, 2022

Algebra and Number Theory Seminar Questions or comments?

3:40 pm 232 Lockett

George Cochran, Mathematics Department, LSU
Mathematics and Gambling

Probability theorems are the foundation of an entire industry, which has a reliable and predictable income stream due to the magic of the Law of Large Numbers and the Central Limit Theorem.

Tuesday, November 11, 2008

Posted October 14, 2008
Last modified November 10, 2008

3:40 pm Lockett 235

Piotr Maciak, Mathematics Department, LSU Graduate Student
A short journey from Gaussian integers to Drinfeld modules

Wednesday, November 12, 2008

Posted November 7, 2008

3:40 pm 285 Lcokett

Intersession Courses

A meeting of instructors discussing the future of intersession courses in the department.

Thursday, November 13, 2008

Posted October 27, 2008
Last modified November 3, 2008

3:40 pm – 4:30 pm Lockett 235

Jinhyun Park, Purdue University
What can an algebraist do for Euclidean geometry?

Abstract: The 3rd problem of Hilbert, one of the firstly solved
Hilbert problems, studied the scissors congruence for the
3-dimensional Euclidean space: two polyhedra are said to be in
scissors congruence if one can cut the first along straight lines and
reassemble the components to get the second. Are all polyhedra of a
fixed volume then scissors congruent? The answer was negatively given
by Max Dehn, a student of Hilbert in around 1900. Though the problem
was solved, it opened many new doors during the next 100 years. We
will describe this problem from scratch, and mention how it is related
to some number theoretic questions and how it mysteriously gives new
problems in algebraic geometry.

There will be coffee and cookies in the lounge at 3:00.

Friday, November 14, 2008

Posted November 25, 2008

5:10 pm – 6:00 pm Wednesday, November 12, 2008 285 Lockett Hall

Mark Bilinski, LSU, Mathematics
On the Reconstruction of Planar Graphs

Monday, November 17, 2008

Posted October 1, 2008

3:40 pm – 4:30 pm Lockett 381

Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Unitary Independent Increment Processes and Representations of Hilbert Tensor Algebras

Posted November 3, 2008
Last modified November 7, 2008

3:40 pm – 4:30 pm Room 235 Lockett Hall

Phuc Nguyen, Department of Mathematics, Louisiana State University
Quasilinear and Hessian equations with super-critical exponents and singular data

Tuesday, November 18, 2008

Posted November 11, 2008

3:40 pm – 4:30 pm Lockett 235

Ivo Babuska, Institute for Computational Engineering and Sciences, University of Texas, Austin
Computational Science, Mathematics and Where Are We Going

Abstract: A major goal of Computational Science is to predict physical
and other phenomena. The problem is how confident can we be that the
computed results describe reality well enough so that they can be the
basis for crucial decisions. ( Do we have enough courage to sign the
blueprints based on the computation?) The notions of Verification and
Validation and their mathematical contains will be explained. These
notions are the basis for the confidence that the computed results
could be used for the decisions. A few examples of engineering
accidents and their reasons will be presented. Brief comments of the
repercussions for the educations at the universities will be
made. References to the basic literature will be given.

There will be coffee and cookies in the lounge at 3:00.

Wednesday, November 19, 2008

Posted October 20, 2008
Last modified February 20, 2022

3:40 pm 232 Lockett

Brian Marx, LSU Department of Experimental Statistics
Leonard F. Richardson, Mathematics Department, LSU
Applying to Graduate School

Posted November 17, 2008
Last modified October 1, 2021

3:40 pm – 4:30 pm X-lab: Lockett 233

Lawrence Roberts, Michigan State University
Knot Floer homology for some fibered knots

I will talk about a computing the knot Floer homology of a class of fibered knots in rational homology spheres, for which the computation is particularly simple.

Joint virtual seminar with UIowa, Rice, UMiami, Boise State, GWU .

Friday, November 21, 2008

Posted November 14, 2008

SIAM Student Chapter Event

1:00 pm Johnston 338

Robert Lipton, Mathematics Department, LSU
Shapes with extremal properties

Abstract: Starting with Dido\'s problem the mathematical investigation of extremal shapes has enjoyed a rich history. Here we report on recent work that identifies configurations of materials inside a body which minimize the internal stress when the body is subjected to a simple shear or uniform pressure.

Posted November 25, 2008

5:10 pm – 6:00 pm 285 Lockett Hall

Carolyn Chun, Victoria University in Wellington, New Zealand Former LSU graduate student
A chain theorem for internally 4-connected binary matroids

Monday, November 24, 2008

Posted November 10, 2008
Last modified November 23, 2008

3:40 pm Lockett 9

Meeting of the faculty

Dean Guillermo Ferreyra will meet with the faculty to answer questions and discuss the department\'s upcoming decision of whether to locate the department in A&S or BASC.

Tuesday, November 25, 2008

Posted November 20, 2008

Meeting of the Algebra Faculty

3:40 pm Lockett 276

Planning of graduate courses in algebra for 2009-2010

Monday, December 1, 2008

Posted November 11, 2008

11:00 am – 12:00 pm Johnston Hall 338

Robert M. Kirby, University of Utah
Visualization of High Order Finite Element Methods

Tuesday, December 2, 2008

Posted November 24, 2008

CCT Lecture Events organized by the LSU Center for Computation and Technology

2:00 pm – 3:00 pm 338 Johnston Hall

Robert M. Kirby, University of Utah
Building Symbiotic Relationships Between Formal Verification And High Performance Computing

http://www.cct.lsu.edu/events/talks/437

Posted November 21, 2008

3:10 pm Lockett 5

Meeting of the faculty

Discussion of the department\\\'s upcoming decision of whether to locate the department in A&S or BASC.

Wednesday, December 3, 2008

Posted December 2, 2008

3:40 pm – 4:30 pm X-lab: Lockett 233

Leah Childers, LSU
Birman-Craggs-Johnson Homomorphism of the Torelli Group

Virtual Seminar together with UIowa, Rice University, UMiami, Boise State University, George Washington University

Posted November 24, 2008

3:40 pm – 4:30 pm Lockett 381

Jens Christensen, Mathematics Department, LSU
A Wavelet Decomposition of Besov Spaces on the Forward Light Cone

We will show how the Besov spaces on the Forward Light Cone (defined for general symmetric cones by Bekolle, Bonami, Garrigos and Ricci) can be described using wavelet theory. As part of this description we will discuss work carried out by the presenter and Gestur Olafsson for constructing Banach spaces using representation theory.

Posted November 18, 2008
Last modified February 20, 2022

3:40 pm 232 Lockett

Research Experience for Undergraduates: A Panel Presentation by Faculty and Students

The United States National Science Foundation (NSF) funds many research opportunities for undergraduates through its REU Sites program. An REU Site consists of a group of ten or so undergraduates who work in the research programs of the host institution. Each student is associated with a specific project, where he/she works closely with faculty and other researchers. Students are granted stipends and, in many cases, assistance with housing and travel. Undergraduates supported with NSF funds must be citizens or permanent residents of the United States or its possessions. The speaker will give advice on how to apply for REU jobs.

Professor Hoffman received his PhD in Mathematics from Harvard University and has been at LSU since 1979. He is a noted researcher in algebraic geometry, and is one of three professors who organize the LSU math REU.

Friday, December 5, 2008

Posted December 4, 2008

1:30 pm – 2:30 pm Lockett 233

Alvaro Guevara, Dept of Mathematics, LSU
Mathematical methods in kinesiology and voice analysis: two case studies.

A growing number of research projects have used mathematics as a tool to integrate approaches from many disciplines. Two case studies of this type will be discussed, namely, (1) local stability properties of human gait, and (2) voice data analysis of populations at risk for developing schizophrenia-related disorders. In these projects, mathematical ideas from nonlinear dynamical systems were used in (1), and Shannon entropy and information theory in (2). We will describe our contributions that implemented the theory, and generated effective quantitative tools that provided fresh insights to the researchers of these studies. This research was conducted in the context of the Mathematical Consultation Clinic at LSU. Finally, I will briefly address my dissertation work, involving impulsive solutions to optimal control problems.

Posted December 2, 2008
Last modified December 4, 2008

5:10 pm – 6:00 pm Lockett 285

Xingxing Yu, Georgia Institute of Technology
Judicious partitions of hypergraphs

Abstract: Judicious partition problems on graphs and hyper graphs ask for partitions that optimize several quantities simultaneously. In this talk Professor Yu will discuss several judicious partition problems for hyper graphs, and present several results on hyper graphs whose edges have size at most 3. He will also outline the martingale approach for proving these results.

Monday, December 8, 2008

Posted November 19, 2008
Last modified December 5, 2008

3:40 pm – 4:30 pm Lockett 285

Stephen Shipman, Mathematics Department, LSU
Field sensitivity to L^p perturbations of a scatterer

This will be an informal presentation as part of the weekly material science discussion group. I will discuss the title problem and some related problems I would like to solve.

Wednesday, December 10, 2008

Posted December 1, 2008
Last modified December 9, 2008

12:00 pm James Keisler Lounge

Holiday Party

Everyone is invited to share in the Season\'s Spirit. Please bring a dish to share.

Tuesday, January 6, 2009

Posted October 27, 2008
Last modified December 12, 2008

1:00 pm – 4:00 pm 285 Lockett

Comprehensive/PhD Qualifying Exam in Algebra

This test is part of the PhD Qualifying Examination in Mathematics, and it can serve also as part of the written test for the non-thesis MS degree.

Wednesday, January 7, 2009

Posted October 27, 2008

1:00 pm – 4:00 pm 285 Lockett

Comprehensive/PhD Qualifying Exam in Analysis

This test is part of the PhD Qualifying Exam in Mathematics, and it can serve also as part of the written exam for the non-thesis MS degree.

Friday, January 9, 2009

Posted October 27, 2008

1:00 pm – 4:00 pm 285 Lockett

Comprehensive/PhD Qualifying Exam in Topology

This test is part of the PhD Qualifying Exam in Mathematics. It can serve also as part of the Final Exam for the non-thesis MS degree.

Thursday, January 15, 2009

Posted December 8, 2008
Last modified December 12, 2008

3:40 pm – 4:30 pm Lockett 285 (provisionally)

Burak Aksoylu, Department of Mathematics and CCT
Rigorously Justified Solvers for Rough Coefficients

Abstract:
Roughness of PDE coefficients causes loss of robustness of
preconditioners. The main goal is to recover robustness and obtain
rigorous structural understanding of the involved process. A
qualitative understanding of the PDE operators and their dependence on
the coefficients is essential for designing preconditioners. This
process draws heavily upon effective utilization of theoretical tools.

According to experience, the performance of a preconditioner depends
essentially on the degree to which the preconditioned operator
approximates the properties of the underlying infinite dimensional
operator. For this reason, controlling the infinite dimensional
problem provides a basis for the construction of preconditioners. We
use tools from operator theory for this. On the other hand, another
basis is the control of the finite dimensional discretized
problem. For that, we use singular perturbation analysis (SPA). After
obtaining a preconditioner through SPA, a fundamental need is to
explain the effectiveness of the preconditioner and to justify that
rigorously. With the insights provided by operator theory and SPA, we
are in control of the effectiveness and computational feasibility
simultaneously.

Based on ideas developed for porous media flow, we present a new
preconditioning strategy which is computationally comparable to
algebraic multigrid, but with rigorous justification. We will also
demonstrate how SPA gives valuable insight to the asymptotic behavior
of the solution of the underlying PDE, hence, provides feedback for
preconditioner construction.

There will be coffee and cookies in the lounge at 3:00.

Friday, January 16, 2009

Posted January 12, 2009
Last modified February 20, 2022

3:40 pm

Stephen Shipman, Mathematics Department, LSU
Discrete Dynamics, Chaos, and a Connection to Number Theory

The connection is the Möbius transform. We begin with the sequence 1, 2, 6, 12, 30, 54, 126, 240, 504, 990, … and find out how it is generated and what it means in terms of a simple discrete dynamical system on the unit circle.

Wednesday, January 21, 2009

Posted December 4, 2008
Last modified January 21, 2009

Student Colloquium Speaker

3:40 pm – 4:30 pm Lockett 9

Thomas Struppeck, Casualty Actuarial Society
Career Opportunities for Mathematicians in Insurance and Finance

What opportunities in the finance arena are there today for mathematics majors? Hs the collapse of the mortgage market (and several large hedge funds) reduce the demand for 'quants'? Where could graduating undergraduate mathematics majors look for jobs? How about graduate students?

This talk will try and shed some light on these and related questions. A good way to break into these fields is through the actuarial exams. Of course, the actuarial exams can also lead to a career as a traditional actuary in addition to opening doors into related fields.

There will be time for questions at the end of the talk.

Thursday, January 22, 2009

Posted December 4, 2008
Last modified January 21, 2009

Student Colloquium Speaker

3:40 pm – 4:30 pm Lockett 2

Thomas Struppeck, Casualty Actuarial Society
The Mathematics of the Sub-Prime Meltdown

Asset backed securities: Collateralized Debt Obligations
Or
How to take some bad loans, assemble them into a pile, and almost bring down the world's financial system.

Years ago banks sought out deposits and then lent the money out to homebuyers. More recently, banks found that they made most of their money at the time that the loan was made, so they changed how they did business. They started selling their loans to investors shortly after making them. This gave the banks their money back immediately so they could quickly lend money to another homebuyer. This was a good thing, because it increased the number of loans being made to homebuyers. It also greatly increased the supply of loans for investors. Wall Street bankers found ways to package these loans so that they could be sold to investors. In this talk we will look at some of the mathematics behind how these packages work (and how they didn't work).

Now knowledge of financial mathematics will be assumed.

Friday, January 23, 2009

Posted October 19, 2008
Last modified January 13, 2009

CCT Lecture Events organized by the LSU Center for Computation and Technology

2:30 pm – 3:30 pm Coates Hall 145

Linda Petzold, UC Santa Barbara Member, National Academy of Engineering
Multiscale Simulation Of Biochemical Systems

rescheduled from September 5, 2008

In microscopic systems formed by living cells, the small numbers of some reactant molecules can result in dynamical behavior that is discrete and stochastic rather than continuous and deterministic. An analysis tool that respects these dynamical characteristics is the stochastic simulation algorithm (SSA). Despite recent improvements, as a procedure that simulates every reaction event, the SSA is necessarily inefficient for most realistic problems. There are two main reasons for this, both arising from the multiscale nature of the underlying problem: (1) the presence of multiple timescales (both fast and slow reactions); and (2) the need to include in the simulation both chemical species that are present in relatively small quantities and should be modeled by a discrete stochastic process, and species that are present in larger quantities and are more efficiently modeled by a deterministic differential equation. We will describe several recently developed techniques for multiscale simulation of biochemical systems, and outline some of the future challenges. Complete details can be found at http://www.cct.lsu.edu/events/talks/448

Monday, January 26, 2009

Posted January 13, 2009
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

2:30 pm – 3:30 pm Coates Hall 145

Margaret Wright, New York University Member, National Academy of Sciences, National Academy of Engineering
What Can Be More Important Than "Faster" And "Bigger"?

For decades, the high-end computing community has come to expect continuing gains in the speed of computation and the size of data storage, and these expectations have consistently been fulfilled in remarkable ways. But \"faster\" and \"bigger\" are not the only things that count. We\'ll show how other factors, such as advances in mathematics and theoretical computer science, are just as important, leading to the obvious conclusion that an optimal strategy needs to be \"faster, bigger, and smarter.\"

Complete details can be found at http://www.cct.lsu.edu/events/talks/450

Tuesday, January 27, 2009

Posted December 8, 2008
Last modified January 27, 2022

3:40 pm – 4:30 pm Lockett 285 (provisionally)

Michael Shapiro, Escuela Superior de Fisica y Matematicas del Instituto Politecnico Nacional, Mexico
On some basic ideas of hypercomplex analysis

“Hypercomplex analysis” is a generic name for those generalizations of one-dimensional complex analysis which involve hypercomplex numbers. Quaternionic analysis is the oldest and the most known version of it. In the talk, it will be discussed, first of all, in which sense quaternionic analysis is a “proper” or a “closest” version in low dimensions which includes as particular cases, or sub-theories, such classic theories as vector analysis and holomorphic mappings in two complex variables, as well as some systems of partial differential equations. This allows one, by developing quaternionic analysis, to obtain new results for the above classic theories and to refine known ones; some applications of this approach to harmonic analysis, operator theory, mathematical physics, will be mentioned. Some comments on Clifford analysis and its applications will be also made.

There will be coffee and cookies in the lounge at 3:00.

Thursday, January 29, 2009

Posted December 8, 2008
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 285 (provisionally)

Maria Elena Luna-Elizarraras, Escuela Superior de Fisica y Matematicas del Instituto Politecnico Nacional, Mexico
On functional analysis with quaternionic scalars

There will be coffee and cookies in the lounge at 3:00.

Friday, January 30, 2009

Posted January 28, 2009
Last modified February 20, 2022

3:40 pm – 4:30 pm Keisler Lounge, Lockett 321

Movie: "Music of the Primes: From Riemann to Ramanujan"

“With the advent of Bernhard Riemann's zeta-hypothesis, the study of prime numbers took on astonishing new dimensions—including a way to predict the appearance of primes. … Using state-of-the-art 3D animation, the film guides viewers through the zero-punctuated pattern [of the zeta-function] that Riemann unveiled. It also describes the friendship between G. H. Hardy and Srinivasa Ramanujan and the difficulties both men experienced as they confronted problems in number theory.” (from the DVD jacket)

There will be food.

Math Club webpage

Monday, February 2, 2009

Posted January 13, 2009

2:00 pm – 3:00 pm Johnston Hall 338

Jack Dongarra, University Of Tennessee And Oak Ridge National Laboratory Member, National Academy of Engineering
An Overview Of High Performance Computing And Challenges For The Future

In this talk we examine how high performance computing has changed over the last 10-year and look toward the future in terms of trends. These changes have had and will continue to have a major impact on our software. A new generation of software libraries and algorithms are needed for the effective and reliable use of (wide area) dynamic, distributed and parallel environments. Some of the software and algorithm challenges have already been encountered, such as management of communication and memory hierarchies through a combination of compile--time and run--time techniques, but the increased scale of computation, depth of memory hierarchies, range of latencies, and increased run--time environment variability will make these problems much harder. We will focus on the redesign of software to fit multicore architectures. Additional details can be found at http://www.cct.lsu.edu/events/talks/449

Friday, February 6, 2009

Posted January 29, 2009
Last modified March 3, 2021

2:40 pm – 3:30 pm Lockett 381

Dimitar Grantcharov, University of Texas, Arlington
Weight Modules of Affine Lie Algebras

The problem of classifying irreducible weight modules with finite dimensional weight spaces over affine Lie algebras has been studied actively or the last 20 years. Remarkable results include the classification of integrable modules by V. Chari, the study of parabolically induced modules by V. Futorny, and the study of weight modules with bounded weight multiplicities by D. Britten and F. Lemire. There are two important classes of irreducible weight modules with finite dimensional weight spaces: the parabolically induced modules and the loop modules. Several authors made conjectures that would imply that these exhaust all irreducible weight modules with finite dimensional weight spaces. In a joint work with I. Dimitrov we confirm that these conjectures are correct and as a result obtain the classification. In this talk we will present the main ideas and results from our joint work.

Tuesday, February 10, 2009

Posted January 13, 2009
Last modified February 9, 2009

3:10 pm LOCKETT 232

Meeting of the Tenured Faculty

Consideration of a contract renewal to tenure.

Wednesday, February 11, 2009

Posted February 10, 2009
Last modified October 1, 2021

3:40 pm – 4:40 pm Lockett 233

Chad Giusti, University of Oregon
Virtual Seminar: Unstable Vassiliev Theory

This week's AccessGrid virtual seminar will be presented locally by Chad Giusti.

Monday, February 16, 2009

Posted November 24, 2008
Last modified January 13, 2009

11:00 am – 12:00 pm Johnston Hall 338

Marsha Berger, Courant Institute Member, National Academy of Science and National Academy of Engineering
Computing Fluid Flows In Complex Geometry

We give an overview of the difficulties in simulating fluid flow in complex geometry. The principal approaches use either overlapping or patched body-fitted grdis, unstructured grids, or Cartesian (non-body-fitted) grids, with our work focusing on the latter. Cartesian methods have the advantage that no explicit mesh generation is needed, greatly reducing the human effort involved in complex flow computations. However it is a challenge to find stable and accurate difference formulas for the irregular Cartesian cells cut by the boundary. We discuss some of the steps involved in preparing for and carrying out a fluid flow simulation in complicated geometry. We present some of the technical issues involved in this approach, including the special discretizations needed to avoid loss of accuracy and stability at the irregular cells, as well as how we obtain highly scalable parallel performance. This method is in routine use for aerodynamic calculations in several organizations, including NASA Ames Research Center. Many open problems are discussed. Additional details can be found at http://www.cct.lsu.edu/events/talks/443

Refreshments will be served at 10:30.

Wednesday, February 18, 2009

Posted February 17, 2009
Last modified October 1, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 233 Lockett

Scott Baldridge, Louisiana State University
Virtual Seminar: Cube knots and knot Floer homology from cube diagrams

This week's AccessGrid virtual seminar will be presented locally by Scott Baldridge.

Posted February 10, 2009
Last modified February 12, 2009

SIAM Student Chapter Event

4:00 pm Johnston Hall 338

Stephen Shipman, Mathematics Department, LSU
Radiation conditions in wave scattering

Abstract: Correct physical and mathematical formulation of problems of scattering of waves by an obstacle requires a precise condition characterizing the scattered, or diffracted wave. For bounded obstacles, this condition is the Sommerfeld radiation condition (Helmholtz equation) or the Silver-Muller condition (Maxwell system). For unbounded obstacles, the condition is not always so obvious. A radiation condition takes on various forms, such as (1) an asymptotic outgoing condition for the far field, (2) a nullspace condition involving the Calderon boundary-integral projectors, and (3) a Dirchlet-to-Neumann map, appropriate for variational formulations of the PDE.

Thursday, February 26, 2009

Posted February 17, 2009
Last modified February 18, 2009

Student Seminar/SIAM Student Chapter

4:00 pm Lockett Hall 233

Yue Chen, Mathematics Department, LSU
Optimal lower bounds on the strain and stress inside prestressed, random two-phase elastic composites

I will present the optimal lower bounds for the L^p norm of pre-stress inside random media, and also give the microstructure which attains some optimal lower bounds. This is the research work under the direction of Prof. Lipton.

Tuesday, March 3, 2009

Posted February 27, 2009

3:40 pm – 4:30 pm Lockett 285

Robert Perlis, Mathematics Department, LSU
The 1-2-3's of Zeta functions of Graphs

In 1968, Ihara introduced the zeta function of a finite graph, with important contributions coming later in papers of Hashimoto, Bass, and Stark and Terras. More recently Mizuno and Sato considered the zeta function of a fully directed graph. (Zeta functions are proliferating like kudzu! Somebody, please make them stop!) In 2003, Sato found a rational expression for the zeta function of a connected, simple, partially directed graph.
This talk will be an elementary introduction to the subject of zeta functions of graphs (undirected, fully directed, partially directed) and end with a new theorem giving an Ihara-type formula for the zeta function of any partially directed graph without Sato's assumptions of connected and simple.

Thursday, March 5, 2009

Posted February 26, 2009

LSU AWM Student Chapter LSU AWM Student Chapter Website

12:30 pm – 2:00 am Keisler Lounge Room 321

Welcome Event

For more info: http://www.math.lsu.edu/awm/images/AWM.pdf

Posted February 2, 2009
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 285

Stephen Sawin, Fairfield University
Supersymmetry, Quantum Mechanics and the Gauss-Bonnet-Chern Theorem

In joint work with Dana Fine at UMass Dartmouth, we will give a rigorous construction of the path integral describing the time-evolution operator for imaginary time quantum mechanics, with and without $N=1$ supersymmetry. The path integral is constructed as a limit of finite-dimensional approximating integrals, with concrete uniform estimates on the convergence. Consequences of this include an alternative construction of the Laplace and Laplace–Beltrami heat kernels. We will use this construction to give a rigorous version of Witten–Alvarez-Gaumé–Friedan and Windey's path integral "proof" of the Gauss–Bonnet–Chern Theorem, and explain how we expect a minor variation to make rigorous their proof of the general Index Theorem.

There will be coffee and cookies in the lounge at 3:00.

Monday, March 9, 2009

Posted February 26, 2009

SIAM Student Chapter Event

11:00 am Johnston Hall 338

Blaise Bourdin, Department of Mathematics and Center for Computation & Technology, LSU
A Panorama of the Variational Approach to Fracture

Fracture Mechanics may be viewed as a grand success of the last century: planes do not fall out of the sky, ships do not split in two, and buildings don't collapse. Yet, unexpected dramatic failures remind us that all is not fully understood. In this talk, I will briefly describe the achievements and open issues of the classical methods for Fracture Mechanics. Then, I will present a variational approach originally devised by G.A. Francfort and J.-J. Marigo, and based on the concept of competition between bulk and surface energy. I will illustrate the numerical implementation of the model by numerical experiments in 2 and 3 dimensions. In the last part of my talk, I will describe open research opportunities in the form of several possible extensions and applications of the model.

Thursday, March 12, 2009

Posted February 19, 2009
Last modified March 3, 2009

3:40 pm – 4:30 pm Lockett 285

Charles Livingston, Indiana University
Four-dimensional aspects of classical knot theory

Abstract: Classical knot theory studies knots in 3-space; that is, embeddings of the unit circle, S^1, into R^3. Higher dimensional knot theory generalizes this, for instance by considering embeddings of the 2-sphere, S^2, into R^4. In this talk I will discuss an aspect of knot theory between the low and high-dimensional realms: the study of knots in 3-space in terms of the surfaces they bound in upper 4-space, H^4, the set of points (x,y,z,w) in R^4 with w > 0. Three of the goals of the presentation will be to: (1) give some intuitive insight into how knots can bound such surfaces; (2) describe a few of the central topics in geometric topology that motivate looking at knots in this way; and (3) summarize some recent advances in the area.

There will be coffee and cookies in the lounge at 3:00.

Friday, March 13, 2009

Posted February 11, 2009

3:40 pm – 4:30 pm

Monica Torres, Department of Mathematics, Purdue University
The structure of solutions of systems of hyperbolic conservation laws

Hyperbolic systems of conservations laws model many areas of physics, including fluid mechanics, acoustics, etc. One of the main challenges in the analysis of these equations is that solutions develop singularities even if the initial data is smooth. These singularities are known as shock waves. Existence theorems only show that entropy solutions belong to some $L^p$ space and satisfy an entropy inequality in the distributional sense. Therefore, an open problem is to study the structure of solutions and regularity of the shock waves. In this talk we present results in this direction, which include some Liouville-type results for systems of conservation laws.

Tuesday, March 17, 2009

Posted February 10, 2009
Last modified February 19, 2009

3:40 pm – 4:30 pm Lockett 285

Stratos Prassidis, Canisius College
Detecting Linear Groups

Abstract: Linear groups are subgroups of general linear groups. Deciding if
a group is linear or not is an old problem in group theory. Linear groups
became important in topology after the Isomorphism Conjecture was proved for
discrete linear groups. We present criteria that guarantee that a group is
linear and some applications. At the end, we will show a hands-on proof that
the holomorph of the free group on two generators is linear.

There will be coffee and cookies in the lounge at 3:00.

Wednesday, March 18, 2009

Posted February 7, 2009

Student Colloquium Speaker

3:40 pm – 4:30 pm Lockett 285

Mark Sepanski, Mathematics Department, Baylor University
Just Can't Stop Counting

We all begin our mathematical life by studying the integers. And while the integers are pretty cool, you can only multiply so many seven digit numbers before you call it quits and move on to the rational numbers. After that, you hit the real numbers and eventually move on to the complex numbers. But what comes next--if anything? In this talk we'll give one version of the answer to this question.

Thursday, March 19, 2009

Posted February 7, 2009
Last modified March 13, 2009

Student Colloquium Speaker

12:00 pm – 1:00 pm Keisler Lounge

Mark Sepanski, Mathematics Department, Baylor University
Why Torture Us With Proofs?

In this discussion, we\'ll look at a number of obviously true patterns and theorems. Unfortunately, some of these obvious results turn out to be quite false! As a result, we\'ll see why mathematicians blab so incessantly about proofs.

Posted February 2, 2009
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 285

Jiazu Zhou, Southwest University, China
Geometric measures and geometric inequalities

There will be coffee and cookies in the lounge at 3:00.

Friday, March 20, 2009

Posted February 19, 2009
Last modified March 3, 2021

2:40 pm – 3:30 pm Lockett 381

Martin Laubinger, University of Münster
Groups acting on Trees

The action of $SL(2,\R)$ on the upper half plane is an important tool in the representation theory of $SL(2,\R)$. We explain the $p$-adic analogue, which is an action of $SL(2,Q_p)$ on a tree. This tree is one of the simplest examples of a Bruhat-Tits building. We mention some applications of this action, as well as a generalization: if $K$ is a field with valuation taking values in any ordered abelian group, one can still define a 'tree' associated with $SL(2,K)$.

Tuesday, March 24, 2009

Posted January 20, 2009

Algebra and Number Theory Seminar Questions or comments?

12:00 pm – 1:00 pm Lockett 301D---Conference Room

Final Event of Final Exam for Non-Thesis MS

Each student applying to receive an MS in May 2009 must sign up also with the Graduate School for the final exam final event as listed here. The Committee will be Profs. Richardson (Chair), Dasbach, and He.

Posted March 12, 2009
Last modified May 8, 2021

3:40 pm – 4:30 pm Lockett 235

Robert Peck, Department of Music, Louisiana State University
Applications of Wreath Products to Music Theory

Wreath products are familiar structures in mathematics, but they are relatively new to music theory. This study proposes an investigation into the musical relevance of wreath products, drawing on examples from selected musical literature of the nineteenth and twentieth centuries. We begin by examining a few commonly used groups in music theory, and observe how we may use permutation isomorphism to relate certain orbit restrictions of these groups. Next, we define a direct product of such orbit restrictions. Finally, we allow a permutation of the orbit restrictions themselves, which yields a wreath product. We include examples from Robert Schumann's “Im wunderschönen Monat Mai,” from Dichterliebe, op. 48; Richard Wagner's Siegfried; and Anton Webern's Cantata, op. 29.

Friday, March 27, 2009

Posted March 20, 2009
Last modified March 3, 2021

LSU AWM Student Chapter LSU AWM Student Chapter Website

3:40 pm – 4:30 pm Lockett 381
(Originally scheduled for Monday, March 23, 2009)

Daniel Sage, Mathematics Department, LSU
An explicit basis of lowering operators for irreducible representations of unitary groups

It is well-known that the dimensions of irreducible representations of unitary groups can be computed in terms of Young tableaux. More specifically, each irreducible representation contains a unique highest weight which may be interpreted as a Young diagram, and the dimension of any weight space of this representation is given by the number of semistandard Young tableaux with content determined by the weight. In the usual Lie-theoretic construction of these representations as highest-weight modules, it is easy to see that a spanning set for each representation is obtained by applying lowering operators to the highest weight vector; however, extracting a basis from this spanning set is less straightforward. In this talk, I describe a general method for finding such bases. In particular, I show how to associate a monomial lowering operator to any semistandard tableau in such a way that the lowering operators corresponding to the semistandard tableaux of shape l and content m give rise to a basis for the m-weight space of the irreducible representation with highest weight l. This work is joint with Larry Smolinsky.

Tuesday, March 31, 2009

Posted March 20, 2009

9:30 am – 10:30 am Room 331 Johnston Hall

Conversation with Prof. Lisa Fauci

Prof. Lisa Fauci from Tulane University is visiting LSU on March 31st. The Chapter members are invited to meet with her from 9:30-10:30a.m in Johnston Hall Room 331. Refreshments will be served.

Posted March 13, 2009

11:00 am – 12:00 pm Johnston Hall 338

Lisa Fauci, Tulane University
Interaction of Elastic Biological Structures with Complex Fluids

Posted March 5, 2009
Last modified February 20, 2022

Algebra and Number Theory Seminar Questions or comments?

2:00 pm – 3:00 pm Keisler Lounge, Lockett Hall 321

Victor Moll, Department of Mathematics, Tulane University
What do I learn if I decide to compute integrals?

The study of the evaluation of definite integrals is full of surprises. This talk will present some of them in relation to Dynamical Systems, Number Theory, and Combinatorics. The first example deals with the rational integral \[N_{0,4}(a;m) := \int_0^∞ \frac{dx}{(x^4+2ax^2+1)^{m+1}}.\] The numbers \[d_l(m) := 2^{−2m} \sum_{k=l}^m 2^k {2m-2k \choose m-k} {m+k \choose k} {k \choose l} \] play an important role in its evaluation.

The sequence $\{d_l(m) : 0 ≤ l ≤ m \}$ has many intriguing properties, some of which remain to be decided. (=Looking for collaborators).

Here is a nice non-linear dynamical system \[ \begin{split} a &\mapsto \frac{ab+5a+5b+9}{(a+b+2)^{4/3}}\\ b &\mapsto \frac{a+b+6}{(a+b+2)^{2/3}}\\ \end{split} \] Where do these formulas come from? Integrals, of course.

Posted March 25, 2009

3:40 pm – 4:30 pm Lockett 285

Augusto Nobile, Mathematics Department, LSU
Algorithmic resolution and equiresolution of singularities

We\'ll review the theory of algorithmic (or constructive) resolution of singularities of algebraic varieties (and some related objects) in characteristic zero and discuss the problem of simultaneous resolution when we have a family, in a way compatible with a chosen resolution algorithm (even in the case when the parameter space is not reduced, e.g. the spectrum of an Artinian ring).

Thursday, April 2, 2009

Posted March 26, 2009

3:40 pm – 4:30 pm Lockett 285

Gregor Masbaum, University Paris 7
Trees , Pfaffians and Complexity (or How not to win a million dollars)

There will be coffee and cookies in the lounge at 3:00.

Monday, April 13, 2009

Posted March 30, 2009
Last modified April 13, 2009

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm Lockett 301D (Conference Room)

Jeremy Becnel, Stephen F. Austin State University
Forming the Radon Transform and Support Theorem in Infinite Dimensions

Tuesday, April 14, 2009

Posted April 13, 2009

3:40 pm – 4:30 pm Lockett 285

Augusto Nobile, Mathematics Department, LSU
Algorithmic resolution and equiresolution of singularities II

Wednesday, April 15, 2009

Posted March 5, 2009

1:00 pm – 2:00 pm Johnston Hall 338

Claude Le Bris, ENPC and INRIA, France
Computational Multiscale Mechanics: A Mathematical Perspective

The talk will overview recent progress in the mathematical understanding of numerical approaches coupling an atomistic and a continuum description of matter. The talk is based upon a series of works in collaboration with X. Blanc (Univ Paris 6), F. Legoll (ENPC), P.-L. Lions (College de France). The perspective is mathematical. The purpose is to describe the theoretical tools and concepts that allow for a better foundation of the numerical approaches. It is also to point out some important unsolved mathematical issues.

Thursday, April 16, 2009

Posted April 14, 2009

Communicating Mathematics Talk First-year graduate student presentation

3:15 pm – 3:35 pm 235 Lockett Hall

Irina Craciun, Department of Mathematics, LSU Graduate Student
The Wirtinger Presentation of Knot Groups

Posted March 30, 2009
Last modified March 31, 2009

3:30 pm – 5:30 pm Lockett Hall, Room 2 (Basement)

Career Day Event

The LSU Student Chapter of the Association for Women in Mathematics, the LSU Chapter of the Society of Industrial and Applied Mathematics, and the Mathematics Department are cosponsoring a Career Day for the Mathematics Graduate Students. The goal is to give advice to students about the job application process and career options.

Posted April 14, 2009

Communicating Mathematics Talk First-year graduate student presentation

3:35 pm – 3:55 pm 235 Lockett Hall

Matthew Dawson, Centro de Investigacion en Matematicas
Cluster Sets: How Bad Can the Discontinuities Be?

Posted April 14, 2009

Communicating Mathematics Talk First-year graduate student presentation

3:55 pm – 4:15 pm 235 Lockett Hall

Ying Hu, Department of Mathematics, LSU Graduate Student
The Classification of G-Coverings

Posted April 14, 2009

Communicating Mathematics Talk First-year graduate student presentation

4:15 pm – 4:35 pm 235 Lockett Hall

Dennis Hall, Department of Mathematics, LSU Graduate Student
Introduction to Knot Theory and the Jones Polynomial

Monday, April 20, 2009

Posted March 16, 2009
Last modified April 13, 2009

11:00 am – 12:00 pm

Luke Owens, Texas A&M University
Solving the Eikonal equation on adaptive triangular and tetrahedral meshes

Posted March 6, 2009
Last modified March 31, 2009

Student Colloquium

12:30 pm – 1:30 pm Keisler Lounge

Carlos Castillo-Chavez, Arizona State University Regents and Juaquin Bustov Jr. Professor
Opportunities in the Mathematical Sciences: What should I study if I am interested in interdisciplinary research?

A recent article in the Wall Street Journal reported that the best career is that of a mathematician. Why is this so? Why is the training in mathematics so critical? And what do we mean by mathematical training? In this lecture, I will provide some personal responses to the above questions and show the advantages of redirecting mathematics training from what I have learned in the context of undergraduate and graduatte research.

Posted March 6, 2009
Last modified March 31, 2009

Student Colloquium

2:40 pm – 3:30 pm Lockett 5

Carlos Castillo-Chavez, Arizona State University Regents and Juaquin Bustov Jr. Professor
Mathematical Epidemiology: Challenges and Opportunities

We hear almost daily about the dangers of potential bird \"flu\" epidemics, the risk of catching deadly diseases in hospitals, or the level of preparedness that our country has as it plans its responses to the dangers posed by the deliberate releases of biological agents. We also hear about new medical advances that include the development of new vaccine including the rotavirus vaccine as well as the continuous search for ways of fighting HIV.

In this lecture, I will discuss the role that modeling and the mathematical sciences have played in the study of the dynamics and control of infectious diseases. I will briefly review the history of mathematical and theoretical epidemiology which goes back to the times of the Bernoulli family and highlight some current application in the context of specific diseases. This lecture should be of interest to mathematicians interested in applications as well as to biologists and social scientists interested in the development and testing of intervention strategies

Posted January 20, 2009
Last modified April 17, 2009

3:40 pm – 4:30 pm Lockett Hall 285

David Dobson, Department of Mathematics, University of Utah
Electromagnetic transmission resonances in periodic hole arrays

Recently there has been increasing interest in terahertz-frequency electromagnetic radiation in the engineering community. Improved methods of generating such radiation has led to hopes of applications in communications, imaging, and spectroscopy. Unfortunately almost all materials are highly absorptive in the terahertz range, making device design difficult. One method of manipulating terahertz radiation is by filtering through thin, perforated metal plates. Such plates exhibit interesting, and sometimes unexpected transmission properties. The transmission spectrum depends strongly on both the hole pattern and the aperture shape. This talk will describe some work on developing a model for transmission through periodic hole arrays, including analysis and numerical methods. We conclude with some preliminary work on the problem of optimal design of aperture shape to produce a desired transmission spectrum.

Host: Stephen Shipman

Tuesday, April 21, 2009

Posted March 30, 2009

SIAM Student Chapter Event

8:30 am – 10:00 am Keisler Lounge, Lockett Hall 321

Carlos Castillo-Chavez, Arizona State University Regents and Juaquin Bustov Jr. Professor
Conversation with Prof. Carlos Castillo-Chavez

Prof. Carlos Castillo-Chavez from Arizona State University is visiting LSU on April 20th-21st. The SIAM Chapter members and all graduate students in math department are invited to meet with him from 8:30-10:00a.m in Keisler Lounge, Lockett Hall 321. Refreshments will be served.

Posted April 21, 2009

Communicating Mathematics Talk First-year graduate student presentation

3:15 pm – 3:35 pm 235 Lockett Hall

Jacob Aguilar, Department of Mathematics, LSU Graduate Student
The Sensitivity of Linear Systems

Posted April 16, 2009

3:30 pm Lockett 284

Meeting of the full professors

Promotion case.

Posted April 21, 2009

Communicating Mathematics Talk First-year graduate student presentation

3:35 pm – 3:55 pm 235 Lockett Hall

Sen Yang, Department of Mathematics, LSU Graduate Student
Bezout Theorem

Posted April 21, 2009

Communicating Mathematics Talk First-year graduate student presentation

3:55 pm – 4:15 pm 235 Lockett Hall

Adam Cross, Department of Mathematics, LSU Graduate Student
Non-Associative Addition and Non-Euclidean Geometry

Posted April 21, 2009

Communicating Mathematics Talk First-year graduate student presentation

4:15 pm – 4:35 pm 235 Lockett Hall

Yunyun Yang, Department of Mathematics, LSU Graduate Student
Introduction to Clifford Algebra

Thursday, April 23, 2009

Posted April 12, 2009
Last modified October 4, 2021

2:40 pm – 3:30 pm Lockett 285
(Originally scheduled for Monday, April 20, 2009)

Ivan Dimitrov, Queen's University (Canada)
A geometric realization of extreme components of the tensor product of modules over algebraic groups

In this talk I will explain how the celebrated theorem of Borel–Weil–Bott provides a natural realization of some extreme components of the tensor product of two irreducible modules of simple algebraic groups. I will also discuss a number of connections of our construction with problems coming from Representation Theory, Combinatorics, and Geometry, including questions about the Littlewood–Richardson cone related to Horn's conjecture, settled by Knutson and Tao in the late 1990s.

The talk is based on a joint work with Mike Roth.

There will be coffee and cookies in the lounge at 2:00.

Posted April 23, 2009

Communicating Mathematics Talk First-year graduate student presentation

3:15 pm – 3:35 pm 235 Lockett Hall

Joel Geiger, Department of Mathematics, LSU Graduate Student
Introduction to Knot Theory: Knot Invariants

Posted April 23, 2009

Communicating Mathematics Talk First-year graduate student presentation

3:35 pm – 3:55 pm 235 Lockett Hall

Xinyao Yang, Department of Mathematics, LSU Graduate Student
Introduction to Free Probability Theory

Posted April 23, 2009

Communicating Mathematics Talk First-year graduate student presentation

3:55 pm – 4:15 pm 235 Lockett Hall

Daniel Guillot, Department of Mathematics, LSU Graduate Student
Coloring Graphs of Thickness t

Friday, April 24, 2009

Posted April 22, 2009
Last modified February 20, 2022

3:30 pm Keisler Lounge, Lockett Hall 321

Math Movie

We will vote for either “Fermat\'s Room” or a BBC documentary. Pizza and popcorn will be served.

Monday, April 27, 2009

Posted March 13, 2009
Last modified March 15, 2009

3:40 pm – 4:30 pm

Tadele Mengesha, Louisiana State University
TBA

Posted April 13, 2009

3:40 pm – 4:30 pm Lockett 285

Tadele Mengesha, Louisiana State University
Sufficient conditions for smooth strong local minima

The talk addresses the conjecture that uniform quasiconvexity and uniform positivity of the second variation are sufficient for a smooth extremal to be a strong local minimizer. Our result holds for a class of variational integrals with integrands of polynomial growth at infinity. The proof is based on the decomposition of an arbitrary variation into its purely strong and weak parts. We show that these two parts act independently on the functional. The action of the weak part can be described in terms of the second variation. While the uniform positivity of the second variation prevents the weak part from decreasing the functional, the uniform quasiconvexity conditions prevent the strong part from doing the same. This is a joint work with Yury Grabovsky.

Tuesday, April 28, 2009

Posted April 23, 2009

IGERT Seminar Series

3:00 pm 338 Johnston Hall

Miroslav Krstic, University of California, San Diego IEEE Fellow
Compensation of Long Input Delays for Unstable Nonlinear and PDE Systems

Here is an abstract.

Posted April 30, 2009

Communicating Mathematics Talk First-year graduate student presentation

3:15 pm – 3:35 pm 235 Lockett Hall

Laura Rider, Department of Mathematics, LSU Graduate Student
Introduction to Varieties

Posted April 30, 2009

Communicating Mathematics Talk First-year graduate student presentation

3:35 pm – 3:55 pm 235 Lockett Hall

Dongxiang Yan, Department of Mathematics, LSU Graduate Student
An Introduction to Black-Scholes Option-Pricing Model

Posted April 30, 2009

Communicating Mathematics Talk First-year graduate student presentation

3:55 pm – 4:15 pm 235 Lockett Hall

B. Nicholas Wahle, Department of Mathematics, LSU Graduate Student
When is K_{1,n} not a Minor?

Posted April 30, 2009

Communicating Mathematics Talk First-year graduate student presentation

4:15 pm – 4:35 pm 235 Lockett Hall

Yi Zhang, Department of Mathematics, LSU Graduate Student
The Cauchy Functional Equation

Wednesday, April 29, 2009

Posted April 20, 2009
Last modified March 3, 2021

2:40 pm – 3:30 pm Lockett 381

Boris Rubin, Louisiana State University
Comparison of volumes of convex bodies in real, complex, and quaternionic spaces

The classical Busemann-Petty problem (1956) asks, whether origin-symmetric convex bodies in $R^n$ with smaller hyperplane central sections necessarily have smaller volumes. The answer is known to be affirmative if $n\le 4$ and negative if $n>4$. The same question for equilibrated convex bodies in the $n$-dimensional complex space $C^n$ has an affirmative answer if and only if $n\le 3$. We show that the similar problem in the $n$-dimensional quaternionic space $H^n$ has an affirmative answer if and only if $n=2$. Our method relies on the properties of Radon and cosine transforms on the unit sphere.

Posted March 24, 2009

3:30 pm The James Kiesler Lounge 319 Lockett Hall

Spring Math Awards Ceremony

Thursday, April 30, 2009

Posted April 30, 2009

Communicating Mathematics Talk First-year graduate student presentation

3:15 pm – 3:35 pm 235 Lockett Hall

Jesse Taylor, Department of Mathematics, LSU Graduate Student
Nowhere-Zero Flows in Graphs

Posted April 30, 2009

Communicating Mathematics Talk First-year graduate student presentation

3:35 pm – 3:55 pm 235 Lockett Hall

Mustafa Hajij, Department of Mathematics, LSU Graduate Student
Asymptotic Power Series in a Complex Variable

Posted April 30, 2009

Communicating Mathematics Talk First-year graduate student presentation

3:55 pm – 4:15 pm 235 Lockett Hall

Derek Van Farowe, Department of Mathematics, LSU Graduate Student
Simplicial Homology and the Euler Characteristic

Posted April 30, 2009

Communicating Mathematics Talk First-year graduate student presentation

4:15 pm – 4:35 pm 235 Lockett Hall

Tyler Moss, Department of Mathematics, LSU Graduate Student
List-Coloring Graphs

Friday, May 1, 2009

Posted April 30, 2009

3:40 pm – 4:30 pm 285 Lockett Hall

Ken Shoda, George Washington University
Semi-Magic Square Matroids: A Super-exponential family of nonisomorphic matroids having the same Tutte polynomial

Monday, May 4, 2009

Posted April 23, 2009

11:00 am – 12:00 pm Lockett 381

Huajun Huang, Auburn University
On Simultaneous Isometry of Subspaces

Let $(V,b)$ be a metric space with a nonsingular symmetric, skew-symmetric, Hermitian, or skew-Hermitian form $b$. Witt\'s theorem states that an isometry between two subspaces of $V$ can be extended to an isometry of the whole space $V$. In this talk, I will present several results that extend Witt\'s theorem to simultaneous isometries of subspaces by using matrix analysis techniques. As applications, I will illustrate some examples in isometry groups orbits and invariants. The results could be applied to isometry problems in Hilbert spaces.

Posted April 22, 2009

Award Ceremony

5:00 pm Pleasant Hall Math Lab

Award Ceremony

Our LSU Math Lab in Pleasant Hall has been selected to receive the Pearson Education Teaching and Technology Leadership Award.

Monday, June 15, 2009

Posted May 7, 2009

Control and Optimization Seminar Questions or comments?

11:00 am – 12:00 pm 338 Johnston Hall

Jiangguo Liu, Colorado State University
The Enriched Galerkin (EG) Method For Local Conservation

In this talk, we present a locally mass-conservative finite element method based on enriching the approximation space of the continuous Galerkin (CG) method with elementwise constant functions. The proposed method has a smaller number of degrees of freedom than the discontinuous Galerkin (DG) method. Numerical results on coupled flow and transport problems in porous media are provided to illustrate the advantages of this method. Optimal error estimates of the EG method and comparison with related post-processing methods will be discussed also. This is a joint work with Shuyu Sun at Clemson University.

Monday, June 29, 2009

Posted June 28, 2009
Last modified May 8, 2021

10:00 am Lockett 301D (Conference Room)

Michael Malisoff, LSU Roy P. Daniels Professor
Strict Lyapunov Function Constructions under LaSalle Conditions with an Application to Lotka-Volterra Systems

This informal seminar is by special request of Guillermo Ferreyra and is open to all faculty and graduate students. See abstract and related papers and slides.

Wednesday, July 15, 2009

Posted July 7, 2009

SIAM Student Chapter Event

10:00 am Johnston Hall 338

Personal Webpage Construction and Design Seminar

The speakers are Jeffrey Sheldon, Nikkos Svoboda, Silvia Jimenez and Jens Christensen. They will present on setting up departmental based website, basic commands and webpage design, and webpage for job applications.

Wednesday, August 12, 2009

Posted August 7, 2009

12:00 pm Johnston Hall 338

Jintao Cui, Mathematics Department, LSU
Introduction to LSU SIAM Student Chapter

The LSU SIAM Student Chapter is inviting all the students who are participating in the GEAUX program and Math Tune-up program to a pizza lunch and we would like to give a general introduction to the Chapter and our activities. You are all welcome to attend this event.

Monday, August 17, 2009

Posted August 11, 2009

1:00 pm – 4:00 pm 285 Lockett Hall

Comprehensive / PhD Qualifying Exam: ALGEBRA

Wednesday, August 19, 2009

Posted August 11, 2009

1:00 pm – 4:00 pm 285 Lockett Hall

Comprehensive / PhD Qualifying Exam: ANALYSIS

Friday, August 21, 2009

Posted August 11, 2009

1:00 pm – 4:00 pm 285 Lockett Hall

Comprehensive / PhD Qualifying Exam: TOPOLOGY

Tuesday, August 25, 2009

Posted August 20, 2009

3:00 pm – 3:50 pm 338 Johnston Hall

Michael Neilan, Louisiana State University
Numerical Methods for Fully Nonlinear Second Order PDEs and Applications

Fully nonlinear second order PDEs arise in many areas of science including optimal transport, meteorology, differential geometry, and optimal design. However, numerical methods for general fully nonlinear second order PDEs still remains a relatively untouched area. In this talk, I will introduce a new notion of solutions for these equations called moment solutions which are based on a constructive limiting process called the vanishing moment method. I will then present three finite element methods based on the vanishing moment method. Finally, I will demonstrate the effectiveness of the method with numerical examples.

Wednesday, August 26, 2009

Posted August 17, 2009
Last modified May 5, 2020

3:40 pm Lockett 15

Faculty meeting

Thursday, August 27, 2009

Posted August 11, 2009
Last modified October 5, 2023

3:40 pm – 4:30 pm Lockett 285

Pramod Achar, Mathematics Department, LSU
Positivity, sheaves, and representation theory

The celebrated “Kazhdan-Lusztig polynomials” of an algebraic group have an elementary combinatorial definition, but the proof that all their coefficients are nonnegative requires very deep results from algebraic geometry—the Weil conjectures, proved by Deligne in the 1970s. The link between combinatorics and algebraic geometry is furnished by sheaf theory, especially the so-called "perverse sheaves." I will explain how "positivity" results come out of the interaction of these topics, and I will also discuss more recent developments in which perverse sheaves are replaced by vector bundles and coherent sheaves.

Friday, August 28, 2009

Posted July 27, 2009
Last modified July 28, 2009

11:00 am – 12:00 pm Johnston Hall 338

Michele Benzi, Emory University
Key Moments In The History Of Numerical Analysis

The talk will highlight some of the key moments in the evolution of numerical analysis into an independent mathematical discipline. The necessary context and background behind technical developments will be carefully exposed, as well as biographical information about the major figures in the field. The main focus of the talk will be on the early history of matrix iterations.

Additional details can be found at http://www.cct.lsu.edu/events/talks/489

Monday, August 31, 2009

Posted August 24, 2009

3:40 pm – 4:30 pm Room 233 Lockett Hall

Robert Lipton, Mathematics Department, LSU
Strength of Elastic - Plastic Composites Made From Random Configurations of Two Materials

Posted August 28, 2009
Last modified February 20, 2022

3:40 pm Keisler Lounge, Lockett Hall 321

Susan Abernathy, Louisiana State University
Knot theory

Knot theory connects to a wide variety of areas in mathematics. In this talk, we will review some basics of knots and introduce some of the diverse techniques used to differentiate knots, including certain knot invariants and Morse theory.

Tuesday, September 1, 2009

Posted August 24, 2009
Last modified August 25, 2009

3:10 pm – 4:00 pm 338 Johnston Hall

Andrew Barker, Louisiana State University
Monolithically Coupled Scalable Parallel Algorithms For Simulation Of Fluid-structure Interaction

Simulation of fluid-structure interaction is a computationally difficult problem that is important in a variety of applications. Doing it well requires not only accurately modeling physics for the fluid and the structure, but also coupling them together in a stable and efficient manner, and developing scalable numerical methods for this highly nonlinear problem is a challenge. In this talk we describe and examine parallel, scalable techniques in the multilevel Newton-Krylov-Schwarz family for solving the fully implicit fluid-structure interaction system on dynamic unstructured moving finite element meshes in the arbitrary Lagrangian-Eulerian framework. Our emphasis is on tight monolithic coupling of the physical systems and the computational mesh, and on the parallel scalability of the method. We present applications of the method to the simulation of blood flow on vessel geometries derived from patient-specific clinical data.

Friday, September 4, 2009

Posted August 11, 2009
Last modified August 14, 2009

3:40 pm – 4:30 pm Lockett 285

Habib Ouerdiane, University of Tunis El Manar
Generalized fractional evolution equations

Abstract:
In this talk we study the generalized Riemann-Liouville (resp. Caputo)
time fractional evolution equation in infinite dimensions. We show that
the explicit solution is given as the convolution between the initial
condition and a generalized function related to the Mittag-Leffler
function. The fundamental solution corresponding to the Riemann-Liouville
time fractional evolution equation does not admit a probabilistic
representation while for the Caputo time fractional evolution equation
it is related to the inverse stable subordinators.

There will be coffee and cookies in the lounge at 3:00.

Tuesday, September 8, 2009

Posted August 28, 2009

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm 338 Johnston Hall

Xiaoliang Wan, Louisiana State University
Noise-induced Transition for the Kuramoto-Sivashinsky Equation

Noise-induced transition in the solutions of the Kuramoto-Sivashinsky equation is investigated using the minimum action method derived from the large deviation theory. This is then used as a starting point for exploring the configuration space of the Kuramoto-Sivashinsky equation. The particular example considered here is the transition between a stable fixed point and a stable traveling wave. Five saddle points, up to constants due to translational invariance, are identified based on the information given by the minimum action path (MAP). Heteroclinic orbits between the saddle points are identified. Relations between noise-induced transitions and the saddle points are examined.

Posted September 2, 2009

3:40 pm Lockett 285

Marco Schlichting, Louisiana State University
Grothendieck-Witt groups and a counterexample to invariance under derived equivalences

Posted September 3, 2009

4:30 pm Keisler Hall: Lockett 321

Movie Night! NOVA: Fractals

Hunting the Hidden Dimension. Come eat free pizza and enjoy a movie about mysteriously beautiful fractals that are shaking and deepening our understanding of nature.

Posted August 28, 2009

5:00 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial Student Association Meeting

Electing our officers for the upcoming year. As always, we welcome new members who wish to learn about the actuarial program at LSU and/or the profession in general. We will also be organizing study groups for the actuarial exams.

Thursday, September 10, 2009

Posted August 11, 2009
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 285

Fernanda Cipriano, University of Lisbon
Statistical solutions for the 2D Euler equation

In the study of Euler and Navier-Stokes equations we can consider two different approaches. The most classical one consist in the study of the equations with specific initial and boundary conditions. Another approach, the so-called stochastic approach, consist in the construction of suitable probability measures and study its evolution in time according to the corresponding dynamic. The framework of stochastic analysis can be used to construct solutions. In our presentation, we follow the second point of view to present some results on the 2D Euler equation with periodic boundary conditions. We construct surface type measures on the level sets of the renormalized energy and establish the existence of weak solutions living on such level sets. We also prove the existence of weak solutions for the forward and backward transport equations associated with the 2D Euler equation. Such solutions can be interpreted, respectively, as a statistical Lagrangian and statistical Eulerian description of the motion of the fluid.

There will be coffee and cookies in the lounge at 3:00.

Friday, September 11, 2009

Posted September 14, 2009

3:40 pm – 5:30 pm Lockett 285

Fernanda Cipriano, University of Lisbon
Habib Ouerdiane, Faculte des Sciences de Tunis, Tunis
Presentations on the Bargmann-Segal Transform and the Navier-Stokes Equation

Monday, September 14, 2009

Posted September 6, 2009

3:30 pm – 4:30 pm Room 233 Lockett Hall

Yaniv Almog, Department of Mathematics, LSU
Superconductivity Near the Normal State in the presence of electric current.

We consider the linearization of the time-dependent Ginzburg-Landau near the normal state. We assume that an electric current is applied through the sample, which captures the whole plane, inducing thereby, a magnetic field. We show that independently of the current, the normal state is always stable. Using Fourier analysis the detailed behaviour of solutions is obtained as well. Relying on semi-group theory we then obtain the spectral properties of the steady-state elliptic operator. We shall also consider the spectral properties of the same elliptic operator near a flat wall, and obtain the critical current in the limit of small and large normal conductivity

Posted September 10, 2009
Last modified February 20, 2022

4:30 pm Keisler Lounge, Lockett Hall 321

Election of officers

Come eat free pizza, vote for your new officers, and play some fun math games. If you are interested in running for office, contact Josh Moulton.

Thursday, September 17, 2009

Posted August 11, 2009
Last modified September 11, 2009

3:40 pm – 4:30 pm Lockett 285

Milen Yakimov, LSU
Poisson geometry of flag varieties, ring theory and combinatorics

Abstract:
The geometry of Poisson Lie groups and Poisson homogeneous spaces was
actively studied after Drinfeld's celebrated 1986 ICM talk in which he
describe its importance for the representation theory of quantum groups.

In this talk we will go over various aspects of the geometry of Poisson
structures on flag varieties for complex simple Lie groups
(results with K. Brown and K. Goodearl). We will apply them to ring theory
to resolve several problems for the De Concini-Kac-Procesi algebras from
about 10-15 years ago: determining the torus invariant prime ideals of those
algebras, their inclusions, finding effective generating sets for the
ideals. We will also describe applications to combinatorics: 1. obtaining a
simple proof of the recent result of Knutson, Lam and Speyer for cyclicity
of the Lusztig stratification of Grassmannians, 2. combinatorial formulas
for Hecke algebras (with F. Brenti), 3. Deodhar's stratification of open
Richardson varieties (with B. Webster).

There will be coffee and cookies in the lounge at 3:00.

Friday, September 18, 2009

Posted September 9, 2009

3:30 pm Lockett Hall 233

Anna Zemlyanova, Department of Mathematics, LSU
Single- and double-spiral-vortex models for a supercavitating wedge in a jet

In this talk we study the effect which a cavity closure condition has on the flow of liquid around a supercavitating wedge in a jet. The comparison is made for the single- and double-spiral-vortex models proposed by Tulin. Both models are solved in closed form by the method of conformal mappings.

Monday, September 21, 2009

Posted July 27, 2009
Last modified January 27, 2022

3:40 pm – 4:30 pm Lockett 285

Stephen Smith, University of Illinois Chicago Circle
Revisiting the classification of the finite simple groups (an outline)

Most mathematicians are aware that the classification of the finite simple groups involved hundreds of researchers and thousands of journal pages.

In 1983, Daniel Gorenstein published the first volume of a general outline of this massive work—covering the “non-characteristic 2 type” case (correspondingly roughly to simple matrix groups over fields of odd order).

But he could not publish the projected second and final volume, on the characteristic 2 type case—due to the non-publication of Mason's expected work on “quasithin groups”. That gap was not filled until the 2004 publication by Aschbacher and Smith of a more general quasithin treatment. This finally left the way open for the second volume of the overall outline of the CFSG---a first draft of this outline has now been completed by Aschbacher, Lyons, Solomon, and Smith.

The talk will be an elementary exposition of some of the ideas in this overall outline; including mention of certain of the new ideas and approaches which have arisen since the 1980s.

There will be coffee and cookies in the lounge at 3:00.

Posted September 14, 2009

3:40 pm – 4:30 pm Room 233 Lockett Hall

Scott Armstrong, Department of Mathematics, Louisiana State University
Self-similar solution and long-time asymptotics for fully nonlinear parabolic equations

I will present results on the existence and uniqueness of a self-similar solution of a fully nonlinear, parabolic equation (an example of which include the Bellman-Isaacs equation arising in the theory of stochastic optimal control and stochastic differential game theory). As an application, we are able to describe the long-time behavior of solutions to the Cauchy problem, and derive a conservation law which generalizes the conservation of mass in the case of the heat equation. The scaling invariance property of the self-similar solution depends on the nonlinear operator, and is in general different from that of the heat kernel. We will see that this difference has an interesting interpretation in terms of controlled diffusion processes. This work is joint with M. Trokhimtchouk.

Wednesday, September 23, 2009

Posted September 14, 2009
Last modified September 23, 2009

3:30 pm – 4:30 pm Lockett 285

Ambar Sengupta, Mathematics Department, LSU
Noise: from White to Free

Abstract: We will discuss results of Wigner and Voiculescu connecting
classical probability theory with the algebraic theory of free probability.
Applying these ideas to a classical matrix white noise process produces a free analog.

Friday, September 25, 2009

Posted September 22, 2009
Last modified September 23, 2009

2:45 pm – 3:30 pm Lockett Hall 233

Jacob Blanton, Mathematics Department, LSU
Max-Plus Algebra and Optimal Control Theory

A common approach to controlling nonlinear systems involves utilizing the dynamic programming principle (DPP). This approach leads to a control solution via the solution of a corresponding Hamilton-Jacobi (HJ) PDE. It has the advantage of yielding an optimal control solution as the value function of the control problem is interpreted as the viscosity solution of the associated HJ PDE. The semigroup that propagates the solutions of these PDE's is identical to the dynamic programming principle. The above will be surveyed along with an introduction to max-plus algebra in order to highlight the result that the semigroup associated with the HJ PDE's above is a max-plus linear operator.

Posted August 27, 2009
Last modified March 2, 2022

3:40 pm – 4:30 pm 233, Lockett Hall

Matthew Knepley, Computation Institute, University of Chicago
Tree-based methods on GPUs

We examine the performance of the Fast Multipole Method on heterogeneous computing devices, such as a CPU attached to an Nvidia Tesla 1060C card. The inherent bottleneck imposed by the tree structure is ameliorated by a refactoring of the algorithm which exposes the fine-grained dependency structure. Also, common reduction operations are refactored in order to maximize throughput. These optimizations are enabled by our concise yet powerful interface for tree-structured algorithms. Examples of performance are shown for problems arising from vortex methods for fluids

Tuesday, September 29, 2009

Posted August 28, 2009
Last modified September 1, 2009

3:10 pm Lockett 235

Meeting of the tenured and tenure-track Faculty

Promotion cases.

Posted September 8, 2009

5:00 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial Student Association Meeting

Monday, October 5, 2009

Posted October 4, 2009

3:40 pm – 4:30 pm Lockett 285

Padmanabhan Sundar, Mathematics Department, LSU
On a class of stochastic partial differential equations

Posted October 2, 2009

Algebra and Number Theory Seminar Questions or comments?

4:30 pm Keisler Lounge, room 321, Lockett Hall

Weekly meeting

Math activities, discussion of upcoming movie, and pizza.

Tuesday, October 6, 2009

Posted October 5, 2009

3:40 pm Lockett 285

Helena Verrill, Mathematics Department, LSU
Noncongruence lifts of projective congruence subgroups

Wednesday, October 7, 2009

Posted October 5, 2009

3:40 pm 285 Lockett

Basic Sciences undergraduate breadth requirements

Posted September 30, 2009
Last modified March 2, 2021

4:30 pm – 6:00 pm Johnston Hall 338

I still don't know what you did last summer!

There will be a panel with students who participated in math related activities during the Summer 2009 sharing their experiences and explain how to apply for these programs. We hope that all Chapter members and graduate students would be benefitted from their experience. There will be a pizza dinner after.

Thursday, October 8, 2009

Posted August 11, 2009
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 285

Dmitry Ryabogin, Kent State University
On the local version of Mahler Conjecture

There will be coffee and cookies in the lounge at 3:00.

Monday, October 12, 2009

Posted September 14, 2009

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Room 233 Lockett Hall

Christo Christov, University of Louisiana at Lafayette
Stochastic Functional Expansions for Heterogeneous Continuous Media and Chaotic Regimes of Nonlinear Dynamical Systems

Tuesday, October 13, 2009

Posted October 5, 2009
Last modified October 13, 2009

3:40 pm Lockett 285

Heather Russell, Mathematics Department, LSU
A combinatorial construction of the Springer representation

Springer varieties are studied because their cohomology carries a natural
action of the symmetric group and their top-dimensional cohomology is
irreducible. In his work on tangle invariants, Khovanov constructed a
family of Springer varieties as subvarieties of a product of spheres. We
show that these varieties can be embedded antipodally in the product of
spheres and that the natural symmetric group action on the product induces
the Springer representation. Our construction admits an elementary (and
geometrically natural) combinatorial description, which we use to prove
that the Springer representation is irreducible in each degree. This work
is joint with Julianna S. Tymoczko at The University of Iowa.

Friday, October 16, 2009

Posted October 12, 2009

3:30 pm – 4:30 pm Lockett Hall 233

Rick Barnard, LSU Department of Mathematics Graduate Student
The Minimal Time Function and Stratified Domains

In this talk, we introduce the minimal time problem over a stratified domain. In such a problem, dynamical systems are regular only when restricted to a prescribed set of submanifolds. We show that the minimal time function satisfies an appropriate Hamilton-Jacobi equation.

Posted October 13, 2009

4:40 pm – 5:30 pm Lockett Hall 285

Xiangqian Zhou
On minimally k-connected matroids

Monday, October 19, 2009

Posted September 20, 2009
Last modified March 2, 2022

3:40 pm – 4:30 pm Room 233 Lockett Hall

Truyen Nguyen, University of Akron
Hamilton–Jacobi equation in the space of measures associated with a system of conservation laws

We introduce a class of action functional defined over the set of continuous paths in the Wasserstein space of probability measures on $\mathbf{R}^d$. We show that minimizing path for such action exists and satisfies compressible Euler equation in a weak sense. Moreover, we prove that both Cauchy and resolvent formulations of the associated Hamilton–Jacobi equations are well-posed and their unique viscosity solutions are given by the dynamic programming principle. The characteristics of these Hamilton–Jacobi equations in the space of probability measures are solutions of the compressible Euler equation in $\mathbf{R}^d$. This is joint work with Jin Feng of the University of Kansas.

Posted October 19, 2009

4:30 pm Keisler Lounge, Lockett Hall 321

Introduction to Number Theory

Clueless about what number theory is and how it relates to your everyday life? Come and find out!

Tuesday, October 20, 2009

Posted September 8, 2009
Last modified October 15, 2009

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm 338 Johnston Hall

Eun-Hee Park, Louisiana State University
A Domain Decomposition Method Based On Augmented Lagrangian With A Penalty Term

Posted October 7, 2009
Last modified October 20, 2009

3:40 pm Lockett 285

Christopher Bremer, Mathematics Department, LSU
Moduli for connections of cuspidal type

In my last talk, I described the Riemann-Hilbert correspondence for irregular singular point connections. Although this theory dates back to the work of Malgrange and Sibuya in the 70s, the Riemann-Hilbert map itself was not well understood until recently. In the past decade, Boalch has shown that the Riemann-Hilbert map gives a symplectic isomorphism between a coarse moduli space of connections, and a Poisson Lie group of `Stokes multipliers.' The theory of fundamental strata is a combinatorial tool for describing connections of cuspidal type. Recent work (joint with D S Sage) has shown that the fundamental stratum of a connection can be used to generalize Boalch's work. I will describe our preliminary results, and give some indication of how strata characterize the irregular Riemann-Hilbert map in the cuspidal case.

Wednesday, October 21, 2009

Posted September 17, 2009

Student Colloquium

3:40 pm – 4:30 pm Lockett 285

Virginia Naibo, Department of Mathematics, Kansas State University
Decay properties of wave functions associated to atomic particles.

There will be refreshments in the Keisler Lounge from 3:00pm - 3:30pm. Abstract: This talk is designed for advanced undergraduate and graduate students. Mathematical models describing the motion of an object falling in the atmosphere or the vibration of an elastic string can be obtained using Newton\'s second law of motion. This law fails at the level of atoms and their constituents and it is quantum mechanics that provides a new set of laws and a mode of description for microscopic systems. The counterpart of Newton\'s second law in the microscopic world is the Schrodinger equation. We will go over simple models of this equation and discuss the idea of dispersive estimates for their solutions.

Posted September 30, 2009
Last modified October 20, 2009

3:40 pm – 5:00 pm Lockett B5

Faculty meeting with Dean Kevin Carman

This meeting is arranged by the IRC

Thursday, October 22, 2009

Posted September 17, 2009
Last modified October 19, 2009

Student Colloquium

12:40 pm – 1:30 pm Locket B6

Virginia Naibo, Department of Mathematics, Kansas State University
Cool applications of matrix theory

There will be a light lunch offered from 12:00 to 12:30 pm in the Keisler Lounge preceding the talk.

Abstract: We will discuss the mathematics behind digital image compression models such as JPEG and website ranking algorithms such as Google\'s PageRank.

This talk will be accessible to students who have taken a course on linear algebra.

Monday, October 26, 2009

Posted September 8, 2009
Last modified February 5, 2021

Control and Optimization Seminar Questions or comments?

3:40 pm – 4:30 pm Room 233 Lockett Hall

Rachael Neilan, Department of Oceanography and Coastal Sciences, LSU
Optimal control in disease modeling

Optimal control theory in disease models is used to determine cost-effective disease prevention and treatment strategies. When disease dynamics are governed by ordinary differential equations, Pontryagin's Maximum Principle is used to characterize an optimal control (i.e., optimal treatment strategy). However, many disease models use partial differential equations to describe the spread of infection in space and time. No extension of Pontryagin's Maximum Principle exists for systems of PDEs, but similar techniques are employed to derive optimal spatiotemporal control characterizations. In this talk, we will provide theoretical optimal control results for a system of advection-diffusion equations describing the spread of rabies through a raccoon population. Numerical solutions will illustrate the optimal vaccine distribution on homogeneous and heterogeneous spatial domains.

Tuesday, October 27, 2009

Posted October 9, 2009
Last modified May 8, 2021

10:00 am 117 Electrical Engineering Building

Michael Malisoff, LSU Roy P. Daniels Professor
Constructions of Strict Lyapunov Functions: An Overview

Information on ECE Seminar Web Site.

Posted September 8, 2009
Last modified October 15, 2009

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm 338 Johnston Hall

Hongchao Zhang, Louisiana State University
An Affine-scaling Method For Nonlinear Optimization With Continuous Knapsack Constraints

Posted October 5, 2009
Last modified October 26, 2009

3:40 pm Lockett 285

Anthony Henderson, School of Mathematics and Statistics, University of Sydney
Enhancing the nilpotent cone

Many features of an algebraic group are controlled by the geometry of its nilpotent cone, which in the case of GL_n(C) is merely the variety N of n x n nilpotent matrices. The study of the orbits of the group in its nilpotent cone leads to combinatorial data relating to the representations of the Weyl group, via the famous Springer correspondence. In the case of GL_n(C), the basic manifestation of this correspondence is the fact that conjugacy classes of nilpotent matrices and irreducible representations of the symmetric group are both parametrized by partitions of n.

Pramod Achar and I have shown that studying the orbits of GL_n(C) in the enhanced
nilpotent cone C^n x N leads to exotic combinatorial data of type B/C (previously studied by Spaltenstein and Shoji). As I will explain, this is closely related to Syu Kato's exotic Springer correspondence for the symplectic group, and also to nilpotent orbits in characteristic 2.

Posted October 9, 2009

5:00 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial Student Association Meeting

We will have 1. A visitor from Career Services will give a presentation and answer questions on internships and jobs. 2. A discussion of exams and study groups 3. the selection of officers

Friday, October 30, 2009

Posted October 22, 2009

CCT Lecture Events organized by the LSU Center for Computation and Technology

1:00 pm 338 Johnston Hall

CCT Colloquim Series

Presented by: Arun Bansil, Northeastern University \"Modeling Highly Resolved Spectroscopies of Complex Materials: from Qualitative to Quantitative\" For more information please see cct events. http://www.cct.lsu.edu/events/events.php

Posted October 27, 2009

1:00 pm 301D Lockett

Final Event of the Nonthesis MS Comprehensive Examination

Graduate students who have signed up earlier this semester for the final event of MS Comprehensive Exam to qualify for an MS degree this May will meet with Profs. Perlis, Cohen, and Richardson at 1 PM.

Posted October 21, 2009
Last modified October 22, 2009

3:30 pm – 4:30 pm Lockett Hall 233

Sean Farley, Department of Mathematics, LSU Graduate Student
An Introduction to TikZ: Integrating Graphics within LaTeX

While LaTeX is quite useful for typesetting math, it can be quite the pain for incorporating graphics. Which format do you save your image as? PDF? EPS? JPG? I will introduce a powerful package called TikZ that will enable you to seamlessly integrate graphics into your document. I will present examples in finite elements, beamer, and gnuplot.

Monday, November 2, 2009

Posted September 30, 2009
Last modified March 2, 2022

LSU AWM Student Chapter LSU AWM Student Chapter Website

3:40 pm – 4:30 pm Room 233 Lockett Hall

Scott McKinley, Department of Mathematics, Duke University
Anomalous Diffusion of Distinguished Particles in Bead-Spring Networks. (This is a joint Applied Analysis & Probability Seminar)

Due to recent and compelling experimental observations using passive microrheology there is theoretical interest in anomalous sub-diffusion — stochastic processes whose long-term mean-squared displacement satisfies $\mathbf{E}[x^2(t)] \sim t^\nu$ where $\nu \leq 1$. The canonical example of a sub-diffusive process is fractional Brownian motion, but for reasons we will discuss, this project focuses on a touchstone model from polymer kinetic theory — the Rouse chain — and its natural generalizations.

Our interest is in studying the dynamics of a distinguished particle in a network of thermally fluctuating beads that interact with each other through linear springs. Such processes can be expressed as the sum of a Brownian motion with a large number of Ornstein–Uhlenbeck processes. We introduce a single parameter which can be tuned to produce any sub-diffusive exponent $\nu \in (0,1)$ for the generic sum-of-OU structure and demonstrate the relationship between this parameter and the geometric structure of the bead-spring connection network in which the distinguished particle resides. This development provides a basis to prove a conjecture from the physics community that the Rouse exponent $\nu = 1/2$ is universal among a wide class of models.

Tuesday, November 3, 2009

Posted October 25, 2009

9:30 am – 10:30 am Keisler Lounge, Lockett Hall

A conversation with Prof. Irina Mitrea

Prof. Irina Mitrea, from Worcester Polytechnic Institute, will be visiting LSU to give a Colloquium talk. The LSU Student Chapter of the AWM will host a meeting with her to talk about her career experience. For more information visit http://www.math.lsu.edu/awm/

Posted October 20, 2009
Last modified March 2, 2021

Student Colloquium

12:40 pm – 1:30 am 313 Design Building

Charles Conley, University of North Texas
f(x)=x^{x^{x^{\cdot^{\cdot^{\cdot}}}}}

Please note the unusual location for the talk.

For what real number x does this function make sense? This question was first answered by Euler. Clearly f(2) is infinite, and one might guess that f(x) is infinite for all x greater than 1. In fact this is not true: both the upper and lower bound of f's domain of definition are interesting. In this talk we will deduce these bounds using nothing more advance than the chain rule. En route we will examine some well-known graph a^x and some not-so-well-known graphs a^{a^x}} closely, discovering some enjoyable surprises.

There will be a light lunch served in the Keisler Lounge from 12:00-12:30

Posted August 11, 2009
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 285

Irina Mitrea, Worcester Polytechnic Institute
Boundary Value Problems for Higher Order Elliptic Operators

There will be coffee and cookies in the lounge at 3:00.

Wednesday, November 4, 2009

Posted October 20, 2009
Last modified October 27, 2009

Student Colloquium

3:40 pm – 4:30 pm Lockett 285

Charles Conley, University of North Texas
Vector Fields on the Line

Abstract: This talk will be a gentle introduction to some aspects of the theory of representations of Lie algebras by means of an example: the Lie algebra Vec(R) of vector field on the line. Since the objects involved are quite concrete, no prior knowledge of Lie algebras will be assumed: only basic calculus and linear algebra.

There will be refreshments served in the Keisler Lounge from 3:00 -3:30.

Thursday, November 5, 2009

Posted October 29, 2009
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 285

Charles Conley, University of North Texas
Extremal Projectors.

Let g be a complex finite dimensional reductive Lie algebra. The extremal projector P(g) is an element of a certain formal extension of the enveloping algebra U(g) which projects representations in Category O to their highest weight vectors along their lower weight vectors, provided that the denominator of P(g) does not act by zero. (This denominator is a formal product in U(h), h being the chosen Cartan subalgebra.)

In 1971 Asherova-Smirnov-Tolstoi discovered a noncommutative finite factorization of P(g), and in 1993 Zhelobenko discovered a commutative infinite product formula. We will discuss these results and some more recent formulas for the relative projector P(g,l), the projection to the highest l-subrepresentations, l being a Levi subalgebra.

Friday, November 6, 2009

Posted October 24, 2009

3:30 pm – 4:30 pm Lockett Hall 233

Santiago Fortes, Department of Mathematics, LSU
Subwavelength Plasmonic Crystals: Dispersion Relations and Effective Properties

: The possibility of engineering composite materials with unusual electromagnetic properties (a.k.a. metamaterials) has generated much interest lately. Devices such as invisibility cloaks and superlenses could, in principle, be constructed using such materials. One of the central ideas in the study of metamaterials is that radiation with wavelengths much larger than the inhomogeneities of the material cannot detect internal structure, so that the concepts of effective dielectric permittivity and effective magnetic permeability are valid. I will present a method for obtaining convergent power series representations for the fields and associated dispersion relations of electromagnetic waves propagating in a species of metamaterial known as plasmonic crystal.

Monday, November 9, 2009

Posted November 3, 2009

9:15 am – 10:15 am Johnston Hall 331

Fadil Santosa, Director, Institute for Mathematics and its Applications and School of Mathematics, University of Minnesota
Breakfast and Discussion

LSU SIAM Student Chapter presents a conversation with Prof. Fadil Santosa, the director of IMA (Institute for Mathematics and Applications). Breakfast will be served. It will be an informal meeting with him to talk about his career experience. This meeting is open to everyone.

Posted September 14, 2009
Last modified March 2, 2022

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Room 233 Lockett Hall

Fadil Santosa, Director, Institute for Mathematics and its Applications and School of Mathematics, University of Minnesota
The mathematics of progressive lens design

Progressive addition lenses are prescribed to patients who need correction for both far and near visions. A progressive lens needs to have power that gradually changes from the far vision zone, used for example in driving, and the near vision zone, used for example in reading a map. The basics of optics and lens design will be described. In particular, it will be shown that the problem can be reduced to one of surface design. The surface design problem itself is solved by a variational approach, which can be further simplified by linearization, leading to a fourth order elliptic partial differential equations. Analysis of the resulting equations and development of a computational method are described. Numerical results are presented to illustrate the process of lens design.

Tuesday, November 10, 2009

Posted October 7, 2009
Last modified November 4, 2009

3:40 pm Lockett 285

Jerome W. Hoffman, Mathematics Department, LSU
L-functions and l-adic representations for modular forms

Friday, November 13, 2009

Posted November 4, 2009
Last modified November 11, 2009

Algebra and Number Theory Seminar Questions or comments?

3:40 pm Lockett 285

Moon Duchin, University of Michigan
Limit shapes in groups

Consider larger and larger metric spheres in a group. Under nice circumstances, these converge to a definite "limit shape" as the radius goes to infinity. For instance in finitely generated nilpotent groups one may use a rescaling dilation in the ambient Lie group to shrink down large spheres, and by work of Pansu (extended by Breuillard) this gives a well-defined limit. For a simple example, in the free abelian group Z^2, if we take the standard generating set, the limit shape is a diamond (and the limiting metric, for which this is the unit sphere, is the L^1 metric on the plane). It is natural to ask whether the counting measure on the discrete spheres converges to a measure on the limit shape. I'll discuss our work on this question, and give some ergodic applications and some averaging applications for limit shapes.
Parts of this project are joint work with Samuel Lelièvre, Christopher Mooney, and Ralf Spatzier.

Posted November 13, 2009

4:40 pm – 5:30 pm 285 Lockett Hall

Natalie Hine, LSU Mathematics Graduate Student
Infinite Antichains of Matroids

Abstract: In this talk, I will assume no prior knowledge of matroid theory, so I will begin by defining a matroid and giving some basic examples. Then, I will explain the differences between graphs and matroids with respect to infinite antichains under the minor ordering. Lastly, I will discuss when a minor-closed class of matroids with a single excluded minor does not contain an infinite antichain.

Monday, November 16, 2009

Posted September 30, 2009
Last modified November 10, 2009

3:40 pm – 4:30 pm Room 233 Lockett Hall

Xiaoliang Wan, Louisiana State University
A note on stochastic elliptic models

In this talk we will look at two strategies that introduce randomness into elliptic models. One is to treat the coefficient as an spatial random process, which results in an stochastic elliptic model widely used in engineering applications; the other one is to define the stochastic integral using Wick product, which can be regarded as a generalization of Ito integral. The statistics given by these two strategies can be dramatically different. I will compare these two strategies using a one-dimensional problem and present a new stochastic elliptic model to makes them more comparable. Numerical methods will also be discussed.

Posted November 11, 2009
Last modified February 20, 2022

Algebra and Number Theory Seminar Questions or comments?

4:40 pm

Groups and Graph Theory

Jesse Taylor will discuss Group Theory. He'll be giving a few basic definitions and defining a few key concepts related to Group and Graph Theory.

Tuesday, November 17, 2009

Posted October 5, 2009
Last modified November 12, 2009

3:40 pm Lockett 285

Jorge Morales, Mathematics Department, LSU
Siegel's mass formula and averages of L-functions over function fields

Wednesday, November 18, 2009

Posted October 20, 2009
Last modified November 9, 2009

3:40 pm Lockett 5

Departmental Priorities, Teaching and the Budget

Thursday, November 19, 2009

Posted November 13, 2009
Last modified February 20, 2022

6:00 pm Design Building 103

Movie: "Fermat's Room"

Showing of the movie “Fermat's Room”, in collaboration with the LSU Spanish Club. From the President: “We will watch the movie Fermat's Room at 103 Design Bldg at 6:01pm on 11/19/2009. Entertainment will happen. Approximately 90 minutes later, the movie will end and we will all return to our normal lives as though nothing had happened, yet forever remembering the magic that happened on that fateful November night…”

Friday, November 20, 2009

Posted November 13, 2009

3:30 pm – 4:30 pm Lockett Hall 233

Lee Windsperger, Department of Mathematics, LSU
The Asymptotic Laplace Transform

The asymptotic Laplace transform is a generalization of the classical Laplace transform. Whereas the classical Laplace transform is an analytic tool to solve well-posed problems, the asymptotic Laplace transform is an analytic tool to solve ill-posed problems. This talk will introduce the definition, properties, and advantages of the asymptotic Laplace transform through two elementary partial differential equations.

Posted November 13, 2009

3:40 pm – 4:30 pm Lockett 381

Boris Rubin, Louisiana State University
Radon Transforms on the Heisenberg Group and Transversal Radon Transforms.

Abstract: The notion of the Radon transform on the Heisenberg group was introduced by R. Strichartz and inspired by D. Geller and E.M. Stein. A more general transversal Radon transform integrates functions on the $m$-dimensional real Euclidean space over hyperplanes meeting the last coordinate axis. We obtain new boundedness results and explicit inversion formulas for both transforms on $L^p$ functions in the full range of the parameter $p$. We also show that these transforms are isomorphisms of the corresponding Semyanistyi-Lizorkin spaces of smooth functions. In the framework of these spaces we obtain inversion formulas, which are pointwise analogues of the corresponding formulas by R. Strichartz.

Monday, November 23, 2009

Posted November 12, 2009

3:40 pm – 5:00 pm Lockett B 5

Faculty Meeting

This meeting is arranged by the IRC

Tuesday, November 24, 2009

Posted November 23, 2009

Meeting of the Algebra Faculty

3:40 pm Lockett 285

Planning meeting for graduate courses 2010-2011

Monday, November 30, 2009

Posted November 17, 2009

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Room 233 Lockett Hall

Santiago Fortes, Department of Mathematics, LSU
Electromagnetic wave propagation in Plasmonic Crystals

The possibility of engineering composite materials with unusual electromagnetic properties (a.k.a. metamaterials) has generated much interest lately. Devices such as invisibility cloaks and perfect lenses could, in principle, be constructed using such materials. I will present a method for obtaining convergent power series representations for the fields and associated dispersion relations of electromagnetic waves propagating in a species of metamaterial known as plasmonic crystal. The technology provided by these series lead to a rich scenario in which to explore effective properties in a mathematically rigorous setting. This has allowed us give definite answers regarding the negative index behavior of plasmonic crystals.

Tuesday, December 1, 2009

Posted November 25, 2009
Last modified January 10, 2022

4:00 pm Lockett 285

Alexander Prestel, Universität Konstanz
Axiomatizing the complex unit disc

The Lefschetz principle from algebraic geometry says that every algebraic property over the field of complex numbers involving only polynomials, is also true over any algebraically closed field in characteristic 0. We present a similar transfer principle involving in addition the absolute value of the complex field.

Friday, December 4, 2009

Posted December 1, 2009
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

1:00 pm 338 Johnston Hall

Collin Wick, Louisiana Tech University
Using Computers to Discover Strange Behavior at Water

Wednesday, December 9, 2009

Posted November 26, 2009

12:00 pm James Keisler Lounge

Holiday Party

Everyone is invited to share in the Season\'s Spirit. Please bring a dish to share.

Monday, January 11, 2010

Posted January 2, 2010

1:00 pm – 4:00 pm 285 Lockett Hall

Comprehensive / PhD Qualifying Exam in Algebra

This examination is required for doctoral students who have completed Math 7210 but have not yet passed the examination at the PhD level.

Wednesday, January 13, 2010

Posted January 2, 2010
Last modified January 11, 2010

1:00 pm – 4:00 pm 285 Lockett

Comprehensive / PhD Qualifying Exam in Analysis

This examination is required for doctoral students who have completed Math 7311 but have not yet passed this test at the PhD Qualifying Level.

Friday, January 15, 2010

Posted January 2, 2010

1:00 pm – 4:00 pm 285 Lockett

Comprehensive / PhD Qualifying Exam in Topology

This examination is required for doctoral students who have completed Math 7510 but have not yet passed this test at the PhD Qualifying Level.

Tuesday, January 19, 2010

Posted January 12, 2010
Last modified January 14, 2010

2:00 pm – 3:00 pm Lockett 16

Jiajun Wang, California Institute of Technology Candidate for Assistant Professor Position in Topology
On combinatorial Floer homology

Posted January 7, 2010

3:40 pm – 4:30 pm 338 Johnston Hall

Jason Howell, Carnegie Mellon University Candidate for Assistant Professor Position in Math and CCT
Dual-Mixed Finite Element Methods For Fluids

Jason Howell, Carnegie Mellon University Postdoctoral Associate In The Center For Nonlinear Analysis And The Department Of Mathematical Sciences Bio Jason Howell is a Postdoctoral Associate in the Center for Nonlinear Analysis and the Department of Mathematical Sciences at Carnegie Mellon University. He earned a PhD in Mathematical Sciences at Clemson University in 2007 with a specialty in numerical analysis and computational mathematics. During 2004-2006, he had three appointments as a summer scholar with the Center for Applied Scientific Computing at Lawrence Livermore National Laboratory. He also holds an MS in Mathematical Sciences from Clemson and a BS in Mathematics from the College of Charleston. His research interests lie at the intersection of analysis, computation, and applications, and he currently works on projects in finite element methods for fluid and solid mechanics, numerical methods for non-Newtonian fluids, and numerical methods for fluid/fluid and fluid/structure interaction problems. Abstract Accurate and efficient numerical methods to approximate fluid flows are important to researchers in many fields, including mechanical, materials, and biomedical engineering. In many applications within these fields, it is of paramount importance to accurately predict fluid stresses. However, in most existing numerical schemes for fluids, the primary unknown of interest is the fluid velocity. This motivates the development of dual-mixed finite element methods for fluids, in which the stress is a primary unknown of interest, and the study of inf-sup conditions for single and twofold saddle point problems is an important component of the construction of these methods. This study has led to results that give equivalent sets of inf-sup conditions for twofold saddle point problems, yielding new tools for proofs of well-posedness and finite element compatibility. These tools, together with a macroelement technique, show compatibility of a new dual-mixed method for fluids employing Arnold-Winther symmetric tensor finite elements for stress.

Thursday, January 21, 2010

Posted January 7, 2010
Last modified October 4, 2021

2:00 pm – 3:00 pm 338 Johnston Hall

Shawn Walker, New York University Candidate for Assistant Professor Position in Math and CCT
Shape Optimization Of Peristaltic Pumping

Shawn W. Walker, New York University
Research Scientist, Courant Institute Of Mathematical Sciences

Bio: Shawn W. Walker is a postdoctoral researcher and instructor at New York University's Courant Institute of Mathematical Sciences. He earned his PhD in aerospace engineering and an MSc in applied mathematics and scientific computing from the University of Maryland in 2007 and also holds an MSc in engineering and applied science from Yale University and a BSc in electrical engineering from Virginia Polytechnic Institute & State University. His research interests include finite element methods and PDEs, free boundary problems, shape optimization, and fluid-structure interaction and control. http://www.cims.nyu.edu/~walker/

Abstract: Transport is a fundamental aspect of biology and peristaltic pumping is a fundamental mechanism to accomplish this; it is also important in many industrial processes. We present a variational method for optimizing peristaltic pumping in a two dimensional periodic channel with moving walls to pump fluid. No a priori assumption is made on the wall motion, except that the shape is static in a moving wave frame. Thus, we pose an infinite dimensional optimization problem and solve it with finite elements. Sensitivities of the cost and constraints are computed variationally via shape differential calculus and $L^2$-type projections are used to compute quantities such as curvature and boundary stresses. Our Optimization method falls under the category of sequential quadratic programming (SQP) methods. As a result, we find optimized shapes that are not obvious and have not been previously reported in the peristaltic pumping literature. Specifically, we see highly asymmetric wave shapes that are far from being sine waves. Many examples are shown for a range of fluxes and Reynolds numbers up to Re=500 which illustrate the capabilities of our method.

Posted December 24, 2009
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 285

Jan Dijkstra, Vrije Universiteit Amsterdam
Topological Kadec norms with applications

There will be coffee and cookies in the lounge at 3:00.

Friday, January 22, 2010

Posted January 12, 2010
Last modified January 15, 2010

3:40 pm – 4:30 pm Lockett 285

Andrew Putman, MIT Candidate for Assistant Professor Position in Topology
The Picard Group of the Moduli Space of Curves with Level Structures

Monday, January 25, 2010

Posted January 19, 2010

3:40 pm – 4:30 pm Room 233 Lockett Hall

Anna Zemlyanova, Department of Mathematics, LSU
Method of Riemann surfaces in modelling of cavitating flow

Cavitation is the formation of a vapor filled area in the liquid which usually appears due to low pressures and high velocities. Riemann surfaces are used in fluid mechanics both for mathematical modeling of the cavity closure and for solution of the resulting mathematical problems. In this talk I will discuss most commonly used cavity closure models and present a detailed solution to the problem of a supercavitating wedge in a jet or under a free surface using Tulin\'s single- or double-spiral-vortex cavity closure model. The solution involves the application of Riemann-Hilbert problems on the elliptic Riemann surface. The numerical results will be presented.

Tuesday, January 26, 2010

Posted January 14, 2010
Last modified October 4, 2021

2:10 pm Lockett 10

Richard Kent, Brown University Candidate for Assistant Professor Position in Topology
Analytic functions from hyperbolic manifolds

There will be coffee and cookies in the lounge at 3:00.

Posted January 7, 2010
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 285

Michael Farber, University of Durham
Stochastic algebraic topology and robotics

I will describe solutions to several problems of mixed probabilistic-topological nature which are inspired by applications in topological robotics. These problems deal with systems depending on a large number of random parameters, $n\to \infty$. Our results predict the values of various topological characteristics of configuration spaces of such systems.

There will be coffee and cookies in the lounge at 3:00.

Posted January 21, 2010
Last modified January 24, 2010

4:30 pm Lockett 5

Meeting of the faculty

Department priorities/budget scenarios.

Wednesday, January 27, 2010

Posted January 12, 2010
Last modified January 14, 2010

3:40 pm – 4:30 pm Lockett 285

Mark Colarusso, University of Notre Dame Candidate for Assistant Professor Position in Lie Theory
THE GELFAND-ZEITLIN INTEGRABLE SYSTEM ON g[(n, C)

Thursday, January 28, 2010

Posted August 11, 2009
Last modified January 25, 2010

3:40 pm – 4:30 pm Lockett 285
(Originally scheduled for Tuesday, September 15, 2009)

Frank Sottile, Texas A&M
Orbitopes

Abstract:
An orbitope is the convex hull of an orbit of a compact
group acting linearly on a vector space. Instances of these
highly symmetric convex bodies have appeared in many areas
of mathematics and its applications, including protein
reconstruction, symplectic geometry, and calibrations in
differential geometry.
In this talk, I will discuss Orbitopes from the perspectives
of classical convexity, algebraic geometry, and optimization
with an emphasis on ten motivating problems and concrete examples.
This is joint work with Raman Sanyal and Bernd Sturmfels.

There will be coffee and cookies in the lounge at 3:00.

Friday, January 29, 2010

Posted January 14, 2010

3:40 pm – 4:30 pm Lockett 285

Richard Oberlin, UCLA Candidate for Assistant Professor Position in Analysis
A variation-norm Carleson Theorem

Posted January 28, 2010

4:40 pm – 5:30 pm 235 Lockett Hall

Carolyn Chun, Victoria University in Wellington, New Zealand Former LSU graduate student
Matroid Fragility

Dinner will follow the talk, and will be held at Rama\'s Restaurant, commencing at 6pm.

Monday, February 1, 2010

Posted January 21, 2010
Last modified March 2, 2022

3:40 pm – 4:30 pm Room 233 Lockett Hall

Phuc Nguyen, Department of Mathematics, Louisiana State University
Capacitary inequalities and quasilinear Riccati type equations with critical or super-critical growth

We establish explicit criteria of solvability for the quasilinear Riccati type equation $−\Delta_p u = |∇u|^q + ω$ in a bounded $\mathcal{C}^1$ domain $\Omega ⊂ \mathbb{R}^n$, $n ≥ 2$. Here $\Delta_p$, $p > 1$, is the $p$-Laplacian, $q$ is critical $q = p$ or supper critical $q > p$, and the datum $ω$ is a measure. Our existence criteria are given in the form of potential theoretic or geometric (capacitary) estimates that are sharp when $ω$ is compactly supported in the ground domain $\Omega$. A key in our approach to this problem is capacitary inequalities for certain nonlinear singular operators arising from the $p$-Laplacian.

Posted January 13, 2010
Last modified January 25, 2010

3:40 pm – 4:30 pm Lockett 285

Karl Schwede, University of Michigan Candidate for Assistant Professor Position in algebraic geometry
Singularities of polynomials in characteristic 0 and characteristic p

Tuesday, February 2, 2010

Posted January 7, 2010
Last modified January 28, 2010

3:40 pm – 4:30 pm 338 Johnston Hall

Xuemin Tu Candidate for Assistant Professor Position in Math and CCT
Inexact Balancing Domain Decomposition By Constraints Algorithms

Abstract and Bio available at www.cct.lsu.edu

Thursday, February 4, 2010

Posted January 28, 2010

8:30 am Keisler Lounge, Lockett Hall 321.

Max Gunzburger, Florida State University
Conversation and Breakfast

Prof. Max Gunzburger from Florida State University is visiting LSU. The SIAM Student Chapter presents an informal conversation with him to talk about his career experiences. Breakfast will be served.
This meeting is open to everyone.

Posted November 7, 2009
Last modified January 31, 2010

3:30 pm – 4:30 pm 338 Johnston Hall

Max Gunzburger, Florida State University
Color Printers, Mailboxes, Fish, And Homer Simpson Or Centroidal Voronoi Tesselations: Algorithms And Applications

Refreshments at 3pm. Additional details at: http://www.cct.lsu.edu/events/talks/503

Posted February 2, 2010
Last modified February 20, 2022

5:00 pm Keisler Lounge, Lockett Hall 321

Leah Childers, LSU
Introduction to the mapping class group

We will look at an interesting group associated to surfaces called the mapping class group. Mapping class groups arise in the study of many areas of mathematics including: geometric group theory, low dimensional topology and algebraic geometry. We will explore basic elements of this group as well as some of the relations. No background in topology will be assumed.

Friday, February 5, 2010

Posted November 9, 2009
Last modified February 11, 2022

1:00 pm – 5:00 pm Saturday, February 6, 2010 Louisiana State University

Max Gunzburger, Florida State University
Mac Hyman, Tulane University
Robert Krasny, University of Michigan
SCALA 2010 - Scientific Computing Around Louisiana

The LSU Center for Computation and Technology (CCT) and Tulane University's Center for Computational Science will co-sponsor an inaugural meeting to:
(1) highlight cutting-edge topics in scientific computing,
(2) showcase the research at Louisiana institutions and,
(3) promote collaborations across the state of Louisiana.

This meeting is open to any faculty, post-doctoral researchers or students from any college in and around Louisiana.
Fore more details, please view the official announcement: www.cct.lsu.edu/scala2010

Monday, February 8, 2010

Posted January 15, 2010
Last modified January 28, 2010

3:40 pm – 4:30 pm Lockett 285

Juhi Jang, New York University Candidate for Assistant Professor Position in PDEs/applied math
Vacuum in Gas and Fluid dynamics

Tuesday, February 9, 2010

Posted January 7, 2010
Last modified January 28, 2010

3:40 pm – 4:30 pm 338 Johnston Hall

Yingda Cheng Candidate for Assistant Professor Position with Math and CCT
Discontinuous Galerkin Finite Element Methods And Applications To Boltzmann-Poisson Models In Semiconductor Device Simulation

Abstract and Bio at www.cct.lsu.edu

Wednesday, February 10, 2010

Posted December 15, 2009
Last modified January 29, 2010

Student Colloquium

12:40 pm – 1:30 pm Lockett 2

John Oprea, Cleveland State University
Mathematics and Soap Films

Why do one-celled creatures take the shapes they do? Why do red-blood cells

have their characteristic shape? More and more, in biology as well as other

sciences, the notion of \"shape\" is becoming important. Mathematicians have ways

of measuring shape and of determining shape through optimization. This fits

well with Nature\'s penchant for economy, so it isn\'t surprising (in retrospect)

that soap films, which arise from surface tension\'s ability to shrink surface

area, are a kind of analog computer for the mathematics of minimizing surface

area. This talk will consist of three parts: soap film demonstrations (which

will set the stage for); a bit of mathematics and; computer experimentation and

illustration. Since audience participation is required for soap film

experiments, attendees are encouraged not to wear their best attire!

Thursday, February 11, 2010

Posted January 15, 2010
Last modified February 4, 2010

2:00 pm – 3:00 pm Lockett 112

Leonardo Mihalcea, Baylor University Candidate for Assistant Professor Position in Algebraic Geometry
Quantum K-Theory of Grassmannians and the Geometry of Spaces of Curves

Posted December 15, 2009
Last modified January 29, 2010

Student Colloquium

3:40 pm – 4:30 pm Lockett 15

John Oprea, Cleveland State University
Variational Principles and Real-World Shapes: Balloons and Droplets in Space

When we look at Nature, we see shapes everywhere. In this talk, we will
describe the shape of a Mylar balloon in terms of a variational principle and
see how this can be understood in terms of the physical characteristics of
balloons. (A Mylar balloon is often found at kids\' birthday parties and is
formed by taking two disks of Mylar, sewing them together along their
boundaries and inflating.) This topic is a prime example of the interplay among
physical principles, geometry, analysis and symbolic computation. We will also
discuss the principles determining the shapes arising in water-bubble
experiments aboard the International Space Station.

Posted February 10, 2010

5:00 pm Keisler Lounge, Lockett Hall 321

Pizza and organization of future meetings ...

... with the new president, Tommy Naugle.

Friday, February 12, 2010

Posted February 1, 2010
Last modified February 4, 2010

3:40 pm – 4:30 pm Lockett 285

John Oprea, Cleveland State University
Gottlieb Groups, LS Category and Geometry

Abstract: Gottlieb groups are special subgroups of the homotopy groups which
arise in many homotopical contexts. LS category is a numerical homotopy
invariant that was originally invented to give a bound on the number of
critical points of smooth functions. Strangely enough, these two things are
related, and --- what's more --- they are related via analogues of geometric
theorems. This talk will recall basic notions of algebraic topology,
introduce Gottlieb groups, LS category and their relationships and see how
geometry fits into the mix.

There will be coffee and cookies in the lounge at 3:00.

Wednesday, February 17, 2010

Posted February 10, 2010
Last modified February 17, 2010

3:30 pm – 4:30 pm 338 Johnston Hall

Joscha Gedicke, Humboldt University of Berlin
Optimal Convergence of the Adaptive Finite Element Method

Thursday, February 18, 2010

Posted January 7, 2010
Last modified February 12, 2010

3:40 pm – 4:30 pm Lockett 285

Bojko Bakalov, North Carolina State University
Singularities, root systems, and W algebras

Abstract:
Gromov-Witten invariants are naturally organized in a generating function,
which is a formal power series in infinitely many variables. In many cases
this function is a highest-weight vector for a certain
infinite-dimensional algebra and at the same time is a solution of an
integrable hierarchy of partial differential equations. Similar generating
functions can be introduced for the Frobenius structures coming from
singularities of hypersurfaces. We will start by reviewing the marvelous
relations among singularities, root systems and reflection groups. The
generating function of a simple singularity was shown recently to be a
solution of the Kac-Wakimoto hierarchy. Our main result is that it is also
a highest weight vector for the corresponding W algebra.

There will be coffee and cookies in the lounge at 3:00.

Friday, February 19, 2010

Posted February 19, 2010

3:40 pm – 4:30 pm 285 Lockett Hall

Stan Dziobiak, Department of Mathematics, LSU Graduate Student
An excluded-minor characterization of apex-outerplanar graphs

It is well known that the class of outerplanar graphs is minor-closed and can be characterized by two excluded minors: K_4 and K_{2,3}. The class of graphs that contain a vertex whose removal leaves an outerplanar graph is also minor-closed. We will present the complete list of excluded minors for this class and outline the major steps of the proof.

Thursday, February 25, 2010

Posted February 9, 2010

3:40 pm – 4:30 pm Lockett 285

Scott Armstrong, Department of Mathematics, Louisiana State University
The infinity Laplace equation, tug-of-war games, and minimizing Lipschitz extensions

Abstract: Given a nice bounded domain, and a Lipschitz function defined on
its boundary, consider the problem of finding an extension of this
function to the closure of the domain which has minimal Lipschitz
constant. This is the archetypal problem of the calculus of variations
in $L^\\infty$. There can be many such minimal Lipschitz extensions,
but there is there is a unique minimizer once we properly \"localize\"
this Lipschitz minimizing property. The uniquely specified function is
a solution of the infinity Laplace equation: the Euler-Lagrange
equation for our optimization problem. This PDE is a highly degenerate
nonlinear elliptic equation which does not have smooth solutions. In
this talk we will discuss what we know about the infinity Laplace
equation, what the important open questions are, and some recent
developments. We will even play a two-player random-turn game called
\"tug-of-war\". One advantage of our topic is that it is completely
accessible to graduate students and even perhaps some undergraduates.

There will be coffee and cookies in the lounge at 3:00.

Monday, March 1, 2010

Posted January 25, 2010
Last modified March 2, 2022

3:40 pm – 4:30 pm Room 233, Lockett Hall

Alexander Barnett, Department of Mathematics, Dartmouth College
Robust and accurate computation of photonic crystal band structure using a new integral equation representation of quasi-periodic fields

Host: Stephen Shipman

Photonic crystals are dielectric structures with periodicity on the scale of the wavelength of light. They have a rapidly growing range of applications to signal processing, sensing, negative-index materials, and the exciting possibility of integrated optical computing. Calculating their “band structure” (propagating Bloch waves) is an elliptic PDE eigenvalue problem with (quasi-)periodic boundary conditions on the unit cell, i.e., eigenmodes on a torus. Since the material is piecewise homogeneous, boundary integral equations (BIE) are natural for high-accuracy solution.

In such geometries BIEs are usually periodized by replacement of the free space Greens function kernel by its quasi-periodic cousin. We show why this approach fails near the (spurious) resonances of the empty torus. We introduce a new approach which cures this problem: imposing the boundary conditions on the unit-cell walls using layer potentials, and a finite number of neighboring images, resulting in a second-kind integral equation with smooth data. This couples to existing BIE tools (including high-order quadratures and Fast Multipole acceleration) in a natural way, allowing accuracies near machine precision. We also discuss inclusions which intersect the unit cell walls, and how we use a small number of evaluations to interpolate over the Brillouin zone to spectral accuracy. Joint work with Leslie Greengard (NYU).

Wednesday, March 3, 2010

Posted February 26, 2010
Last modified March 1, 2010

3:40 pm – 4:30 pm 233 Lockett

Jean-Marie Mirebeau, Laboratoire Jacques Louis Lions, Universite Pierre et Marie Curie
Optimally Adapted Finite Element Meshes

Given a function f defined on a bounded domain and a number n>0, we study the properties of the triangulation T_n that minimizes the distance between f and its interpolation on the associated finite element space, over all triangulations of at most n elements. The error is studied in the Lp norm or W1p norm and we consider Lagrange finite elements of arbitrary polynomial order. We establish sharp asymptotic error estimates as n tends to infinity when the optimal anisotropic triangulation is used, and we illustrate these results with numerical experiments.

Friday, March 5, 2010

Posted March 3, 2010

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm 285 Lockett Hall

Lisa Warshauer, LSU Mathematics Graduate student
Graphs that are Almost Series-Parallel

Abstract: Consider the class of graphs G with the property that one can add an edge e and contract it out to obtain a series-parallel graph. This class of graphs is closed under taking minors. We give an excluded-minor characterization for the class.

Monday, March 8, 2010

Posted February 25, 2010

3:40 pm – 4:30 pm Lockett 285

David Gepner, University of Illinois at Chicago
K-theory and additive functors

Posted January 18, 2010
Last modified November 29, 2022

3:40 pm – 4:30 pm Room 233 Lockett Hall

Diego Maldonado, Kansas State University
Bilinear pseudo-differential operators: motivations and recent developments

During the 70s, driven by some problems posed by A. Calderón, R. Coifman and Y. Meyer pioneered a theory of bilinear pseudo-differential operators. These operators later found further applications in topics of analysis and PDEs such as compensated compactness, regularity of solutions to PDEs, boundedness properties of commutators, bilinear singular integrals, and paraproducts, and pointwise multipliers for functional spaces.

Departing from the definition of the Fourier transform, in this talk we will tour the theory of bilinear pseudo-differential operators and some of its applications to finally arrive at the latest results and some open problems.

Tuesday, March 9, 2010

Posted March 3, 2010
Last modified March 6, 2010

2:00 pm Lockett 233

Santiago Fortes, Department of Mathematics, LSU
Power Series Expansions for Waves in High-contrast Plasmonic Crystals (Dissertation Title)

ABSTRACT: the possibility of engineering composite materials with localized internal resonances has generated much interest lately. In such materials, an incoming electromagnetic field can become amplified by several orders of magnitude. Numerical simulations indicate that a composite material known as plasmonic crystal exhibits such resonances. I will present a method for obtaining convergent power series representations for the fields and the first branch of the associated dispersion relations of electromagnetic waves in plasmonic crystals. The existence of these convergent series representations precludes the possibility of internal resonances in the first branch of the dispersion relation.

Light Refreshments will be served at the Keisler lounge at 1:30pm.

Wednesday, March 10, 2010

Posted March 4, 2010
Last modified March 3, 2021

1:40 pm – 2:30 pm Lockett 381

Karl Heinrich Hofmann, Darmstadt University, Germany Professor Emeritus
The probability that two elements commute in a compact group

The FC-center of a group $G$ is the characteristic subgroup $F$ of all elements those conjugacy class is finite. If $G=F$, then $G$ is called an FC-group. We show that a compact group $G$ is an FC-group if and only if its center $Z(G)$ is open (that is, $G$ is center by finite) if and only if its commutator subgroup is finite (that is, $G$ is finite by commutative). Now let $G$ be a compact group and let $p$ denote the Haar measure of the set of all pairs $(x,y)$ in $G\times G$ for which $[x,y]=1$; this is the probability that two randomly picked elements commute. We prove that $p>0$ if and only if the FC-center $F$ of $G$ is open and so has finite index. If these conditions are satisfied, then $Z(F)$ is a characteristic normal abelian open subgroup of $G$ and $G$ is abelian by finite.

Posted March 3, 2010
Last modified October 4, 2021

2:40 pm – 3:30 pm Prescott 205

Gisele Goldstein, University of Memphis
Derivation and Interpretation of Dynamic Boundary Conditions for the Heat and Wave Equations

There will be coffee and cookies in Prescott 205 at 2:00.

Posted March 1, 2010
Last modified March 4, 2010

3:40 pm – 5:40 pm Lockett 6

Meeting with Graduate Students

Topics of Discussion
1.) Departmental changes in TA duties.
2.) The different programs and traineeships that are available. We will also have some of our current trainees discuss their experience with the program.

Thursday, March 11, 2010

Posted March 3, 2010
Last modified October 4, 2021

2:10 pm – 3:00 pm Lockett 10

Jerome Goldstein, University of Memphis
Instantaneous blowup and related nonexistence issues

There will be coffee and cookies in the lounge at 3:00.

Posted February 24, 2010

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 285

Mark Watkins, University of Sydney
A quick tour of Magma features

Abstract:
We give a quick tour of some features of the Magma computer algebra system.
These will include: modular forms, algebraic geometry (sheaf cohomology and
Groebner bases), computing with L-functions, machinery for function fields,
lattices, and some group/representation theory. No experience with Magma
will be assumed.

There will be coffee and cookies in the lounge at 3:00.

Friday, March 12, 2010

Posted February 25, 2010
Last modified March 2, 2021

3:40 pm Lockett 285

Mark Watkins, University of Sydney
A polynomial version of Hall's conjecture

Hall's conjecture asks for small nonzero values of |x^3-y^2| for integers x,y. The polynomial analogue is to ask for f(t)^3-g(t)^2 to be of small degree (compared to that of f,g, which we take to be in \bar Q[t]). The ABC theorem (of Davenport and Mason) gives an explicit lower bound here. Via the use of Belyi functions and covers of P^1 (or work of Stothers), we can count the number of (f,g) that meet this minimal degree, and this turns out to be related to the Catalan numbers. This leaves the question of actually exhibiting (f,g) that minimise the degree. For instance, if there are 14 solutions, we might expect them all to be Galois conjugate in a number field of degree 14. In joint work with Noam Elkies, we explicitly construct solutions for many cases, using a battery of techniques, the most notable of which is multi-dimensional p-adic Newton iteration to solve polynomial system of equations (or at least find isolated points on the solution variety). The fields of definition of these solutions are ramified only at small primes, due to a theorem of Beckmann.

Sunday, March 14, 2010

Posted March 14, 2010

1:30 pm Keisler Lounge, Lockett Hall 321

PI DAY

Friday, March 19, 2010

Posted March 15, 2010

VIGRE@LSU: Student Colloquium Questions or comments?

3:40 pm – 4:30 pm 285 Lockett Hall

Tanya Lueder, LSU Mathematics Graduate Student
A Characterization of Near Outer-Planar Graphs

A graph containing an edge whose removal results in an outer-planar graph is a near outer-planar graph. We present partial results towards the larger goal of describing the class of all such graphs in terms of a finite list of excluded graphs. Specifically, we give a description of those members of this list that are not 2-connected and do not contain a subdivision of a three-spoke wheel.

Monday, March 22, 2010

Posted March 4, 2010
Last modified March 22, 2010

3:40 pm – 4:30 pm Lockett 285

Barry Cipra Barry Cipra is a freelance journalist who writes about mathematics in a very wide range of venues
SeVenn, EleVenn, and Beyond

The speaker will report on recent results on the existence of
rotationally symmetric Venn diagrams -- a problem first posed, by an
undergraduate, in the 1960s, and finally fully solved, by another
undergraduate, almost 40 years later. Many related open problems remain,
perhaps for yet another undergraduate to solve.

Posted March 11, 2010
Last modified October 1, 2021

3:40 pm – 5:00 pm Lockett 276

Gregor Masbaum, University Paris 7
The Arf-invariant formula for graphs on surfaces

Kasteleyn showed how to count dimer coverings (= perfect matchings) on a planar bipartite graph by evaluating the determinant of a certain matrix. The method works for non-bipartite graphs as well, upon replacing the determinant with a Pfaffian. If the graph is not planar, but embedded in a surface of genus g, Kasteleyn stated and Gallucio-Loebl proved a formula expressing the number of dimer coverings as a linear combination of 4^g Pfaffians. The main aim of the talk is to explain a new proof of this formula based on the theory of Arf invariants of quadratic forms on the mod 2 homology of the surface. I will then discuss the question of whether the minimal number of Pfaffians needed to count dimer coverings is always a power of 4. If time remains, I will explain a recent result of Loebl and myself which gives an affirmative answer to the analogous question for the Ising model on a graph.

Tuesday, March 23, 2010

Posted January 12, 2010

VIGRE@LSU: Student Colloquium Questions or comments?

2:00 pm – 3:00 pm Lockett 301D

Final Event of Final Exam for Non-Thesis MS

Each student applying to receive a non-thesis MS in May 2010 must sign up with the Graduate School for the final exam final event as listed here. The Committee will be Profs. Cohen, Perlis, and Richardson (Chair).

Posted March 4, 2010
Last modified March 9, 2010

3:40 pm – 4:30 pm TBA

Barry Cipra Barry Cipra is a freelance journalist who writes about mathematics in a very wide range of venues
Science Writing

Barry Cipra will be addressing the Communicating Math Class. All are welcome to attend.

Posted February 25, 2010
Last modified March 12, 2010

Algebra and Number Theory Seminar Questions or comments?

3:40 pm Lockett 285

Robert Fitzgerald, Southern Illinois University
Extending Hurwitz's proof of the four square theorem

The four square theorem says every positive integer can be represented as a sum of four squares. Lagrange (1770) proved this via Euler's four square identity and a descent argument. Hurwitz (1919) gave a proof using a ring of quaternions whose key property is being norm Euclidean. There are six other norm forms that represent all positive integers. I discuss recent work to construct norm Euclidean rings of quaternions for these cases.

Posted March 16, 2010
Last modified March 18, 2010

4:30 pm – 6:30 pm 338 Johnston Hall

LSU SIAM Chapter meets UIC Chapter - A Student Conference

The SIAM student chapter from the University of Illinois at Chicago is visiting us and we are having a series of student talks. After the talks we will have free pizza. Everyone is invited.

Speakers:

Jun Niu (UIC): Harmonic Series with Random Signs

We consider the harmonic series with random signs. We will discuss the convergence and limit distribution of that summation. We will also show that it has a continuous density function. Some basic probability theorems and analytical techniques are involved.

Rick Barnard (LSU): Using Local Noise Characteristics in Denoising MALDI-TOF Mass Spectrometry

Matrix-Assisted Laser Desorption/Ionization Time-of-Flight(MALDI-TOF) Mass Spectrometry is a useful technique for the identification of polymers and other complex substances. However, noise from background ions leads to the misidentification of false peaks in the data (a crucial step in substance identification) and hides smaller, albeit important, peaks. Current techniques for overcoming this either involve large amounts of data, user interaction, or blindly smoothing out data. This talk will present the advantages of using local properties of the background ions in reducing the presence of background noise without user bias and without excessive data.

Miao Xu (UIC): Asymptotics of the American CEV Options Pricing Model

We examine the early exercise policy and behavior of a one-asset American Option. In particular, we consider the Constant-Elasticity of Variance (CEV) model in the case for β = 1 (the square root process), and we analyze the optimal stopping region by ﬁnding the asymptotic behavior for times close to expiration and at inﬁnite time to expiration.

Jintao Cui (LSU): Nonconforming Finite Element Methods for a Two Dimensional Curl-Curl and Grad-Div Problems

In this talk we discuss both a classical nonconforming ﬁnite element method and an interior penalty version for a two dimensional curl-curl and grad-div problem. The ﬁrst method is based on a discretization using weakly continuous P1 vector ﬁelds and includes two consistency terms involving the jumps of the vector ﬁelds across element boundaries. The second one uses discontinuous P1 vector ﬁelds and includes two additional over-penalization terms. Optimal convergence rates (up to an arbitrary positive ϵ) in both the energy norm and the L 2 norm are established for both methods on graded meshes. We will present both theoretical and numerical results. This is joint work with Susanne C. Brenner, Fengyan Li and Li-yeng Sung.

Thursday, March 25, 2010

Posted January 27, 2010
Last modified October 4, 2021

3:40 pm – 4:30 pm Lockett 285

Charles Weibel, Rutgers University
The Lichtenbaum and Bloch-Kato Conjectures are now Theorems

The Lichtenbaum Conjecture related algebraic K-theory of the integers to the values of the Riemann Zeta function. The Bloch-Kato Conjecture said that the étale cohomology of a field with (odd) finite coefficients) should have a presentation with units as generators and simple quadratic relations (the ring with this presentation is now called the "Milnor K-theory"). For Z/2 coefficients, this is a famous theorem of Voevodsky.

This talk will be a non-technical overview of the ingredients that go in to the proof, and why this conjecture matters to non-specialists. Most of the ingredients are due to Rost and Voevodsky.

Here is a fun consequence of all this. We now know the first 20,000 groups K_n(Z) of the integers, except when 4 divides n. The assertion that these groups are zero when 4 divides n (n>0) is equivalent to Vandiver's Conjecture (in number theory), and if it holds then we have fixed Kummer's 1849 "proof" of Fermat's Last Theorem. If any of them are nonzero, then the smallest prime dividing the order of this group is at least 16,000,000.

There will be coffee and cookies in the lounge at 3:00.

Friday, March 26, 2010

Posted March 26, 2010

CCT Lecture Events organized by the LSU Center for Computation and Technology

1:45 pm – 1:45 pm 218 Johnston

Xiaoliang Wan, Louisiana State University
Spectral hp element method and Nektar, Part I

Posted February 8, 2010
Last modified March 16, 2010

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 285

Michael Anshelevich, Department of Mathematics, Texas A&M University
Characterizations of free Meixner distributions

The free Meixner distributions are a very simple family of measures, relatives of the semicircle law. Despite their simplicity, they have a number of characterizations. For example, their orthogonal polynomials are the only ones with a "resolvent-type" generating function, and stochastic processes with free Meixner distributions are characterized by a quadratic regression property. Many of these characterizations arise in the context of Free Probability Theory, the relevant aspects of which will be explained (and no background in which will be assumed).

Posted March 3, 2010
Last modified January 6, 2021

3:40 pm – 4:30 pm Lockett 237

Charles Weibel, Rutgers University
A 1972 Question of Bass and Hochschild homology

Bass asked if R satisfies K_0(R)=K_0(R[x]) then is K_0(R[x,y]) any different? In joint work with Cortinas, Haesemeyer and Walker, we show that the answer is \'no.\'

Tuesday, March 30, 2010

Posted March 30, 2010

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 338 Johnston Hall

Shiyuan Gu, Mathematics, LSU
Introduction to CUDA

Posted March 22, 2010
Last modified March 3, 2021

3:40 pm Lockett 285

Christopher Bremer, Mathematics Department, LSU
A geometric theory of fundamental strata

In this talk, I will describe a theory of fundamental strata for meromorphic connections developed in joint work with D. S. Sage. Fundamental strata were originally used by Bushnell, Kutzko, Howe and Moy to classify cuspidal representations of GL_n over a local field. In the geometric setting, fundamental strata play the role of the `leading term' of a connection. I will introduce the concept of a regular stratum, which generalizes a condition imposed by Boalch (and previously, by Jimbo, Miwa, and Ueno) to study the geometry of the irregular Riemann Hilbert map. Finally, I will describe an application of our theory to a particular case of the wildly-ramified geometric Langlands conjecture.

Thursday, April 1, 2010

Posted January 7, 2010
Last modified March 17, 2010

3:40 pm – 4:30 pm Lockett 285

Boris Rozovsky, Brown University
Quantization of Stochastic Navier-Stokes Equation

Abstract: We consider a stochastic Navier-Stokes equation driven by a
space-time Wiener process. This equation is quantized by transformation of
the nonlinear term to the Wick product form. An interesting feature of this
type of perturbation is that it preserves the mean dynamics: the expectation
of the solution of the quantized Navier-Stokes equation solves the
underlying deterministic Navier-Stokes equation. From
the stand point of a statistician it means that the perturbed model is an
unbiased random perturbation of the deterministic Navier-Stokes equation.

The quantized equation is solved in the space of generalized stochastic
processes using the Cameron-Martin version of the Wiener chaos expansion. A
solution of the quantized version is unique if and only if the uniqueness
property holds for the underlying
deterministic Navier-Stokes equation. The generalized solution is obtained
as an inverse of solutions to corresponding quantized equations. We will
also demonstrate that it could be approximated by real (non-generalized
processes). A solution of the
quantized Navier-Stokes equation turns out to be non- anticipating and
Markov.

The talk is based on a joint work with R. Mikulevicius.

There will be coffee and cookies in the lounge at 3:00.

Monday, April 12, 2010

Posted March 21, 2010

10:00 am – 11:00 am 338 Johnston Hall

Juan Galvis, Texas A&M University
Wiener-Chaos finite element methods for the approximation of infinite-dimensional stochastic elliptic equations

Posted March 21, 2010
Last modified March 2, 2022

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Room 233 Lockett Hall

Peter Wolenski, LSU Department of Mathematics Russell B. Long Professor
Impulsive systems

An impulsive system is a dynamical system that may exhibit “jumps” in the state variable. We shall introduce a model of such systems driven by a measure, and discuss solution concepts and recent results. A model of synaptic dynamics will be given as an example, which has been introduced in the neuroscience literature to describe neuronal population activity.

Tuesday, April 13, 2010

Posted March 19, 2010
Last modified April 12, 2010

3:40 pm Lockett 285

Daniel Sage, Mathematics Department, LSU
Moduli Spaces of Irregular Singular Connections

An important problem in the geometric Langlands correspondence is the construction of global meromorphic connections on the projective line with specified local behavior. Boalch has studied the moduli space of such connections in the case where the leading term of the connection is regular semisimple at each singular point. In this talk, I will describe joint work with Bremer in which we show how to construct moduli spaces of connections in much greater generality. I will define a more useful notion of the leading term of a connection in terms of fundamental strata, a concept adapted from the representation theory of p-adic groups. In particular, I will introduce the concept of a regular stratum; a formal connection containing a regular stratum generalizes the naive idea of a connection with regular semisimple leading term. I will then explain how to construct the moduli space of connections on the projective line with specified regular local formal isomorphism classes at a collection of singular points. This moduli space is a symplectic reduction of a direct product of manifolds encoding local data at the singularities. I will also show that this moduli space arises as a symplectic quotient of a smooth manifold by a torus action.

Thursday, April 15, 2010

Posted March 12, 2010
Last modified April 5, 2010

LSU AWM and SIAM Chapter Event

3:30 pm – 5:30 pm B5 Lockett Hall (Basement)

Career Day

A panel of graduate students, postdocs, and faculty will provide information on the application process for teaching and research positions and give advice for the life after graduation.
Pizza will be served after the discussion.

Friday, April 16, 2010

Posted January 14, 2010

SPIN. No other department seminars or events to be scheduled this afternoon.

1:00 pm – 4:30 pm TBA

Spring Invitational for students

The college requested that we not schedule department events because of the need for advising Spring Invitational students from 1:00-4:30 pm.

Monday, April 19, 2010

Posted April 8, 2010

Algebra and Number Theory Seminar Questions or comments?

1:00 pm – 2:00 pm 338 Johnston Hall

Luke Owens, Texas A&M University
An Algorithm For Surface Encoding And Reconstruction From 3D Point Cloud Data

Posted March 12, 2010
Last modified April 12, 2010

3:40 pm Lockett 285

Jared Culbertson, Mathematics Department, LSU
Perverse Poisson sheaves on the nilpotent cone

Posted February 27, 2010
Last modified March 2, 2021

Algebra and Number Theory Seminar Questions or comments?

3:40 pm 233 Lockett Hall

Vladislav Kravchenko, Dept. of Mathematics, CINVESTAV del IPN, Unidad Querétaro
Solution of boundary and eigenvalue problems for second order elliptic operators in the plane using pseudoanalytic function theory

We propose a method for solving boundary value and eigenvalue problems for the elliptic operator D=divpgrad+q in the plane using pseudoanalytic function theory and in particular pseudoanalytic formal powers. Under certain conditions on the coefficients p and q with the aid of pseudoanalytic function theory a complete system of null solutions of the operator can be constructed following a simple algorithm consisting in recursive integration. This system of solutions is used for solving boundary value and spectral problems for the operator D in bounded simply connected domains. We study theoretical and numerical aspects of the method.

Host: Stephen Shipman

Tuesday, April 20, 2010

Posted March 20, 2010

3:40 pm Lockett 285

Jerome W. Hoffman, Mathematics Department, LSU
Infinitesimal structure of Chow groups

Thursday, April 22, 2010

Posted April 14, 2010
Last modified March 3, 2021

2:30 pm – 3:20 pm Lockett 381, please note that the times above are sharp

Greg Muller, Cornell University
Calogero-Moser Spaces and Ideals in the Weyl Algebra

The classical nth Calogero-Moser system describes the motion of n-particles on a line, repelling each other proportional to the inverse-cube of their separation. This is completely integrable, and can be explicitly solved for all time; contrast this with inverse-square attraction, which is not integrable even for 3 particles. If the particles are allowed to have complex position, then the phase space for this system has a remarkable compactification, with both an elegant description and unexpected connections to far-reaches of mathematics. One such connection is that it parametrizes left ideal classes in the Weyl algebra, the ring of polynomial differential operators. Time permitting, I will mention how this observation can be used to construct related systems on other smooth algebraic curves.

Posted March 2, 2010
Last modified April 13, 2010

3:40 pm – 4:30 pm Lockett 285

Ben Webster, MIT
Categorification, Lie algebras and topology

Abstract:
It's a long established principle that it is interesting to think
about numbers as the sizes of sets, or as the dimensions of vector spaces,
or better yet, as the Euler characteristic of complexes. You can't have a
map between numbers, but you can have one between sets or vector
spaces. For example, the Euler characteristic of topological spaces is not
functorial, but homology is.

One can try to extend this idea to a bigger stage, by, say, taking a
vector space and trying to make a category by defining morphisms
between its vectors. This approach, interpreted suitably, has been a
remarkable success with the representation theory of semi-simple Lie
algebras (and their associated quantum groups). I'll give an
introduction to this area, with a view toward applications in
topology; in particular to replacing polynomial invariants of knots
that come from representation theory with vector-space-valued
invariants that reduce to knot polynomials under Euler characteristic.

There will be coffee and cookies in the lounge at 3:00.

Monday, April 26, 2010

Posted March 21, 2010
Last modified March 2, 2021

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Room 233 Lockett Hall

M. Gregory Forest, Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina Grant Dahlstrom Distinguished Professor of Mathematics & Biomedical Engineering
Dynamic defect morphology and hydrodynamics of sheared nematic polymers in physically confined geometries

Nematic polymers consist of rigid rod or platelet dispersions where the particles are macromolecules, i.e., larger than liquid crystals but still Brownian. Depending on the properties of the rods or platelets, materials are targeted with extreme barrier, electrical, thermal, mechanical, dielectric or energy storage properties. Unlike fiber processing which yields highly uniform alignment of the rod or platelet phase, film and mold filling processes of nematic polymers typically possess dynamic particle orientational morphology even in steady processing conditions, accompanied by unsteady flow. Furthermore, defects are generic. In this talk we present model equations and boundary conditions, and results from numerical simulations for shear cell and driven cavity experiments of nematic polymers. We use novel defect detection and tracking diagnostics to show defect spawning mechanisms and morphology and flow evolution in these two types of experiments, and sensitivity to boundary conditions as well as initial data. Finally, we report some progress on post-processing of the simulation data to infer the underlying mechanisms for various property enhancements due to the particle phase. This is joint work with several collaborators who will be acknowledged during the lecture.

Tuesday, April 27, 2010

Posted April 13, 2010
Last modified March 3, 2021

3:40 pm Lockett 285

Paulo Lima-Filho, Texas A&M
Integral Deligne cohomology for real varieties and explicit regulators

Abstract: in this talk we introduce a novel version of Deligne cohomology for real varieties for which bigraded ordinary equivariant cohomology replaces the role of singular cohomology in the complex case. We describe explicit "regulator maps" in the level of complexes from Voevodsky's motivic complexes to Deligne cohomology, and present several examples.

Wednesday, April 28, 2010

Posted April 21, 2010
Last modified April 26, 2010

2:40 pm Lockett 16

Alison Ahlgren, University of Illinois at Urbana-Champaign Coordinator: U of I Math Placement Program Coordinator: Quantitative Reasoning Courses
Faculty meeting: ALEKS & Calculus

Demonstration of ALEKS and discussion of changing prerequisites for Math 1550.

Thursday, April 29, 2010

Posted January 7, 2010
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 285

Alexander Its, Indiana University–Purdue University Indianapolis
Special Functions and Integrable Systems

The recent developments in the theory of integrable systems have revealed its intrinsic relation to the theory of special functions. Perhaps the most generally known aspects of this relation are the group-theoretical, especially the quantum-group theoretical, and the algebra-geometrical ones. In the talk we will discuss the analytic side of the Special Functions-Integrable Systems connection. This aspect of the relation between the two theories is less known to the general mathematical community, although it goes back to the classical works of Fuchs, Garnier and Schlesinger on the isomonodromy deformations of the systems of linear differential equations with rational coefficients. Indeed, the monodromy theory of linear systems provides a unified framework for the linear (hypergeometric type) and nonlinear (Painlevé type) special functions and, simultaneously, builds a base for the new powerful technique of the asymptotic analysis — the Riemann-Hilbert method.

In this survey talk, which is based on the works of many authors spanned over more than two decades, the isomonodromy point of view on special function will be outlined. We will also review the history of the Riemann-Hilbert method as well as its most recent applications in the theory of orthogonal polynomials and random matrices.

Coffee and cookies: The James E. Keisler lounge, 3:00.

Posted April 15, 2010

Algebra and Number Theory Seminar Questions or comments?

4:00 pm Keisler Lounge (319 Lockett Hall)

Kanagarajah (Raj) Prabaharan, Associate Professor Southern University PhD Ohio State University, Associate of the Society of Actuaries
Actuarial Student Association.

Club Meeting with special guest speaker.

Friday, April 30, 2010

Posted February 25, 2010
Last modified April 25, 2010

3:40 pm Lockett 285
(Originally scheduled for Friday, March 12, 2010)

Leonardo Mihalcea, Baylor University
Varieties of rational curves in the Grassmannian

Let Ω1 and Ω2 be two Schubert varieties in the Grassmannian, in general position. Given this data, we consider two spaces: the space of rational curves joining Ω1 and Ω2 (a subvariety of the moduli space of stable maps), and the space obtained by taking the union of these curves (a subvariety of the Grassmannian). Both these spaces generalize the much studied Richardson varieties, and play a fundamental role in quantum cohomology. We will study basic properties of these spaces (normality, rationality, singularities), and discuss some applications in quantum K-theory of the Grassmannian and algebraic combinatorics. This is joint work with A. Buch, P.E. Chaput and N. Perrin.

Monday, May 3, 2010

Posted April 30, 2010

9:00 am – 10:45 am Conference Room

Advisory Committee

Meeting with PI\'s and E. Kennedy

Posted April 30, 2010

10:45 am – 11:30 am Conference Room

Advisory Committee

Meeting with VIR Faculty

Posted April 30, 2010

11:30 am – 12:40 pm Lounge - 321 Lockett

Advisory Committee

Lunch/Undergrads Meeting

Posted April 30, 2010

12:40 pm – 1:40 pm Lockett 2

Advisory Committee

Meeting with all Graduate Students

Posted April 30, 2010

1:40 pm – 2:40 pm Lockett 2

Advisory Committee

Meeting with VIGRE@LSU Trainees

Posted April 30, 2010

2:45 pm – 3:30 pm Lounge - Locket 321

Advisory Commitee

Coffee & Refreshments Faculty Meet & Greet

Posted April 30, 2010

3:30 pm – 4:00 pm Conference Room

Advisory Committee

Meeting with Dean Carman

Posted April 27, 2010
Last modified April 29, 2010

3:40 pm – 4:30 pm Lockett 285

Eric Hillebrand, Economics Department, LSU
Temporal Correlation of Defaults in Subprime Securitization

Posted April 30, 2010

4:00 pm – 5:00 pm Conference Room

Advisory Committee

Meeting with Postdoctoral Associates

Tuesday, May 4, 2010

Posted April 30, 2010

9:00 am – 10:00 am Conference Room

Advisory Committee

VIGRE@LSU Steering Committee

Posted April 30, 2010

Control and Optimization Seminar Questions or comments?

10:30 am – 12:00 pm Conference Room

Advisory Committee

Meeting with the PI\'s

Posted January 28, 2010
Last modified April 22, 2010

3:00 pm 117 Electrical Engineering

Michael Malisoff, LSU Roy P. Daniels Professor
New Lyapunov Function Methods for Adaptive and Time-Delayed Systems

Lyapunov functions are an important tool in nonlinear control systems theory. This talk presents new Lyapunov-based adaptive tracking control results for nonlinear systems in feedback form with multiple inputs and unknown high-frequency control gains. Our adaptive controllers yield uniform global asymptotic stability for the error dynamics, which implies parameter estimation and tracking for the original systems. We demonstrate our work using a tracking problem for a brushless DC motor turning a mechanical load. Then we present a new class of dilution rate feedback controllers for two-species chemostat models with Haldane uptake functions where the species concentrations are measured with an unknown time delay. This work is joint with Marcio de Queiroz and Frederic Mazenc.

Posted March 25, 2010
Last modified April 27, 2010

3:30 pm – 4:30 pm 338 Johnston Hall

Xin Li, Dept. of Elect. & Computer Engineering, LSU
Geometric Data Mapping through Shape Decomposition

Abstract:
With the rapid advancement of 3D scanning technologies, high-fidelity geometric datasets of huge size have been acquired through hardware devices. A fundamental and challenging problem is how to compute mapping to correspond different surface and volumetric objects of arbitrarily complicated topological types. Inter-shape mapping, or more specifically, finding a low distorted correspondence between two given shapes is a very powerful enabling tool for various applications. We seek accurate and efficient solutions to this fundamental and important problem. This talk is about our recent work on surface and volumetric mapping computation based on shape decomposition. Compared with existing techniques, our work offers a more effective solution. We envision broader application scopes of mapping in digital entertainment, modeling and simulation, vision, medical imaging, content-driven information retrieval, digital medicine, virtual environments, etc.

Short Bio:
Xin Li is an assistant Professor in Department of Electrical & Computer Engineering, and Center for Computation & Technology, and adjunct professor in Department of Computer Science. He received the Ph.D. (2008) and M.S. (2005) in Computer Science at Stony Brook University (SUNY), and the B.S. (2003) in Computer Science from University of Science and Technology of China. His research interests include computer graphics, geometric modeling and processing, computer aided design, vision, and visualization. For more information please visit http://www.ece.lsu.edu/xinli.

Wednesday, May 5, 2010

Posted May 1, 2010
Last modified May 4, 2010

2:30 pm LOCKETT 232

Meeting of the tenured and tenure-track Faculty

Department policies up for vote. See: http://www.math.lsu.edu/~smolinsk/posts/department policies 5_5_2010.pdf

Posted April 11, 2010

3:30 pm James Kiesler Lounge

Spring Party and Math Awards Ceremony

Annual end of semester recognition of award recipients and party.

Thursday, May 6, 2010

Posted April 21, 2010
Last modified March 2, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm 233 Lockett Hall

Jintao Cui, Mathematics Department, LSU
Zuhal Yeter, LSU Dept of Mathematics
SIAM Student Seminar

Zuhal Yeter: Robust Preconditioners for High Contrast Elliptic Equations
The problem of interest is the elliptic PDEs with high contrast coefficients which models the applications such as fluid flow in highly heterogeneous media or bending of highly composite plates. The high contrast in the coefficients of the PDEs causes loss of robustness of the preconditioners. Our aim is to construct preconditioner that is robust with respect to the coefficient contrast and mesh size and that will work for different kind of elliptic equations with varying discretizations. We prove the robustness of the preconditioner use singular perturbation analysis and numerically demonstrate it.

Jintao Cui: Multigrid Methods for Maxwell's equations
In this talk we discuss finite element methods for two-dimensional Maxwell's equations and their solutions by multigrid algorithms. We first study a nonconforming finite element method on graded meshes for a two-dimensional curl-curl and grad-div problem. Then we consider a class of symmetric discontinuous Galerkin methods for a model Poisson problem on graded meshes that share many techniques with the nonconforming methods for Maxwell's equations. We establish the uniform convergence of W-cycle, V-cycle and F-cycle multigrid algorithms for the resulting discrete problems. Finally, we propose a new numerical approach for two-dimensional Maxwell's equations that is based on the Hodge decomposition and present multigrid results for Maxwell's equations.

Posted April 23, 2010
Last modified March 2, 2021

3:40 pm Lockett 285

Amber Russell, Mathematics Department, LSU
Graham's variety and perverse sheaves on the nilpotent cone

In recent work, Graham has constructed a variety with a map to the nilpotent cone that is similar to the Springer resolution. However, Graham\'s map differs from the Springer resolution in that it is not in general an isomorphism over the principal orbit, but rather the universal covering map. This map gives rise to a certain semisimple perverse sheaf on the nilpotent cone. In this talk, we will describe the summands of this perverse sheaf via the cohomology of the fibers of Graham\'s map.

Thursday, May 13, 2010

Posted March 25, 2010

11:00 am – 12:00 pm 338 Johnston Hall

Leszek Demkowicz, University of Texas at Austin
TBA

Thursday, July 1, 2010

Posted June 28, 2010

10:30 am – 11:30 am Lockett 233

Paul Kirk, Indiana University
Untwisted Whitehead doubles of $(2, 2^k-1)$ torus knots are linearly independent in the smooth knot concordance group.

Abstract: We revisit an argument of Furuta, using SO(3) instanton moduli spaces on 4-manifolds with boundary and estimates of Chern-Simons invariants of flat SO(3) connections on 3-manifolds, to prove that the infinite family of untwisted positive clasped Whitehead doubles of the $(2, 2^k-1)$ torus knots are linearly independent in the smooth knot concordance group. (joint work with Matt Hedden)

Monday, August 16, 2010

Posted June 20, 2010
Last modified July 25, 2021

1:00 pm – 4:00 pm 285 Lockett Hall

Comprehensive / PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, August 18, 2010

Posted June 20, 2010
Last modified July 25, 2021

1:00 pm – 4:00 pm 285 Lockett Hall

Comprehensive / PhD Qualifying Exam in Analysis

This Exam is part of the PhD Qualifying Examination in Mathematics.

Friday, August 20, 2010

Posted June 20, 2010
Last modified July 25, 2021

1:00 pm – 4:00 pm 285 Lockett Hall

Comprehensive / PhD Qualifying Exam in Topology

This Exam is part of the PhD Qualifying Examination in Mathematics.

Friday, August 27, 2010

Posted March 25, 2010
Last modified August 23, 2010

11:00 am – 12:00 pm 338 Johnston Hall

James Nagy, Emory University
Deblurring Images: Matrices, Spectra, and Filtering

Abstract: When we use a camera, we want the recorded image to be a faithful representation of the scene that we see, but every image is more or less blurry. In image deblurring, the goal is to recover the original, sharp image by using a mathematical model of the blurring process. The key issue is that some information on the lost details is indeed present in the blurred image, but this "hidden" information can be recovered only if we know the details of the blurring process. In this talk we describe the deblurring algorithms and techniques collectively known as spectral filtering methods, in which the singular value decomposition (or a similar decomposition with spectral properties) is used to introduce the necessary regularization or filtering in the reconstructed image.

(Light refreshments at 10:30)

Monday, August 30, 2010

Posted August 22, 2010

4:30 pm James E. Keisler Lounge (room 321 Lockett)

Meeting of the Actuarial Student Association

Discussion of the profession, exams, and speakers. Selection of officers.

Friday, September 10, 2010

Posted August 30, 2010
Last modified March 2, 2021

3:40 pm – 4:30 pm Lockett 381

Ivan Dimitrov, Queen's University (Canada)
Borel subalgebras of $gl_\infty$

The purpose of this talk is to describe all Borel (i.e., all maximal locally solvable) subalgebras of $gl_\infty$. Consider $gl_\infty$ as the direct limit of $gl_n$. While the direct limit of Borel subalgebras of $gl_n$ is itself a Borel subalgebra of $gl_\infty$, the converse is not true. It turns out that the Borel subalgebras of $gl_\infty$ are described rather explicitly as the stabilizers of special chains of subspaces in the natural representation of $gl_\infty$. I will state the main result and will illustrate it with a number of examples. At the end of the talk I will discuss a couple of open problems. This talk is based on a joint work with Ivan Penkov.

Monday, September 13, 2010

Posted September 3, 2010
Last modified March 2, 2022

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 233

Robert Lipton, Mathematics Department, LSU
Multi-scale analysis and optimal local basis functions for Generalized Finite Element Methods

Modern structures such as airplane wings exhibit complicated sub structures and make use of composite materials in their construction. The high cost of experimental tests for these hierarchical structures is driving a trend toward virtual testing. This requires the development of multi-scale numerical methods capable of handling large degrees of freedom spread across different length scales. In this talk we review multi-scale numerical methods and introduce the theory of the Kolmogorov n-width as a means to identify optimal local basis functions for use in multi-scale finite element methods. We are able to identify a spectral basis with nearly exponential convergence with respect to the dimension of the approximation space. The convergence result is shown to hold in a very general setting. This is joint work with Ivo Babuska.

Tuesday, September 14, 2010

Posted September 6, 2010
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 240

Sarah Kitchen, University of Utah and Universität Freiburg
Harish-Chandra modules and the geometry of partial flag varieties

Cohomological induction gives an algebraic method for constructing representations of a real reductive Lie group G from irreducible representations of parabolic subgroups. Beilinson-Bernstein localization alternatively gives a geometric method for constructing Harish-Chandra modules for G from certain representations of a Cartan subgroup. The duality theorem of Hecht, Milicic, Schmid and Wolf establishes a relationship between modules cohomologically induced from Borels and the cohomology of the D-modules on the complex flag variety for G determined by the Beilinson-Bernstein construction. The corresponding geometric constructions on partial flag variety introduce homological complications. In this talk, I will explain the generalization of the duality theorem to partial flag varieties, which fully recovers the composition factors of cohomologically induced modules arising from non-minimal parabolics.

Monday, September 20, 2010

Posted September 15, 2010

Algebra and Number Theory Seminar Questions or comments?

3:40 pm 241 Lockett Hall

Curriculum Discussion

To discuss the proposed concentration in computational mathematics, to replace our current Computer Science concentration.

Tuesday, September 21, 2010

Posted September 13, 2010
Last modified September 14, 2010

3:40 pm – 4:30 pm Lockett 240

Pramod Achar, Mathematics Department, LSU
Hyperbolic localization and applications

This will be a mostly expository talk about T. Braden\'s \"hyperbolic localization\" functor. This is a geometric construction that is defined for varieties equipped with an action of the multiplicative group C^*, and it can be described in an elementary way using the language of ordinary algebraic topology. It turns to have very deep connections with purely algebraic aspects of the representation theory of algebraic groups, and it plays a central role in the proof of the celebrated geometric Satake equivalence.

Wednesday, September 22, 2010

Posted September 21, 2010

4:00 pm Keisler lounge

Meeting of new postdocs, new assistant professors and their mentors

Thursday, September 23, 2010

Posted September 10, 2010
Last modified September 17, 2010

3:40 pm – 4:30 pm Lockett 277

Hongyu He, Department of Mathematics, LSU
Theta Correspondence and Unitary Representations

In the late 1950's and early 1960's, motivated by problems from physics
and number theory, Segal, Shale and Weil independently discovered a
projective representation of the symplectic group, often called the
oscillator representation. This representation was later used by
Kashiwara-Vergne and many others to obtain new unitary representation and
automorphic forms for other classical groups. The theory underlying these
developments is often called theta correspondence. In this talk, I will
review Howe's theory of reductive dual pair and theta correspondence. I
will then discuss how theta correspondence can be used to understand the
unitary dual of the noncompact orthogonal groups. With the exception of
rank-one groups and several higher rank groups, the unitary dual of the
noncompact orthogonal groups is not completely classified.

Friday, September 24, 2010

Posted September 14, 2010
Last modified March 3, 2021

3:40 pm – 4:40 pm Lockett 381

Karl Heinrich Hofmann, Darmstadt University, Germany Professor Emeritus
On Spaces Whose Homeomorphism Group is Compact

This is a seminar lecture between algebra and topology. It deals with the following question: Which compact groups $G$ occur as the full homeomorphism group (with the compact open topology) of a Tychonoff space? We argue that any such $G$ has to be profinite, that is, totally disconnected. In fact, this is a consequence of a more general result: If a compact but not profinite group acts effectively on a Tychonoff space $X$, then its homeomorphism group $\mathcal{H}(X)$ contains a subgroup $H$ and a closed subgroup $K$ which is a normal subgroup of $H$ such that $H/K$ is a topological group which is homeomorphic to a separable Hilbert space $\ell^2=\ell^2(N)$. Moreover, the quotient map $h\rightarrow H/K$ has a topological cross section. Under such circumstances $\mathcal{H}(X)$ cannot be locally compact, let alone compact. This is a variation of a theme initiated by James Keesling 1971 by different methods. In the reverse direction we show that every monothetic (compact) profinite group is the homeomorphism group of a compact connected 1-dimensional space. We conjecture here that every profinite group is (isomorphic to) the homeomorphism group of some compact connected space. A new approach is used here which combines graph theoretical and topological methods initiated more than half a century ago by J. De Groot. All unfamiliar concepts will be explained in detail.

Monday, September 27, 2010

Posted September 3, 2010
Last modified September 20, 2010

3:40 pm – 4:30 pm Lockett 233

Blaise Bourdin, Department of Mathematics and Center for Computation & Technology, LSU
Reservoir stimulation: an approach based on variational fracture.

The topic of this talk is to present a first step towards the predictive understanding of the mechanisms used in the creation of the highly connected crack networks required for Enhanced Geothermal Systems and oil shale mining. I will focus on thermal stimulation, where thermal stresses induced by a cold fluid circulating through a hot reservoir lead to nucleation of many short cracks. I will consider the limiting cases of purely diffusive and purely advective heat transfer, corresponding to extreme porosity limits in the reservoir. I will present a mechanistically faithful yet mathematically sound model, based on Francfort and Marigo's generalization of Griffith's idea of competition between bulk and surface energies. I will discuss the virtues of the model, its approximation, and its numerical implementation. Finally, I will present some numerical experiments in 2 and 3 dimensions.

Posted September 22, 2010
Last modified September 24, 2010

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm 241 Lockett

Benedykt Szozda, Department of Mathematics, LSU
New approach to stochastic integration of anticipating stochastic processes

Tuesday, September 28, 2010

Posted September 21, 2010

3:40 pm – 4:30 pm Lockett 240

Greg Muller, Department of Mathematics, LSU
Reflexive and Projective D-modules

I will discuss reflexive and projective D-modules, focusing on the simplest case, the Weyl algebras. They can be reduced to right ideals in D, which can be studied in terms of their images. There is a nice class of ideals on which this image-based technique is effective at producing new results and examples, as well as revealing connections to the `bispectral problem\' in differential equations. I will review the general theory, our new results, give some new interesting examples, and discuss the application to the bispectral problem. Joint with Yuri Berest and Oleg Chalykh.

Thursday, September 30, 2010

Posted September 30, 2010
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:30 pm 338 Johnston Hall (Access Grid Viewing)

Diola Bagayoko, Southern University Southern University Distinguished Professor of Physics, Adjunct Professor of Science and Mathematics Education and Director of the Timbuktu Academy.
A Mathematical Solution to the Theoretical Underestimation of Energy and Band Gaps and Applications to the Search of Novel Materials

Live presentation is at 218 J.B. Moore Hall at Southern University.

Posted September 8, 2010
Last modified September 17, 2010

3:40 pm – 4:30 pm Lockett 277

Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Index Theorems in Quantum Mechanics

Abstract: The notion of the Fredholm index of an operator is extended to
pairs of projections as well as to certain pairs of (unbounded)
self-adjoint operators in a Hilbert space. This index often exhibits
some invariance properties and has applications in Quantum mechanical
problems. There is also a K-theoretic description of the problem.

Friday, October 1, 2010

Posted September 16, 2010
Last modified September 21, 2010

3:40 pm Lockett 138

Meeting of Associate and Full Professors

Wednesday, October 6, 2010

Posted October 5, 2010

Meeting with students

3:30 pm – 5:30 pm

Math 1100 Q & A

Monday, October 11, 2010

Posted September 10, 2010
Last modified March 2, 2022

VIGRE@LSU: Student Colloquium Questions or comments?

3:40 pm – 4:30 pm Lockett 233

Hongchao Zhang, Louisiana State University
A Derivative-free Regularized Trust Region Approach for Least-squares Minimization

We will introduce a class of derivative-free algorithms for the nonlinear least-squares minimization problem. These algorithms are based on polynomial interpolation models and are designed to take advantages of the problem structure. Global and local quadratic convergence properties of the algorithms will be addressed. Promising numerical results compared with other state-of-art software packages indicate the algorithm is very efficient and robust for finding both low and high accuracy solutions.

Friday, October 15, 2010

Posted October 12, 2010

10:40 am – 11:30 am Lockett 277

David Ross, Rochester Institute of Technology
Inferring Gibbs Free Energies from Light Scattering Data

Differences in free energies are the driving forces in chemical changes. The current project originated in our desire to understand phase changes in the protein mixtures in the lens of the human eye; such changes cause cataract disease. We are able to use a PDE to study the free energies as functions of the mixture composition, and we will formulate a well-posed problem for this equation with singular boundary conditions based on the Widom asymptotic form of the free energy.

Posted October 12, 2010
Last modified March 2, 2021

VIGRE@LSU: Student Colloquium Questions or comments?

2:40 pm – 3:30 pm Lockett 277

David Ross, Rochester Institute of Technology
ODEs in Industrial (and other) Applications

In this talk, we discuss several ODE problems from various areas of active research, such as MEMS (Micro-Electro Mechanical Systems) micro-energy harvesting, in which micro-machines built on computer chips glean energy from mechanical vibrations to power circuits, as well as topics in Osteoporosis research, Cataract research, Gear design and Ecological Economics.

Monday, October 18, 2010

Posted September 10, 2010
Last modified October 13, 2010

3:40 pm – 4:30 pm Lockett 233

Tadele Mengesha, Louisiana State University
Weighted and regularity estimates for nonlinear PDEs over rough domains

Global weighted Lp estimates are obtained for the gradient of solutions to nonlinear elliptic Dirichlet boundary value problems over a bounded nonsmooth domain. As an application, Morrey and Holder regularity of solutions are established. These results generalize various existing estimates for nonlinear equations. The nonlinearities are of at most linear growth and assumed to have a uniform small mean oscillation, i.e can have mild discontinuity. The boundary of the domain, on the other hand, may exhibit roughness but assumed to be sufficiently flat in the sense of Reifenberg. Our approach is a perturbation argument that uses maximal function estimates, Vitali covering lemma, and known regularity results of solutions to nonlinear homogeneous equations. This is a joint work with Nguyen Cong Phuc.

Monday, October 25, 2010

Posted October 23, 2010
Last modified March 2, 2022

3:40 pm – 4:30 pm Lockett 223

Shawn Walker, LSU
Shape Optimization of Chiral Propellers in 3-D Stokes Flow

Locomotion at the micro-scale is important in biology and in industrial applications such as targeted drug delivery and micro-fluidics. We present results on the optimal shape of a rigid body locomoting in 3-D Stokes flow. The actuation consists of applying a fixed moment and constraining the body to only move along the moment axis; this models the effect of an external magnetic torque on an object made of magnetically susceptible material. The shape of the object is parametrized by a 3-D centerline with a given cross-sectional shape. No a priori assumption is made on the centerline. We show there exists a minimizer to the infinite dimensional optimization problem in a suitable infinite class of admissible shapes. We develop a variational (constrained) descent method which is well-posed for the continuous and discrete versions of the problem. Sensitivities of the cost and constraints are computed variationally via shape differential calculus. Computations are accomplished by a boundary integral method to solve the Stokes equations, and a finite element method to obtain descent directions for the optimization algorithm. We show examples of locomotor shapes with and without different fixed payload/cargo shapes.

Tuesday, October 26, 2010

Posted October 7, 2010
Last modified October 11, 2010

3:40 pm Lockett 9

Graduate Student Meeting

A meeting for all Math Graduate Students to discuss the NSF site Visit scheduled on November 15th.

Thursday, October 28, 2010

Posted October 7, 2010

3:40 pm – 4:30 pm Lockett 277

Vladimir Dragovic, MI SANU, Belgrade/GFM University of Lisbon
Discriminant separability, Poncelet porisms and Kowalevski top

Abstract. A new view on the Kowalevski top and Kowalevski integration procedure is presented. It is based on a classical notion of Darboux coordinates, a modern concept of n-valued Buchstaber-Novikov groups and a new notion of discriminant separability. Unexpected relationship with the Great Poncelet Theorem for a triangle is established. Further connections between discriminant separability, geometry of pencils of quadrics and integrability are discussed.

Friday, October 29, 2010

Posted October 27, 2010

11:00 am 338 Johnston Hall

Jiawang Nie, Department of Mathematics at UCSD
Introduction to Polynomial Optimization

This talk presents recent work on solving multivariate polynomial
optimization problems by using semi definite programming (SDP) and sum of
squares (SOS) techniques. The talk focuses on Lasserre type SDP relaxation:
sum of squares polynomials, Lasserre\'s relaxation hierarchy, its convergence,
and approximation performance analysis.

Pizza will be served after the talk.

Posted October 29, 2010

3:40 pm – 4:30 pm Lockett 381

Leonardo Mihalcea, Baylor University
Spaces of rational curves in flag manifolds and the quantum Chevalley formula

Abstract: Given Omega a Schubert variety in a flag manifold, one can consider two spaces: the moduli space GW_d(Omega) of rational curves of fixed degree d passing through Omega (a subvariety of the moduli space of stable maps), and the space Gamma_d(\\Omega) obtained by taking the union of these curves (a subvariety of the flag manifold). I will show how some simple considerations about the geometry of these spaces leads to a new, natural, proof of the equivariant quantum Chevalley formula proved earlier by Fulton and Woodward and by the speaker. This is joint work with A. Buch.

Monday, November 1, 2010

Posted August 30, 2010
Last modified December 13, 2022

12:00 pm – 1:00 pm Lockett 301D the Conference Room

Final Event for MS Comprehensive Exam

MS applicants for December 2010 graduation must meet with the following committee members:
Leonard Richardson (Chair)
Richard Litherland
Padmanaban Sundar
in order to complete the process that began with passing the Department's written Comprehensive Examination at the MS Qualifying Level. Apply to the Graduate School to have the Final Exam at this date with the listed committee.

Tuesday, November 2, 2010

Posted October 11, 2010

Algebra and Number Theory Seminar Questions or comments?

3:40 pm Lockett 9

Faculty Meeting

Faculty meeting to prepare for and discuss NSF site visit, which is scheduled for November 15, 2010.

Thursday, November 4, 2010

Posted October 20, 2010
Last modified October 25, 2010

3:40 pm – 4:30 pm Lockett 240
(Originally scheduled for Tuesday, October 26, 2010, 3:40 pm)

Maria Vega, Mathematics Department, LSU
Twisted Frobenius-Schur Indicators for Hopf Algebras

The classical Frobenius-Schur indicators (FS indicators) for finite groups are virtual characters v_n(V) defined for any representation V and any n>=2. In the familiar case n=2, v_2 partitions the irreducible representations over C into real, complex, and quaternionic representations. In recent years, several generalizations of these invariants have been introduced. Bump and Ginzburg, building on earlier work of Mackey, have defined versions of these indicators which are twisted by an automorphism of the group. In another direction, FS indicators have been constructed for semisimple Hopf algebras; this is due to Linchenko and Montgomery for n=2 and Kashina, Sommerhauser, and Zhu for n>2. We have constructed a twisted version of FS indicators for semisimple Hopf algebras that includes all of the above versions as special cases and have similar properties. For example, the n=2 case leads to a partition of the irreducible representations into three classes. This is joint work with Daniel Sage.

Friday, November 5, 2010

Posted November 3, 2010
Last modified March 2, 2021

Graduate Student Seminar

3:40 pm – 4:30 pm Lockett 233

Benedykt Szozda, Department of Mathematics, LSU
An extension of the Itô integral onto a class of anticipating stochastic processes.

The purpose of this talk is to introduce the generalization of the Itô integral to instantly independent stochastic processes. We will review the basics of the Itô integration theory and motivate the need of the extension of the stochastic integral onto a larger class of stochastic processes. We will also take a look at previously introduced extensions. Next, we will introduce a new idea leading to an extension of the Itô stochastic integral onto a class of non-adapted stochastic processes. We will discus basic properties of the new integral and present the Itô formula and the Itô isometry for the new integral. We will also introduce the concept of pre-martingales, which arises naturally in exploration of the properties of the new integral. This is joint work with Professor Hui-Hsiung Kuo and Anuwat Sae-Tang.

There will be refreshments before the talk, at 3:15pm at Keisler Lounge.

Monday, November 8, 2010

Posted November 1, 2010

4:15 pm Lockett Hall - Conference Room

Postdoctoral Researchers Meeting

This meeting has been scheduled to prepare for and discuss the NSF site visit for the VIGRE grant.

Wednesday, November 10, 2010

Posted September 20, 2010

3:40 pm – 4:30 pm Lockett 381

Mark Sepanski, Mathematics Department, Baylor University
Distinguished orbits and the L-S category of simply connected compact Lie groups

We show that the Lusternik-Schnirelmann category of a simple, simply connected, compact Lie group G is bounded above by the sum of the relative categories of certain distinguished conjugacy classes in G corresponding to the vertices of the fundamental alcove for the action of the affine Weyl group on the Lie algebra of a maximal torus of G. This is joint work with M. Hunziker.

Friday, November 12, 2010

Posted October 6, 2010

3:40 pm – 4:30 pm Lockett 381

Yen Do, Georgia Tech
Variational estimates for paraproducts

Abstract: We generalize a family of variation norm estimates of Lepingle with endpoint estimates of Bourgain and Pisier-Xu to a family of variational estimates for paraproducts, both in the discrete and the continuous setting. This expands on work of Friz and Victoir, our focus being on the continuous case and an expanded range of variation exponents. Some applications in time-frequency analysis are also discussed. Joint work with Camil Muscalu and Christoph Thiele.

Monday, November 15, 2010

Posted November 11, 2010

9:20 am – 10:20 am Lockett Hall - Lounge

VIGRE Site Visit Meeting with Faculty

Faculty involved in VIRs and mentoring trainees at the undergraduate, graduate, and postdoctoral level.

Posted November 11, 2010

11:10 am – 11:50 am Lockett Hall - Conference Room

VIGRE Site Visit Meeting with Postdocs

Posted November 11, 2010

12:40 pm – 1:30 pm Lockett Hall - Lounge

VIGRE Site Visit meeting with Undergraduates

Posted November 11, 2010

1:40 pm – 2:30 pm 235 Lockett Hall

VIGRE Site Visit meeting with Graduate Students

Posted October 10, 2010
Last modified March 2, 2022

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 233

Michael Neilan, Louisiana State University
A unified approach to construct and analyze finite element methods for the Monge–Ampère equation

The Monge–Ampère equation is a fully nonlinear second order PDE that arises in various application areas such as differential geometry, meteorology, reflector design, economics, and optimal transport. Despite its prevalence in many applications, numerical methods for the Monge–Ampère equation are still in its infancy. In this talk, I will first discuss the inherent difficulty of approximating this equation and briefly review the numerical literature. I will then discuss a new approach to construct and analyze several finite element methods for the Monge–Ampère equation. As a first step, I will show that a key feature in developing convergent discretizations is to construct schemes with stable linearizations. I will then describe a methodology for constructing finite elements that inherits this trait and provide two examples: $C^0$ finite element methods and discontinuous Galerkin methods. I will briefly show how to prove the well-posedness of such methods as well as derive optimal order error estimates.

Tuesday, November 16, 2010

Posted September 7, 2010
Last modified November 9, 2010

3:40 pm – 4:30 pm Lockett 240

Mahir Can, Tulane University
Unipotent invariant (complete) quadrics

The variety of complete quadrics, which is used by Schubert in his famous computation of the number of space quadrics tangent to 9 quadrics in general position, is a particular compactification of the space of non-singular quadric hypersurfaces in n dimensional complex projective space. In this talk, towards a theory of Springer fibers for complete quadrics, I will describe our recent work on the unipotent invariant complete quadrics. These results involve interesting combinatorics, and in particular, give a
new q-analog of Fibonacci numbers.

This is joint work with Michael Joyce.

Friday, November 19, 2010

Posted November 10, 2010
Last modified November 11, 2010

3:00 pm Lockett 9

Faculty meeting to discuss writing the departmental strategic plan.

Posted November 9, 2010

3:40 pm – 4:30 pm Lockett 381

Alexander Fish, University of Wisconsin
Geometric properties of Intersection Body Operator

Abstract: The notion of an intersection body of a star body was introduced by E. Lutwak: K is called the intersection body of L if the radial function of K in every direction is equal to the (d-1)-dimensional volume of the central hyperplane section of L perpendicular to this direction. The notion turned out to be quite interesting and useful in Convex Geometry and Geometric tomography. It is easy to see that the intersection body of a ball is again a ball. E. Lutwak asked if there is any other star-shaped body that satisfies this property. We will present a solution to a local version of this problem: if a convex body K is closed to a unit ball and intersection body of K is equal to K, then K is a unit ball.

Monday, November 22, 2010

Posted November 22, 2010

Harmonic Analysis Student Seminar

2:30 pm – 3:30 pm 233 Lockett Hall

Hongyu He, Department of Mathematics, LSU
Important Problems in Harmonic Analysis

Posted October 25, 2010
Last modified January 6, 2021

3:40 pm – 4:30 pm Lockett 223

Benjamin Jaye, University of Missouri–Columbia
Quasilinear operators with natural growth terms

Tuesday, November 23, 2010

Posted November 22, 2010

SIAM Graduate Student Seminar

3:40 pm – 4:40 pm 233 Lockett Hall

Hairui Tu, Department of Mathematics, LSU
Resonant Transmission and Reflection by Periodic Slabs

Resonant scattering of plane waves by a periodic slab under conditions close to those that support a guided moded is accompanied by sharp transmission anomalies. We focus on two-dimensional structures and establish sufficient conditions, involving structure symmetry, under which these anomalies are characterized by total transmission and total reflection of plain waves at frequencies separated by an arbitrarily small amount. We discuss the case of a single anomaly and the cases of multiple anomalies excited by the interaction with a single guided mode.

Posted November 22, 2010

Meeting of the Algebra Faculty

3:40 pm – 4:30 pm Lockett 240

Graduate courses for 2011-2012

We will meet to plan graduate course offerings in algebra for the 2011-2012 academic year.

Monday, November 29, 2010

Posted November 22, 2010

Harmonic Analysis Student Seminar

2:30 pm – 3:30 pm 233 Lockett Hall

Important Problems in Harmonic Analysis

Posted October 10, 2010
Last modified March 2, 2022

3:40 pm – 4:30 pm Lockett 233

Young-Ju Lee, Department of Mathematics Rutgers, The State University of New Jersey
Self-Sustaining Oscillations of the Falling Sphere Through the Johnson-Segalman Fluids

In this talk, we review a novel numerical method that can handle the rate-type non-Newtonian equations in a unified fashion and validate the methods in terms of various benchmark solutions as well as theoretical results. We then apply it to the real physical problems. In particular, we present our investigations and attempts to identify a mathematical model for the unusual phenomenon observed in motion of the sphere falling through the wormlike micellar fluids by Jayaraman and Belmonte; a sphere falling in a wormlike micellar fluids undergoes non-transient and continual oscillations. We tackle the Johnson-Segalman models in the parameter regimes that have been unexplored previously for the flow past a sphere and reproduce the self-sustaining, continual, (ir)regular and periodic oscillations. Our results show that the flow instability can be correlated with the critical value of the velocity gradient, as observed in experiments by Jayaraman and Belmonte in 2003. If time permits, we also present recent works on the boundary conditions for the diffusive complex fluids models as well as the fast stokes solvers implemented in a full parallel fashion.

Posted October 27, 2010

4:30 pm Lockett 233

Dmitry Golovaty, University of Akron
Coarse-graining in Atomistic Models of Dislocations

Dislocations and their dynamics play a major role in the response of materials to mechanical and thermal loading. Extensive work has been done on diﬀerent scales of the problem from atomistic level, to dislocation level to macroscopic level. Yet the behavior of material under plastic deformation is still a source of many challenging mathematical problems. In this talk we focus on models at the atomistic level and deal with questions of coarse graining
where higher level models are sought. We focus on distribution functions characterizing the atomic arrangement and discuss energy representation and dislocation motion in terms of these statistical properties. The evolution is
formulated as a gradient ﬂow.

Tuesday, November 30, 2010

Posted November 28, 2010

VIGRE@LSU: Student Colloquium Questions or comments?

3:10 pm

Lockett 09

Wednesday, December 1, 2010

Posted November 9, 2010
Last modified November 12, 2010

2:40 pm – 3:30 pm Lockett 112

Rodolfo Torres, University of Kansas
Somewhere over the (mathematical) rainbow blue birds fly.... Why oh why are they blue?

Refreshments will be served from 2:00-2:30 pm in the Keisler lounge.

There are blue skies and blue birds over the rainbow as the song says, but not all blues are the same. The blue and green colors we see in birds, and even some of the ultraviolet that we cannot see, are produced by the way in which the light interacts with ordered microscopic structures in the tissues of the birds.

This order in the structures can be measured using Fourier analysis, a powerful mathematical tool. Like a prism that decomposes a beam of light into a rainbow of colors, Fourier analysis transforms the geometrical arrangements observed in electron microscope images of the tissues into a mathematical rainbow of basic components that quantify order or periodicities. We will illustrate how Fourier analysis processes the images and helps decipher the colors of birds and other animals. The talk will be accessible to all those who are curious about some of the mathematics and physics behind the bright blue and green colors found in nature.

Thursday, December 2, 2010

Posted November 9, 2010
Last modified November 12, 2010

VIGRE@LSU: Student Colloquium Questions or comments?

12:40 pm – 1:30 pm Lockett 239

Rodolfo Torres, University of Kansas
Discrete decomposition techniques in Fourier analysis.

Refreshments will be served in the Keisler lounge from 12:00- 12:30.

Abstract: Decomposition techniques such as atomic, molecular, wavelet and wave-packet expansions provide a multi-scale refinement of Fourier analysis and exploit a rather simple concept: "waves with very different frequencies are almost invisible to each other". Many of these useful techniques have been developed around the study of certain operators called singular integral operators.

By breaking an operator or splitting the function on which it acts into non-interacting pieces, these tools capture subtle cancellations and quantify properties of an operator in terms of norm estimates in functions spaces. This type of analysis has been extensively used to study linear or multilinear operators with tremendous success.

In this talk we will give some background and motivation for some decomposition techniques and show some basic concepts about how they are used to study operators of interest in Fourier analysis.

Posted September 29, 2010
Last modified November 30, 2010

3:40 pm – 4:30 pm Lockett 277

Dimitar Grantcharov, University of Texas at Arlington
Categories of weight representations of Lie algebras

Abstract: Following works of G. Benkart, D. Britten, S. Fernando, V. Futorny, A. Joseph, F. Lemire, and others, in 2000 O. Mathieu achieved a major breakthrough in representation theory by classifying the simple weight representations of Lie algebras. The next step in the study of weight representations is to look at the indecomposable representations. In this talk we will discuss recent results related to the structure of the indecomposable weight representations and connections with quiver theory and algebraic geometry. This is a joint work with Vera Serganova.

Friday, December 3, 2010

Posted November 12, 2010
Last modified March 3, 2021

10:40 am – 11:30 am Lockett 233

Rodolfo Torres, University of Kansas
Weighted estimates for multilinear singular integrals, commutators, and maximal functions.

We will recall a theory of weights developed for multilinear Calderón-Zygmund operators and describe some recent related results for the multilinear commutators of singular integrals with point-wise multiplication by BMO functions, their iterations, and new multilinear maximal functions.

Posted November 19, 2010

3:40 pm 241 Lockett

Sergey Lototsky, Department of Mathematics, University of Southern California
Wick Product in The Stochastic Burgers Equation: A Curse or a Cure?

Abstract: It has been known for a while that a nonlinear equation driven by singular noise must be interpreted in the re-normalized, or Wick, form. For the stochastic Burgers equation, Wick nonlinearity forces the solution to be a generalized process no matter how regular the random perturbation is, whence the curse. On the other hand, certain multiplicative random perturbations of the deterministic Burgers equation can only be interpreted in the Wick form, whence the cure. The analysis is based on the study of the coefficients of the chaos expansion of the solution at different stochastic scales.

Monday, December 6, 2010

Posted November 19, 2010
Last modified February 5, 2021

3:40 pm – 4:30 pm Lockett 233

Andrés León Baldelli, Université Pierre et Marie Curie
Variational Approach to Fracture Mechanics: Multifissuration and Delamination of Thin Films

Thin film materials such as multilayered composite materials, coating films etc plays a key role in modern engineering applications. The different physical characteristics of the various layers, the production and assembly procedures and the tensile stresses that develop in such systems may induce deformations that can lead to damage and failure. Variational energetic approaches to fracture mechanics [1] has been proved to give a reliable and physically consistent description of these complex phenomena, accurately predicting the experimental results. An extension of this approach to thin film/substrate systems is presented for a film under thermal loads, accounting for the possibility for the film to undergo multifissuration and debonding processes. Analytic results are obtained for the 1D case and compared to those obtained by a FEM approximation.

[1] B. Bourdin, G.A. Francfort, and J.-J. Marigo, "The Variational Approach to Fracture", Springer, 2007.

Tuesday, January 4, 2011

Posted December 30, 2010
Last modified February 11, 2022

8:50 am – 4:30 pm Lockett Hall

Workshop in Analysis and Geometry

Morning session at 8.50 am: Lockett Hall, Basement, Room 2
Afternoon session at 2 pm: Lockett Hall, 2nd floor, Rooms 235, 237, and 241.

See www.math.lsu.edu/~ag2011 for details.

Wednesday, January 5, 2011

Posted January 3, 2011
Last modified February 11, 2022

9:00 am – 4:30 pm Lockett Hall

Workshop in Analysis and Geometry (continuation)

Morning session at 9.00 am: Lockett Hall, Basement, Room 2.
Afternoon session at 2 pm: Lockett Hall, 2nd floor, Rooms 235, 237, and 241.

See www.math.lsu.edu/~ag2011 for details.

Monday, January 10, 2011

Posted September 4, 2010

1:00 pm – 4:00 pm 385 Lockett

Comprehensive/PhD Qualifying Exam in Algebra

This is one third of the PhD Qualifying Examination in Mathematics, and it is one third of the Final Examination for the non-thesis MS degree.

Tuesday, January 11, 2011

Posted December 7, 2010
Last modified December 21, 2010

11:00 am 338 Johnston Hall

Michael Ruge, SIEMENS AG, Munich, Germany
Mathematicians in Industry at Siemens

This presentation is directed at an audience (Mathematicians, Natural Scientists, Engineers) interested at a career in industry, possibly with an international focus.

The presenter will present an overview of the company Siemens he works for close to twenty years with a focus on entry-level positions for master and doctorial graduates.

Wednesday, January 12, 2011

Posted September 4, 2010
Last modified January 12, 2011

1:00 pm – 4:00 pm 285 Lockett

Comprehensive/PhD Qualifying Exam in Analysis

This is one third of the PhD Qualifying Examination in Mathematics, and it is one third of the Final Examination for the non-thesis MS degree.

Friday, January 14, 2011

Posted September 4, 2010
Last modified January 12, 2011

1:00 pm – 4:00 pm 285 Lockett

Comprehensive/PhD Qualifying Examination in Topology

This is one third of the PhD Qualifying Examination in Mathematics, and it is one third of the Final Examination for the non-thesis MS degree.

Thursday, January 20, 2011

Posted October 7, 2010
Last modified January 8, 2011

3:40 pm – 4:30 pm Lockett 277

Birgit Speh, Cornell University
Branching rules of unitary representations: Examples and applications to automorphic forms

One of the basic problems of representations theory is to understand how a representation is built up of irreducible representations. For finite dimensional representations of compact groups there exist well known combinatorial algorithms. In this talk we will examine the problem for infinite dimensional representations of semisimple Lie groups, give some examples as well as applications to automorphic forms and locally symmetric spaces.

Friday, January 21, 2011

Posted January 19, 2011

3:40 pm – 4:30 pm Lockett 277

Aaron Lauda, Columbia University
Categorifying quantum groups and link invariants

Abstract: The Jones polynomial can be understood in terms of the representation theory of the quantum group associated to the Lie algebra sl2. This description facilitated a vast generalization of the Jones polynomial to other quantum link and tangle invariants called Reshetikhin-Turaev invariants. These invariants, which arise from representations of quantum groups associated to simple Lie algebras, subsequently led to the definition of quantum 3-manifold invariants. In this talk we categorify quantum groups using a simple diagrammatic calculus that requires no previous knowledge of quantum groups. These diagrammatically categorified quantum groups not only lead to a representation theoretic explanation of Khovanov homology but also inspired Webster\'s recent work categorifying all Reshetikhin-Turaev invariants of tangles.

Monday, January 24, 2011

Posted January 21, 2011

9:40 am – 10:30 am Lockett 233

Elizabeth Dan-Cohen, Jacobs University Bremen
Structure and representation theory of finitary Lie algebras (virtual talk from Bremen)

ABSTRACT: Finitary Lie algebras are the simplest possible infinite-dimensional version of the classical Lie algebras. These infinite-dimensional algebras arise in many contexts in mathematics. However, their structure theory was underdeveloped until recently, and the representation theory is still in its early stages. I have been part of a recent series of contributions first to the structure and then most recently to the representation theory.

Tuesday, January 25, 2011

Posted November 26, 2010
Last modified January 11, 2011

3:40 pm – 4:30 pm Lockett 277

Vyacheslav Futorny, University of Sao Paulo
Representations of Lie algebra of vector fields on a torus

Representation theory of Lie algebra of vector fields on a circle, centerless Virasoro algebra, is well known due to results of O. Mathieu who proved Kac's conjecture. On the other hand, representations of Lie algebra of vector fields on n-dimensional torus are far less studied. We are going to discuss certain classes of representations whose construction is based on the theory of vertex algebras. These representations provide free-fields realizations of our Lie algebra. These are joint results with Yuly Billig (Ottawa, Canada).

Wednesday, January 26, 2011

Posted January 20, 2011

2:40 pm – 3:30 pm Lockett 285

John Baldwin, Princeton University
Contact structures, open books, and Khovanov homology

I will describe an important class of geometric objects on 3-manifolds called contact structures, and will survey Giroux\'s celebrated correspondence between contact structures and more topological objects called open books. I will summarize progress on some open questions related to this connection, and will explain how link invariants like Khovanov homology may be used to provide further insights.

Thursday, January 27, 2011

Posted January 27, 2011

4:40 pm – 5:30 pm 285 Lockett Hall

Winfried Hochstättler, FernUniversität in Hagen
Flows in Matroids I

Friday, January 28, 2011

Posted January 20, 2011

3:40 pm – 4:30 pm Lockett 277

Song Yao, University of Michigan
Optimal Stopping for Dynamic Convex Risk Measures

Abstract: We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an equivalent zero-sum game of control and stopping, between an agent (the "stopper") who chooses the termination time of the game, and an agent (the "controller", or "nature") who selects the probability measure.

Monday, January 31, 2011

Posted January 27, 2011

4:00 pm – 5:00 pm 338 Johnston Hall

Thomas Sterling, Louisiana State University
Enabling Exascale Computing through the ParalleX Execution Model

Wednesday, February 2, 2011

Posted January 20, 2011
Last modified January 24, 2011

3:40 pm – 4:30 pm Lockett 277

Karl Mahlburg, Princeton University
Percolation, partitions, and probability

I will discuss the surprising connections between finite-size scaling in families of bootstrap percolation models, the combinatorics of integer partitions, and limiting entropies for Markov-type processes. A combinatorial characterization of the percolation processes relates their metastability threshold exponents to the cuspidal asymptotics of generating functions for partitions with restricted sequence conditions. These generating functions are hypergeometric q-series that are of number-theoretic interest, as in many cases they are equal to the product of modular forms and Ramanujan's famous mock theta functions. In other cases, both the percolation processes and partition functions are best understood through entropy bounds for probabilistic sequences with gap conditions. These sequences can be understood as Markov-type processes with varying transition probabilities, and techniques from the theory of linear operators are used in order to bound the dominant eigenvalue.

Thursday, February 3, 2011

Posted January 31, 2011

4:40 pm – 5:30 pm 285 Lockett Hall

Winfried Hochstättler, FernUniversität in Hagen
Flows in Matroids II

Friday, February 4, 2011

Posted January 20, 2011
Last modified January 24, 2011

3:40 pm – 4:30 pm Lockett 277

Nam Quang Le, Columbia University
Regularity results for the mean curvature flow

Mean curvature flow is the evolution of a hypersurface moving with normal velocity equal to its mean curvature vector. If the initial hypersurface is compact then the flow will develop singularities in finite time. In this talk, we will present some recent regularity results on the compact mean curvature flow. Our focus will be on optimal conditions for the existence of smooth solutions to the mean curvature flow. We will show that if the flow is of type I then the mean curvature controls the flow in the sense that singularities cannot occur if the mean curvature is uniformly bounded. In the case of surfaces, we will show that the mean curvature controls the flow provided that either the Multiplicity One Conjecture of Ilmanen holds or the Gaussian density is less than two. When the mean curvature of our flow blows up, i.e., when singularities occur, we will also give its (sharp) blow-up rate.

Tuesday, February 8, 2011

Posted January 20, 2011
Last modified February 1, 2011

VIGRE@LSU: Student Colloquium Questions or comments?

3:40 pm – 4:30 pm Lockett 277

Leonardo Mihalcea, Baylor University Candidate for Assistant Professor Position in Algebraic Geometry
Rational curves in flag manifolds and Gromov-Witten invariants

Abstract: Gromov-Witten (GW) invariants for a flag manifold count rational curves subject to certain incidence conditions. These numbers satisfy remarkable equations, equivalent to the associativity relations of the quantum cohomology algebra, and were successfully used to solve many classical problems in enumerative geometry. In connection to Mirror Symmetry and Integrable systems, Givental and his collaborators defined the equivariant and K-theoretic GW invariants, which allow the corresponding space of rational curves to be positive dimensional. The purpose of my talk is to introduce the "quantum=classical" phenomenon, which in many instances allows us to compute explicitly 3-point GW invariants (of all flavors), and to obtain algorithms for multiplication in the (generalized) quantum cohomology algebra. In the case of Grassmannians, this is surprisingly related to positroids - varieties connected to Lusztig's totally positive stratification.

Wednesday, February 9, 2011

Posted January 20, 2011

4:10 pm – 5:00 pm Lockett 277

Andrei Zelevinsky, Northeastern University
Quiver representations and their mutations

A quiver is a finite directed graph, that is, a finite set of vertices some of which are joined by arrows. A quiver representation assigns a finite-dimensional vector space to each vertex, and a linear map between the corresponding spaces to each arrow. A fundamental role in the theory of quiver representations is played by Bernstein-Gelfand-Ponomarev reflection functors associated to every source or sink of a quiver. We discuss two recent modifications of these functors. The first (joint work with R.Marsh and M.Reineke) introduces decorated quiver representations and makes modified reflection functors act as isomorphisms of the corresponding Grothendieck groups. The second (joint work with H.Derksen and J.Weyman) extends reflection functors from sources and sinks to arbitrary vertices. This construction requires the quiver representations in question to satisfy relations of a special kind imposed by the framework of quivers with potentials. Motivations for this work come from several sources: superpotentials in physics, Calabi-Yau algebras and categories, clusteralgebras. However no knowledge is assumed in any of these subjects.

Thursday, February 10, 2011

Posted November 8, 2010
Last modified January 22, 2011

3:40 pm – 4:30 pm Lockett 277

Robert Stanton, Ohio State University
Symplectic methods in Lie theory

Abstract: The non-degenerate Cartan-Killing form on a semisimple Lie algebra provides a natural conformal class of pseudo-Riemannian metric in Lie theory. The resulting interplay of differential geometry and harmonic analysis on Lie groups and symmetric spaces is well known. At the other extreme is the presence of a non-degenerate skew-symmetric form. We will illustrate the usefulness of symplectic techniques by several applications ranging from classical invariant theory to exceptional Lie algebras to modern differential geometry. The talk is intended for a general audience and is based on joint work with M. Slupinski.

Posted February 1, 2011
Last modified February 6, 2011

6:00 pm James E. Keisler Lounge (room 321 Lockett)

Meeting of the Actuarial Student Association

Pizza and discussion.

Friday, February 11, 2011

Posted January 27, 2011
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 381

Benjamin Harris, MIT
Fourier Transforms of Nilpotent, Coadjoint Orbits and Leading Terms of Tempered Characters.

Suppose $\pi$ is an irreducible, admissible representation of a reductive Lie group with character $\Theta_{\pi}$. By results of Barbasch-Vogan and Schmid-Vilonen, the leading term of $\Theta_{\pi}$ at one is an integral linear combination of Fourier transforms of nilpotent coadjoint orbits. The first half of this talk will be about understanding Fourier transforms of nilpotent coadjoint orbits. I will state the most powerful theorem in the subject due to Rossmann and Wallach. Then I will explicitly write down Fourier transforms of nilpotent coadjoint orbits for $\text{GL}(n,\mathbb{R})$. The second half of this talk will be about understanding which orbits occur in leading terms of characters. In particular, I will state a necessary condition for an orbit to occur in the wave front cycle of a tempered representation. Then I will give an analogue of Kirillov's dimension formula for tempered representations of reductive Lie groups.

Saturday, February 12, 2011

Posted February 9, 2011

Workshop on Lie Groups, Lie Algebras, and their Representations

9:30 am – 12:00 pm Sunday, February 13, 2011 Lockett Hall 277

Workshop on Lie Groups, Lie Algebras and their Representations

The workshop start on Saturday, February 12, at 9:30 am and ends at 12pm on Sunday February 13. See the following webpage: http://www.math.lsu.edu/lieworkshop

Tuesday, February 15, 2011

Posted November 11, 2010
Last modified January 18, 2011

3:40 pm – 4:30 pm Lockett 277

Joseph Wolf, University of California, Berkeley
Classical Analysis and Nilpotent Lie Groups

Classical Fourier analysis has an exact counterpart in group theory and in some areas of geometry. Here I'll describe how this goes for nilpotent Lie groups and for a class of riemannian manifolds closely related to a nilpotent Lie group structure.

Tuesday, February 22, 2011

Posted February 22, 2011

Harmonic Analysis Student Seminar

11:40 am – 12:30 pm Lockett 233

Gestur Olafsson, Mathematics Department, LSU
The cos^lambda-transform, SL(n+1,K) and intertwining operators

Thursday, February 24, 2011

Posted February 22, 2011

Harmonic Analysis Student Seminar

11:10 am – 12:00 pm Lockett 381

Gestur Olafsson, Mathematics Department, LSU
The cos^lambda-transform, SL(n+1,K) and intertwining operators

Posted September 14, 2010
Last modified February 16, 2011

3:40 pm – 4:30 pm Lockett 277

Noriko Yui, Queen's University
The modularity (automorphy) of Calabi-Yau varieties over the rationals

Abstract: According to the Langlands Philosophy, every algebraic variety defined over the rationals or a number field should be modular (automorphic).

In this talk, I will concentrate on a special class of algebraic varieties, called Calabi-Yau varieties (of dimension at most three), defined over the rationals, and report on the current status of their modularity (automorphy).

Friday, February 25, 2011

Posted February 15, 2011

Algebra and Number Theory Seminar Questions or comments?

3:30 pm 338 Johnston Hall

LSU SIAM Student Chapter Webpage Design Workshop

LSU SIAM Student Chapter is organizing a personal webpage construction and design workshop. The speakers (Jeff Sheldon, Heather Russell and Laura Rider) will discuss setting up department based websites, basic commands in webpage design and webpages for job applications.

Posted February 17, 2011
Last modified March 2, 2021

3:40 pm – 4:30 pm Lockett 277

Noriko Yui, Queen's University
The modularity of certain K3-fibered Calabi-Yau threefolds over Q

We consider certain K3-fibered Calabi-Yau threefolds defined over Q. These Calabi-Yau threefolds are constructed using the method of Voisin and Borcea, and are realized as smooth resolutions of quotients of S × E by some involution. (Here S is an algebraic K3 surface and E is an elliptic curve.)

First we will discuss the modularity of K3 surfaces S. We look into the famous 95 families of K3 surfaces found by Reid and Yonemura. Among them, we will pick K3 surfaces with involution. Our first result is to show that some of these K3 surfaces are of CM type.

Next, we will discuss the modularity of Calabi-Yau threefolds over Q obtained from products S × E. We establish the modularity (automorphicity) of some of these Calabi-Yau threefolds and also their mirror partners (if exist), in the sense of Arthur and Clozel. Several explicit examples are discussed.

This reports on a joint work in progress with Y. Goto (Hakodate) and R. Livne (Jerusalem).

Wednesday, March 2, 2011

Posted February 7, 2011
Last modified March 1, 2011

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 277

Skip Garibaldi, Emory University
Matrix groups and diagonalizable matrices

This talk is about groups of matrices over a field, like GL_n (the group of n-by-n invertible matrices) or a special orthogonal group. Since Elie Cartan's 1894 PhD thesis, at least, the theory of such groups starts with studying a connected abelian subgroup consisting of diagonalizable matrices—we call such a thing a torus. This talk concerns the classical question: If every maximal torus in one group is isomorphic to a maximal torus in another group, are the two groups necessarily isomorphic? This problem is related to questions in differential geometry and classical algebra and there is serious recent progress.

This talk will discuss the recent solution of the problem over number fields (by Gopal Prasad and Andrei Rapinchuk in Pub. Math. IHES, and a small part due to the speaker) and a more elementary version with weaker results over general fields by the speaker and David Saltman.

Thursday, March 3, 2011

Posted February 27, 2011

Harmonic Analysis Student Seminar

11:10 am – 12:00 pm Lockett 381

Gestur Olafsson, Mathematics Department, LSU
The cos^lambda-transform, SL(n+1,K) and intertwining operators

Posted October 29, 2010
Last modified March 1, 2011

3:40 pm – 4:30 pm Lockett 277

Skip Garibaldi, Emory University
Did a 1-dimensional magnet detect a 248-dimensional Lie group?

Abstract: In a January 2010 article in Science, a team of physicists reported that they had "detected evidence of E8 symmetry" in a neutron scattering experiment on a quasi-1-dimensional cobalt niobate magnet. Their article details their experimental results, but it does not explain how these are connected with E8, a 248-dimensional Lie group. This talk will survey the chain of reasoning leading from those results to E8.

This talk does not require any previous knowledge of advanced physics.

Saturday, March 5, 2011

Posted March 11, 2011

Algebra and Number Theory Seminar Questions or comments?

3:40 pm Lockett 277

Math Instructor meeting

Wednesday, March 9, 2011

Posted March 3, 2011

3:40 pm – 4:30 pm Lockett 277

Sabin Cautis, Columbia University
A categorification of the Heisenberg algebra

Monday, March 14, 2011

Posted January 20, 2011
Last modified March 2, 2021

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 277

Grigory Litvinov, Independent University of Moscow
Integral Geometry, Hypergroups, and I.M. Gelfand's Question

It is well known that the Radon Transform is closely related to the classical Fourier transform and harmonic analysis on the additive groups of finite dimensional real linear spaces. In this talk we discuss ``similar'' interrelations between standard problems of Integral Geometry (in the sense of Gelfand and Graev) and harmonic analysis on certain commutative hypergroups (in the sense of J. Delsarte). These interrelations may be interpreted as an answer to an old question of I.M. Gelfand concerning algebraic foundations of Integral Geometry.

Tuesday, March 15, 2011

Posted March 15, 2011

Online Homework Software Presentation

1:40 pm – 3:00 pm Lockett 243

WebAssign

Representatives from Brooks/Cole, the publishers of Stewart Calculus, will present WebAssign.

Posted February 17, 2011
Last modified March 11, 2011

2:40 pm – 3:30 pm Lockett 284

Linhong Wang, Southeastern Louisiana University
Noncommutative infinite series rings

Skew power series rings T:=R[[y;\tau,\delta]], for suitably conditioned right noetherian complete semilocal rings R, automorphisms \tau of R, and \tau-derivations $\delta$ of R, were introduced by Venjakob
in the study of noncommutative Iwasawa theory. In this talk, I will discuss iterated skew power series rings and skew inverse power series rings. With suitable base rings and defining relations, these noncommutative infinite series rings give new examples of local, noetherian, zariskian (in the sense of Li and Van Oystaeyen) domains that are related to quantum algebras. Our study on the q-commutative power series ring k_q[[x]] provides a detailed account of its prime ideal structure. Our results, parallel those found for
quantum affine spaces, include normal separation and finite stratification by commutative noetherian spectra. Combining this normal separation with results of Chan, Wu, Yekutieli, and Zhang, we are able to conclude that k_q[[x]] is catenary. Following the approach of Brown and Goodearl, we also show that links between prime ideals are provided by canonical automorphisms. The new results in this talk are joint work with Edward Letzter.

Posted March 11, 2011

3:40 pm Lockett 239

Math Instructor meeting

Posted January 8, 2011
Last modified January 20, 2011

3:40 pm – 4:30 pm Lockett 277

Grigory Litvinov, Independent University of Moscow
Dequantization and tropical mathematics

Tropical mathematics can be treated as a result of a dequantization of the traditional mathematics over numerical fields as the Planck constant tends to zero taking imaginary values. Tropical mathematics is a part of the idempotent mathematics (calculus) in the sense of V.P. Maslov and his collaborators. The basic paradigm is expressed in terms of an idempotent correspondence principle. This principle is similar to N. Bohr's correspondence principles in Quantum Physics (and closely related to it). A systematic application of the idempotent correspondence principle leads to a variety of results, often quite unexpected (e.g., the Legendre transform is a tropical version of the Fourier transform). As a result, in parallel with the traditional mathematics, its "classical shadow" appears.

Wednesday, March 16, 2011

Posted February 25, 2011

4:40 pm – 5:30 pm Lockett 9

VIGRE Applications for Traineeships

The application deadline for traineeships during the summer 2011 and the academic year 2011/2012 is March 31. Gestur Olafsson will review the application process and answer questions. Mark Davidson will discuss the SMILE program and planned activities during the summer 2011. Information can be found at http://www.math.lsu.edu/vigre/Traineeship and http://www.math.lsu.edu/vigre/SMILE_LSU

Friday, March 18, 2011

Posted February 14, 2011
Last modified March 2, 2021

2:00 pm – 3:00 pm 233 Lockett

Andrew Barker, Louisiana State University
Evolutionary Game Theory and the Traveler's Dilemma

Monday, March 21, 2011

Posted January 30, 2011

11:00 am – 12:00 pm Lockett 301D

Final Event of Final Exam for Non-Thesis MS

Each student applying to receive a non-thesis MS in May 2011 must sign up with the Graduate School for the final exam final event as listed here. The Committee will be Profs. Cohen, Richardson, and Litherland(Chair).

Posted March 15, 2011
Last modified March 21, 2011

Algebra and Number Theory Seminar Questions or comments?

5:00 pm James E. Keisler Lounge (room 321 Lockett)

Shelly Johnson visits with ASA members

Shelly Johnson is a consultant for the two state retirement systems: Teachers Retirement System of Louisiana (TRSL) and Louisiana State Employees Retirement System (LASERS). There will be a presentation, discussion, and pizza.

Tuesday, March 22, 2011

Posted March 15, 2011

Online Homework Software Presentation

1:40 pm – 3:00 pm Lockett 243

Calc-Portal

Representatives from Freeman, publishers of Rogawski\'s Calculus, will present Calc-Portal.

Posted February 16, 2011
Last modified March 11, 2011

2:40 pm – 3:30 pm Lockett 284

Matthew Housley, University of Utah
TBA

Posted October 14, 2010
Last modified February 17, 2011

Pasquale Porcelli Lecture Series Special Lecture Series

3:40 pm – 4:30 pm 103 Design Auditorium

Craig Evans, University of California, Berkeley
Linearity and linearization

Abstract: In this expository lecture aimed at a general audience, I will first discuss the profound advantages of linear structure in mathematical problems and then survey several interesting ways to "linearize" nonlinear problems, primarily differential equations. Examples and applications will include perturbation and implicit function procedures, blow-up techniques, kinetic formulations, and adjoint methods based upon formal linearization.

Wednesday, March 23, 2011

Posted February 17, 2011

Pasquale Porcelli Lecture Series Special Lecture Series

3:40 pm – 4:30 pm 103 Design Auditorium

Craig Evans, University of California, Berkeley
Convexity as one-sided linearity

Abstract: I will continue the themes of the previous talk, surveying for differential equations various convexity methods that can be interpreted as "one-sided linearity" tricks. These are especially useful since, as I will show, several important and highly nonlinear problems possess "hidden" convex structures of various sorts.

Thursday, March 24, 2011

Posted February 17, 2011

Pasquale Porcelli Lecture Series Special Lecture Series

3:40 pm – 4:30 pm 103 Design Auditorium

Craig Evans, University of California, Berkeley
Linear adjoint methods for sup-norm variational problems

Abstract: This final lecture will present some technical details about a recent application of linearization and adjoint methods for proving differentiability for weak solutions of the so-called "infinity Laplacian" PDE. This highly degenerate and nonlinear equation is fundamental in the emerging field of sup-norm variational problems and their applications.

Friday, March 25, 2011

Posted March 10, 2011

4:00 pm Lockett 277

Tenured Faculty Meeting

Tuesday, March 29, 2011

Posted March 15, 2011

Online Homework Software Presentation

1:40 pm – 3:00 pm Lockett 243

Connect

Representatives from McGraw-Hill, publishers of Smith-Minton\'s Calculus, will present \'Connect\'.

Posted March 18, 2011
Last modified March 29, 2011

3:40 pm – 4:30 pm 276 Lockett

Kate Kearney, Indiana University
An Obstruction to Knots Bounding Moebius Bands

Wednesday, March 30, 2011

Posted March 17, 2011

3:40 pm Lockett 277

Faculty Meeting

Thursday, March 31, 2011

Posted March 21, 2011
Last modified October 4, 2021

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 277

Igor Verbitsky, University of Missouri-Columbia Curators' Professor
Hessian Sobolev inequalities, $k$-convex functions, and the fractional Laplacian

Tuesday, April 12, 2011

Posted March 11, 2011

3:40 pm – 4:30 pm Lockett 277

Aaron Lauda, Columbia University
TBA

Thursday, April 14, 2011

Posted March 22, 2011

3:40 pm – 4:30 pm Lockett 277

Tadele Mengesha, Louisiana State University
Global estimates for nonlinear elliptic equations over nonsmooth domains

In this talk we discuss new global regularity estimates for solutions to a class of nonlinear elliptic boundary value problems over nonsmooth domains. The nonlinear coefficients are allowed to be discontinuous but assumed to have a small mean oscillation. The boundary of the domain may be nonsmooth but sufficiently flat in the sense of Reifenberg. The main regularity estimates obtained are in weighted Lorentz spaces. As an application, these estimates will be used to obtain other regularity results in Lorentz-Morrey, Morrey, and Holder spaces. This is joint work with Phuc Nguyen.

Monday, April 25, 2011

Posted February 7, 2011

11:00 am – 12:00 pm 338 Johnston Hall

Mac Hyman, Tulane University
Good Choices for Great Careers in the Mathematical Sciences

The choices that students make early in their careers will impact them for a lifetime. I will use the experiences of scientists who have had great careers to identify universal distinguishing traits of good career choices that can guild decisions in education, choice of profession, and job opportunities to increase your chances of having a great career with long-term sustained accomplishments. I ran a student internship program at Los Alamos National Laboratory for over 20 years. For the last couple of years I have been tracking the careers past students and realized that the scientists with great careers weren\'t necessarily the top students, and that some of the most brilliant students now had some of the most oh-hum careers. I will describe how the choices made by the scientists with great careers were based on following their passion, building their talents into a strength supporting their profession, and how they identified a supportive engaging work environment. I will describe some simple guidelines that can help guide your choices, in school and in picking the right job that can lead to a rewarding career and more meaningful life. The topic is important because, so far as I can tell, life is not a trial run - we have one shot to get it right. The choices you are making right now to planning your career will impact your for a lifetime. Please join us for an engaging discussion on how to make the choices that will lead to a great career.

Posted February 7, 2011

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 338 Johnston Hall

Mac Hyman, Tulane University
Simple Mathematical Models Can Provide New Insights into Stopping Epidemics

Public health workers are reaching out to mathematical scientists to use disease models to understand, and mitigate, the spread of emerging diseases. Mathematical and computational scientists are needed to create new tools that can anticipate the spread of new diseases and evaluate the effectiveness of different approaches for bringing epidemics under control. Simple epidemic models can be used in the classroom to provide insight into how mathematical sciences can improve the health of our world and save lives. The talk will provide an overview, for general audiences, of what type of insights these models can provide. I will describe some of the mathematical advances needed to create the next generation of models, and share my personal experiences in controlling the spread of HIV/AIDS, SARS, malaria, foot and mouth disease, and the novel H1N1 (swine) flu.

Tuesday, April 26, 2011

Posted April 25, 2011
Last modified September 17, 2021

Joint ECE and ME Control Seminar

10:00 am 2520 Taylor (formerly CEBA)

Aleksandra Gruszka, LSU Department of Mathematics PhD Student of Prof. Malisoff
On Tracking for the PVTOL Model with Bounded Feedbacks

This talk will be repeated as a 3:40PM April 27th Applied Analysis Seminar.

Posted March 9, 2011

3:40 pm – 4:30 pm Lockett 277

David Chapman, Mathematics Department, LSU Graduate student
TBA

Wednesday, April 27, 2011

Posted April 15, 2011
Last modified April 25, 2011

VIGRE@LSU: Student Colloquium Questions or comments?

3:40 pm Lockett 233

Aleksandra Gruszka, LSU Department of Mathematics PhD Student of Prof. Malisoff
On tracking for the PVTOL model with bounded feedbacks

We study a class of feedback tracking problems for the planar vertical takeoff and landing (PVTOL) aircraft dynamics, which is a benchmark model in aerospace engineering. After a survey of the literature on the model, we construct new feedback stabilizers for the PVTOL tracking dynamics. The novelty of our contribution is in the boundedness of our feedback controllers and their applicability to cases where the velocity measurements may not be available, coupled with the uniform global asymptotic stability and uniform local exponential stability of the closed loop tracking dynamics, the generality of our class of trackable reference trajectories, and the input-to-state stable performance of the closed loop tracking dynamics with respect to actuator errors. Our proofs are based on a new bounded backstepping result. We illustrate our work in a tracking problem along a circle.

Tuesday, May 3, 2011

Posted May 2, 2011

SIAM Student Chapter & AWM Student Chapter

9:00 am – 10:00 am Lockett Hall 321, Keisler Lounge

Suzanne Lenhart, University of Tennessee
A Conversation with Prof. Suzanne Lenhart

Prof. Suzanne Lenhart from University of Tennessee is visiting LSU on May 3rd. The SIAM Chapter and AWM Chapter members and all graduate students in math department are invited to meet with her from 9:00 to 10:00a.m in Keisler Lounge, Lockett Hall 321. Refreshments will be served.

Posted April 26, 2011
Last modified May 2, 2011

10:40 am – 11:30 am 276 Lockett Hall

Suzanne Lenhart, University of Tennessee
Optimal Harvesting in Fishery Models

We discuss two types of partial differential equation models of fishery harvesting problems. We consider steady state spatial models and diffusive spatial-temporal models. We characterize the distribution of harvest effort which maximizes the harvest yield, and in the steady state case, also minimizes the cost of the effort. We show numerical results to illustrate various cases. The results inform ongoing debate about the use of reserves (regions where fishing is not allowed), and are increasingly relevant as technology enables enforcement of spatially structured harvest constraints.

Posted April 26, 2011
Last modified May 2, 2011

VIGRE@LSU: Student Colloquium Questions or comments?

1:40 pm – 2:30 pm 276 Lockett Hall

Suzanne Lenhart, University of Tennessee
The power of optimal control: from confining rabies to improving CPR

Refreshments will be served in the Keisler Lounge from 1:00 to 1:30. This talk will present optimal control of two examples which are discrete in time. The first example involves difference equations that model cardiopulmonary resuscitation. The goal is to design an external chest and abdomen pressure pattern to improve the blood flow in the heart in standard CPR procedure. The second example is an epidemic model for rabies in raccoons on a spatial grid. The goal is to find the optimal distribution pattern for vaccine baits to slow the spread of the disease.

Wednesday, May 4, 2011

Posted April 29, 2011

3:40 pm Lockett 277

Michael Malisoff, LSU Roy P. Daniels Professor
Uniform global asymptotic stability of adaptive cascaded nonlinear systems with unknown high-frequency gains

We study adaptive tracking problems for nonlinear systems with unknown control gains. We construct controllers that yield uniform global asymptotic stability for the error dynamics, and hence tracking and parameter estimation for the original systems. Our result is based on a new explicit, global, strict Lyapunov function construction. We illustrate our work using a brushless DC motor turning a mechanical load. We quantify the effects of time-varying uncertainties on the motor electric parameters.

Note: This talk will be understandable to faculty, staff, students, and visitors who are familiar with the material in Math 7320 (Ordinary Differential Equations) at LSU. No background in control is needed.

Friday, May 6, 2011

Posted May 2, 2011

SIAM Student Seminar

3:40 pm 233 Lockett Hall

Guillaume Dupre
Finite Element Method for Moving Curves

Abstract:
The finite element method (FEM) is a numerical method for finding approximate solutions of partial differential equations. In this project, we use a finite element method to compute the time-dependent motion of a closed curve in the 2D plane. In particular, the motion law we use, is called Mean Curvature Flow, which says that each point on the curve moves in the normal direction at a speed proportional to the curvature at that point. In this talk, after a brief overview of FEM, we consider this flow with the additional constraints of constant enclosed area and avoidance of impenetrable obstacles, and we derive the modified motion law via calculus of variations. We then describe a finite element method that accounts for these constraints and discuss some of its properties. We also show numerical results (movies) to illustrate the behavior of the flow. We conclude with potential applications.

Monday, May 9, 2011

Posted April 29, 2011
Last modified March 2, 2022

3:40 pm – 4:30 pm Room 233 Lockett Hall

Cody Pond, Department of Mathematics Tulane University
Effective boundary conditions on insulated bodies

The temperature of perfectly insulated body can be modeled by the heat equation with Neumann (or no-flux) boundary condition. In reality there are no perfect insulators and the actual boundary condition on the body may be only approximately Neumann. In this talk we will see how properties of a layer of insulation affect the boundary condition experienced by the insulated body. We we also see how ignoring physical restrictions in the model can produce some exotic boundary conditions.

Friday, May 13, 2011

Posted May 13, 2011

School of the Coast and Environment Spring Seminar Series

11:30 am Energy Center, Dalton Woods Auditorium

Rachael Neilan, Department of Oceanography and Coastal Sciences, LSU
Optimal Management Controls for Maximizing the Recovery of an Endangered Fish Species

Posted May 10, 2011

Controls Seminar

1:40 pm 233 Lockett

Aleksandra Gruszka, LSU Department of Mathematics PhD Student of Prof. Malisoff
Bounded Backstepping Methods for Tracking PVTOL Trajectories

In my last Control Seminar, I discussed a class of feedback tracking problems for the planar vertical takeoff and landing (PVTOL) aircraft dynamics, which is a benchmark model in aerospace engineering. I explained how to construct bounded thrust and rolling moment controllers for tracking a general class of PVTOL reference trajectories. The construction applies to cases where the velocity measurements may not be available, and also gives input-to-state stable performance of the closed loop tracking dynamics with respect to actuator errors. The tracking proof is based on a bounded backstepping lemma. In this talk, I will briefly review the construction and then discuss the proof of the lemma. Note: This talk will be understandable to faculty, staff, students, and visitors who are familiar with the material in Math 7320 (Ordinary Differential Equations) at LSU. No background in control is needed.

Monday, June 13, 2011

Posted June 5, 2011

3:30 pm – 4:30 pm Lockett 233

Christopher Davis, UNCC
Meshless Boundary Particle Methods for Elliptic Problems

Monday, August 15, 2011

Posted July 19, 2011
Last modified July 25, 2021

1:00 pm – 4:00 pm 285 Lockett Hall

Comprehensive / PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, August 17, 2011

Posted July 19, 2011
Last modified July 25, 2021

1:00 pm – 4:00 pm 285 Lockett Hall

Comprehensive / PhD Qualifying Exam in Analysis

This Exam is part of the PhD Qualifying Examination in Mathematics.

Friday, August 19, 2011

Posted July 19, 2011
Last modified July 25, 2021

1:00 pm – 4:00 pm 285 Lockett Hall

Comprehensive / PhD Qualifying Exam in Topology

This Exam is part of the PhD Qualifying Examination in Mathematics.

Tuesday, August 23, 2011

Posted July 27, 2011
Last modified August 20, 2011

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Johnston Hall 338

Higher Order Estimates In Time For The Arbitrary Lagrangian Eulerian Formulation In Moving Domains

Speaker: Andrea Bonito

Posted August 18, 2011
Last modified May 8, 2021

3:40 pm – 4:30 pm Lockett 240

Paul Smith, University of Washington
A 3-Calabi-Yau algebra with G_2 symmetry that is related to the octonions

This talk concerns an associative graded algebra $A$ that is the enveloping algebra of a Lie algebra with exponential growth. The algebra is a coherent, 3-Calabi-Yau, Koszul algebra, and the exceptional group of type $G_2$ acts as automorphisms of it. The algebra $A$ seems to have first appeared in a physics paper. $A$ can be defined in many ways. If $V$ is the 7-dimensional irreducible representation of the complex semisimple Lie algebra of type $G_2$, then $A$ is isomorphic to the tensor algebra $T(V)$ modulo the ideal generated by the submodule of $V \otimes V$ isomorphic to $V$. Alternatively, $A$ can be defined as a superpotential algebra derived from a 3-form on $R^7$ having an open $GL(7)$ orbit and compact isotropy group. $A$ can also be defined in terms of the product on the octonions. $A$ can also be defined in terms of the exterior derivatives of seven 1-forms that appear in E. Cartan's “Five variables” paper. Classification of the finite-dimensional representations of $A$ is equivalent to classifying square matrices $Y$ with purely imaginary octonion entries such that the imaginary part of $Y^2$ is zero. There is a derived equivalence relating graded $A$-modules to representations of a certain quiver (with relations). This equivalence is analogous to Beilinson's equivalence for the derived category of coherent sheaves on $P^n$. $A$ can also be defined in terms of the incidence relations for the Fano plane, the projective plane over the field of two elements. These incidence relations give the simplest example of a Steiner triple system. Mariano Suarez-Alvarez has shown that every Steiner triple system gives rise to an algebra analogous to $A$ that is also coherent, 3-Calabi-Yau, and Koszul, though these more general algebras do not seem to have an interesting Lie group acting as automorphisms.

Wednesday, August 24, 2011

Posted August 18, 2011
Last modified March 3, 2022

3:40 pm – 4:30 pm Locket 233

Charles Frohman, University of Iowa
Virtual Seminar: Projective Representations of the Mapping Class group of a surface with boundary coming from TQFT

(Joint with Joanna Kania-Bartoszynska and Mike Fitzpatrick)

For each odd prime p, and primitive 2pth root unity, there is a projective representation of the mapping class group of a torus of dimension 2, that comes from the projective action of the mapping class group of a one punctured torus ( aka the modular group) on a portion of the state space assigned to a once punctured torus. I will prove up to conjugacy, this family extends to a continuous family of representations of the modular group defined on the unit circle. This family includes a twisted version of the canonical representation of the modular group. This means that the dilation coefficient of pseudo-anosov mapping classes can be computed as a limit of quantum invariants of mapping tori. It also means that the hyperbolic volume should also be computable, though the connection is less direct.

Posted August 24, 2011

4:10 pm Lockett 005

Math Faculty Meeting

Thursday, August 25, 2011

Posted August 4, 2011
Last modified August 9, 2011

3:40 pm – 4:30 pm Lockett 284

Paul Smith, University of Washington
Penrose tilings of the plane and noncommutative algebraic geometry

Abstract: The space X of Penrose tilings of the plane has a natural
topology on it. Two tilings are equivalent if one can be obtained from the
other by a translation. The quotient topological space X/~ is bad: every
point in it is dense. The doctrine of non-commutative geometry is to
refrain from passing to the quotient and construct a non-commutative
algebra that encodes some of the data lost in passing to X/~. In this
example (see Connes book for details) the relevant non-commutative algebra
is a direct limit of products of matrix algebras. We will obtain this
non-commutative algebra by treating the free algebra on two variables x
and y modulo the relation y2=0 as the homogeneous coordinate ring of a
non-commutative curve. The category of quasi-coherent sheaves on this
non-commutative curve is equivalent to the module category over a simple
von Neumann regular ring. That von Neumann regular ring is the same as the
direct limit algebra that Connes associates to X/~. We will discuss
algebraic analogues of various topological features of X/~. For example,
the non-vanishing of extension groups between simple modules is analogous
to the fact that every point in X/~ is dense (which is analogous to the
fact that any finite region of one Penrose tiling appears infinitely often
in every other tiling).

Tuesday, August 30, 2011

Posted July 15, 2011
Last modified August 20, 2011

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Johnston Hall 338

A Diffuse Interface Model For Electrowetting

Speaker: Abner J. Salgado

Posted August 18, 2011
Last modified August 23, 2011

3:40 pm – 4:30 pm Lockett 240

Peter Fiebig, Universität Erlangen-Nürnberg
Moment graphs in topology and representation theory

Moment graphs originated in the work of Goresky, Kottwitz and MacPherson on the equivariant topology of complex varieties with a torus action. In particular, they showed how one can calculate the hypercohomology of a large class of equivariant sheaves using only their restriction to the 1-skeleton (i.e. the moment graph) of the torus action. Building on these ideas, Braden and MacPherson gave an explicit description of the equivariant intersection cohomology of certain complex varieties using sheaves on the moment graph. Now these sheaves also appear in the study of multiplicity questions in representation theory. When combined, one obtains proofs of fundamental conjectures of Lusztig and Kazhdan-Lusztig. In the talk I will explain these ideas in some detail.

Thursday, September 1, 2011

Posted August 19, 2011
Last modified August 31, 2011

VIGRE@LSU: Student Colloquium Questions or comments?

3:40 pm – 4:30 pm Lockett 235

Artem Pulemotov, University of Chicago
The prescribed Ricci curvature problem

We will discuss the problem of finding a Riemannian metric with given Ricci curvature on a compact manifold M. This problem has been intensively studied by mathematicians since the early 1980\'s.

It is partially resolved in the case where M is a closed manifold, but almost completely unresolved on manifolds with boundary. In the first part of the talk, we will review the history of the subject. After that, our focus will be on new results regarding the situation where M is a solid torus.

Monday, September 5, 2011

Posted September 20, 2011

3:40 pm – 4:30 pm Wednesday, October 5, 2011 Lockett 243

Dan Cranston, Virginia Commonwealth University
The Search for Moore Graphs: Beauty is Rare

Abstract: A Moore Graph is k-regular, has diameter 2, and has k^2+1 vertices- that\'s the most vertices you could hope for in such a graph. These graphs are vertex-transitive and evoke a wonderful sense that \"everything fits just right.\" It\'s not hard to find Moore graphs when k is 2 or 3; they\'re the 5-cycle and the Petersen graph. But for larger k, they\'re very rare. In 1960, Hoffman and Singleton gave a beautiful proof that Moore Graphs can only exist when k is 2, 3, 7, or 57. For k equal to 2, 3, or 7, they showed that there exists a unique Moore Graph. When k is 57, nobody knows. I\'ll present Hoffman and Singleton\'s proof and take a wild stab at what they might have been thinking when they discovered it.

Dan Cranston is an invited speaker of the Student Colloquium Committee, which is funded by the VIGRE grant.

Tuesday, September 6, 2011

Posted August 20, 2011
Last modified August 31, 2011

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Johnston 338

Computational Math Group
Research Summaries

Faculty members in the computational mathematics group (Bourdin, Brenner, Sung, Walker, Wan and Zhang) will give short presentations on their current research. Refreshments will be served at 3:00 pm.

Posted August 29, 2011

3:40 pm – 4:30 pm Lockett 240

Pramod Achar, Mathematics Department, LSU
Geometric Satake, Springer correspondence, and small representations

Let G be a reductive group, and let W be its Weyl group. (For example, take G = GL_n and W = S_n.) In this talk, I will explain how to construct a commutative diagram relating the following four things:
(1) Representations of W
(2) Geometry of the nilpotent cone for G
(3) Representations of G
(4) Geometry of the affine Grassmannian for G
Some parts of the commutative diagram are well-known: (1) and (2) are related by the Springer correspondence; (3) and (4) are related by the geometric Satake isomorphism; and there is a functor from (3) to (1) that can be described as \"take the zero weight space.\" So the main point of the talk will to explain how to related (2) and (4). This is joint work with A. Henderson.

Friday, September 9, 2011

Posted September 6, 2011

3:30 pm – 4:30 pm Lockett Hall 241

Perry Iverson, Mathematics Department, LSU
Internally 4-connected projective graphs

Abstract: Archdeacon showed that projective graphs are characterized by 35 excluded minors. We show that the class of internally 4-connected projective graphs can be characterized by 23 excluded minors. In doing so, we discuss general methods for improving connectivity.

Monday, September 12, 2011

Posted September 9, 2011

3:40 pm – 4:30 pm 240 Lockett

Joonhee Rhee, Soongsil University, South Korea
A Defaultable Bond Pricing under the Change of Filtration

Tuesday, September 13, 2011

Posted August 31, 2011
Last modified November 29, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Johnston 338

Jiangguo Liu, Colorado State University
Mathematical Modeling For HIV-1 Gag Protein Trafficking And Assembly

The group-specific antigen (Gag) protein is encoded by human immunodeficiency virus type 1 (HIV-1), which causes the Acquired Immuno Deficiency Syndrome (AIDS). A better understanding of the mechanisms of trafficking and assembly of the HIV-1 Gag proteins inside the infected host cells will be undoubtedly helpful for developing new drugs for treatment of HIV. In this talk, we will present a mathematical model for HIV-1 Gag protein trafficking that accounts for both active transport on microtubules and diffusion in cytoplasm. The convection-diffusion equation can be efficiently solved using characteristic finite element methods. Our in silico results are in good agreement with the in vitro experimental data for several cell lines. We shall also discuss math models for Gag multimerization inside cytoplasm and on cell membrane. The mechanism for kinesin-based viral egress will be examined to illustrate the stochastic features of protein trafficking. This is a joint work with Chaoping Chen, Roberto Munoz-Alicea, Simon Tavener at ColoState and Qing Nie at UC Irvine.
Additional information can be found at http://www.cct.lsu.edu/events/talks/577

Posted August 22, 2011
Last modified September 11, 2011

3:40 pm – 4:30 pm Lockett 240

Karl Mahlburg, Department of Mathematics, LSU
Coefficient Asymptotic for Kac-Wakimoto characters

In Kac and Peterson's study of characters for affine Lie algebras, they proved a number of "Denominator identities" that related the weight multiplicities of irreducible submodules to theta functions. They then used modular inversion formulas and Tauberian theorems in order to derive asymptotics for these weight multiplicities; one of the simplest examples of affine Lie algebras leads to Hardy and Ramanujan's famous formula for the asymptotics of p(n), the integer partition function.

In this talk I will present joint work with K. Bringmann on the characters for affine Lie superalgebras that were later introduced by Kac and Wakimoto. In this setting, the characters are products of theta functions and Appell-type sums, which have recently been studied using developments in the theory of mock modular forms and harmonic Maass forms. We find asymptotic series expansions for the coefficients of the characters with polynomial error.

Wednesday, September 14, 2011

Posted September 9, 2011
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 244

Daniel Maier, University of Tübingen
Compact Monothetic Groups in Dynamical Systems

We give a short introduction in compact monothetic groups and show the interplay between such groups and dynamical systems. Especially, we construct measure preserving dynamical systems which are isomorphic to rotations on compact monothetic groups.

Posted August 29, 2011
Last modified October 1, 2021

LSU AWM Student Chapter LSU AWM Student Chapter Website

3:40 pm – 4:30 pm Locket 233

Greg Muller, Department of Mathematics, LSU
Virtual Seminar: Skein algebras of marked surfaces

Given a surface with boundary and a collection of marked points on the boundary, one may consider all curves in the surface which end at the marked points. One may define the Kauffman skein algebra (at q=1) generated by these curves; this generalizes the `unmarked' definition where only loops are allowed. Generalizing results of Bullock, Barrett and Przytycki-Sikora, this algebra can be realized as the algebra of functions on a space of (twisted) SL_2(C) local systems with extra data at the marked points. Additionally, new phenomena arise in the marked case which do not generalize any unmarked results. When there are enough marked points for the surface to admit a triangulation, then each triangulation gives an embedding of the skein algebra into a ring of Laurent polynomials. Through these embeddings, it can be shown that the skein algebra coincides with the `upper cluster algebra' of the marked surface, an algebra with significance in combinatorics, Lie theory and Teichmüller theory. Part of this work is joint with Peter Samuelson.

Friday, September 16, 2011

Posted September 6, 2011

12:00 pm – 1:30 am Keisler Lounge, Lockett Hall 3rd Floor

Welcome Event

Come enjoy pizza and soda with the LSU Student Chapter of the AWM and find out more about the organization. All interested parties are welcome. Feel free to come late or leave early.

Monday, September 19, 2011

Posted September 16, 2011

3:40 pm – 4:30 pm 240 Lockett

Joonhee Rhee, Soongsil University, South Korea
Defaultable Bond Pricing under a Change of Filtration: Part II

Tuesday, September 20, 2011

Posted September 12, 2011

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Johnston 338

Yi Zhang, Department of Mathematics, LSU Graduate Student
A Quadratic C0 Interior Penalty Method For The Displacement Obstacle Problem Of Clamped Plates

The displacement obstacle problem of clamped plates is an example of a fourth order variational inequality whose numerical analysis is more subtle than that of second order variational inequalities. In this talk we will introduce C0 interior penalty methods for this problem. Both error estimates and numerical results will be discussed. This is joint work with Susanne Brenner, Li-yeng Sung and Hongchao Zhang.

Posted August 22, 2011
Last modified September 13, 2011

3:40 pm – 4:30 pm Tuesday, September 6, 2011 Lockett 240

Elizabeth Dan-Cohen, Department of Mathematics, LSU
A Koszul category of representations of finitary Lie algebras

We find an interesting category of representations of the three simple finitary Lie algebras. The modules in question are weight modules for every splitting Cartan subalgebra. We describe the injective modules in this category, and show that the category is antiequivalent to the category of locally unitary finite-dimensional modules over a direct limit of finite-dimensional Koszul algebras. Joint with Ivan Penkov and Vera Serganova.

Wednesday, September 21, 2011

Posted September 12, 2011
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett 244

Karl Heinrich Hofmann, Darmstadt University, Germany Professor Emeritus
Compact Groups in which any Two Closed Subgroups Commute

We shall discuss compact groups in which any pair of closed subgroups $M$, $N$ satisfies $MN=NM$. After reviewing the existing literature we shall see that it remains to complete the classification by describing profinite metabelian $p$-groups for a prime $p$. The groups we are looking for are quotients of a semidirect product of some power $\Z_p^J$ of the additive group of the ring $\Z_p$ of $p$-adic integers by the group $\Z_p$ acting as the $p$-component of the group $\Z_p^\times$ of units of this ring under scalar multiplication. These quotients are explicitly described. This topic provides the motivation to take a closer look at some of the basic properties of the ring $\Z_p$ of $p$-adic integers. Joint work with Francesco Russo, Università degli studi, Palermo.

Thursday, September 22, 2011

Posted September 21, 2011

Evolution Equations Seminar

3:00 pm – 4:00 pm Prescott 203

Fatih Bayazit, Univerity of Tübingen Graduate Fellow (Friedrich-Ebert-Stiftung)
Floquet representations and asymptotics of periodic evolution families

We use semigroup techniques to describe the asymptotic behavior of contractive, periodic evolution families on Hilbert spaces. In particular, we show that such evolution families converge almost weakly to a Floquet representation with discrete spectrum.

Posted September 15, 2011
Last modified September 20, 2011

3:30 pm – 4:30 pm Lockett 239

Tyler Moss, Department of Mathematics, LSU Graduate Student
A minor-based characterization of matroid 3-connectivity

There are several well-known characterizations of matroid 2-connectivity. In this talk, I give a characterization of 3-connectivity.

Friday, September 23, 2011

Posted August 31, 2011
Last modified March 2, 2022

3:40 pm Lockett 233

Catalin Turc, Case Western Reserve University
Fast, high-order solvers based on regularized integral equations for acoustic and electromagnetic scattering problems

We present a class of solvers based on Nystrom discretizations to produce fast and very accurate solutions of acoustic and electromagnetic scattering problems in small numbers of Krylov-subspace iterations. At the heart of our approach is a general methodology that uses certain regularizing operators to deliver integral equation formulations that possess excellent spectral properties for scattering problems, including smooth and non-smooth geometries and a variety of boundary conditions. Our computational methodology relies on a novel Nystrom approach based on use of a overlapping/non-overlapping-patch technique, Chebyshev discretizations and an acceleration method based on equivalent sources and 3D FFT's.

Monday, September 26, 2011

Posted September 24, 2011

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm 240 Lockett

Ambar Sengupta, Mathematics Department, LSU
Model-free Pricing Formulas

Tuesday, September 27, 2011

Posted August 30, 2011

3:40 pm – 4:30 pm Lockett 240

Greg Muller, Department of Mathematics, LSU
TBA

Wednesday, September 28, 2011

Posted September 9, 2011
Last modified March 3, 2022

VIGRE@LSU: Student Colloquium Questions or comments?

3:40 pm – 4:30 pm Lockett 233

Shin Satoh, Kobe University
Virtual Seminar: Quandle cocycle invariants of roll-spun knots

We have two fundamental families in 2-knot theory; one is a ribbon 2-knot and the other is a deform-spun knot. Since any ribbon 2-knot is represented by a diagram with no triple point, the quandle cocycle invariant is always trivial. As special families of deform-spun knots, we have twist-spun knots and roll-spun knots. The invariant of a twist-spun knot have been studied in many papers. The aim of this talk is to explain how to calculate the quandle cocycle invariant of a roll-spun knot and give several properties.

Tuesday, October 4, 2011

Posted September 20, 2011

1:30 pm – 2:00 pm Keisler Lounge in Lockett Hall

Refreshments for the Student Colloquium Talk

We will be having refreshments during this time period leading up to Dan Cranston\'s talk.

Dan Cranston is an invited speaker of the Student Colloquium Committee, which is funded by the VIGRE grant.

Posted September 20, 2011

VIGRE@LSU: Student Colloquium Questions or comments?

2:00 pm – 3:00 pm Lockett 112

Dan Cranston, Virginia Commonwealth University
A Proof of Bertrand's Postulate

This talk is aimed at undergraduate students.

Abstract: Bertrand's Postulate states: For every positive integer n, there is some prime number p with n < p \\le 2n. This result was conjectured in 1845 by Joseph Bertrand, who verified it for all n < 3 \\times 10^6, and it was proved five years later by Chebyshev (nearly 50 years before the prime number theorem was proved). I'll present a beautiful proof of this result due to Paul Erd\"os.

Dan Cranston is an invited speaker of the Student Colloquium Committee, which is funded by the VIGRE grant.

Posted September 14, 2011

3:30 pm – 4:30 pm Johnston Hall 338

Mayank Tyagi, Louisiana State University
Fluid Flow Simulations of Diverse Petroleum Engineering Processes at the Rock Pores-, System Components- and Reservoir Field- Scales

Wednesday, October 5, 2011

Posted August 29, 2011
Last modified September 26, 2011

VIGRE@LSU: Student Colloquium Questions or comments?

3:40 pm – 4:30 pm Locket 233

Trenton Schirmer, Department of Mathematics, University of Iowa
Virtual Seminar: The degeneration ratio of tunnel number under connect sum

The tunnel number $t(L)$ of a link $L$ in $S^3$ is the minimal number of arcs $\{t_1, .... , t_n\}$ that can be embedded in the closure of $S^3-N(L)$ so that S^3-N(L \cup t_1 \cup ... \cup t_n is a handlebody. When $L$ is a knot $t(K)+1$ is just the Heegaard genus of its complement. The ``degeneration ratio'' of a connect sum $L =L_1$ # $L_2$ is defined as t L/(t(L_1)+t(L_2)). We give some new examples of links for which the degeneration ratio becomes low.

Posted September 20, 2011

3:40 pm – 4:30 pm Lockett 243

Dan Cranston, Virginia Commonwealth University
The Search for Moore Graphs: Beauty is Rare

This talk is aimed at graduate students.

Abstract: A Moore Graph is k-regular, has diameter 2, and has k^2+1 vertices- that\'s the most vertices you could hope for in such a graph. These graphs are vertex-transitive and evoke a wonderful sense that \"everything fits just right.\" It\'s not hard to find Moore graphs when k is 2 or 3; they\'re the 5-cycle and the Petersen graph. But for larger k, they\'re very rare. In 1960, Hoffman and Singleton gave a beautiful proof that Moore Graphs can only exist when k is 2, 3, 7, or 57. For k equal to 2, 3, or 7, they showed that there exists a unique Moore Graph. When k is 57, nobody knows. I\'ll present Hoffman and Singleton\'s proof and take a wild stab at what they might have been thinking when they discovered it.

Dan Cranston is an invited speaker of the Student Colloquium Committee, which is funded by the VIGRE grant.

Thursday, October 6, 2011

Posted September 16, 2011
Last modified October 5, 2011

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 239

Dan Cranston, Virginia Commonwealth University
The Game of Revolutionaries and Spies on a Graph

We study a pursuit game between two teams on a graph; it can be viewed as modeling a problem of network security. The first team consists of r revolutionaries; the second consists of s spies. The revolutionaries seek a one-time meeting of m revolutionaries free of oversight by spies. Initially, the revolutionaries take positions at vertices, and then the spies do the same. In each subsequent round, each revolutionary may move to an adjacent vertex or not move, and then each spy has the same option. Everyone knows where everyone else is at all times.

The revolutionaries win if after a round there is an unguarded meeting, where a meeting consists of (at least) m revolutionaries on one vertex, and it is unguarded if no spy is there. The spies win if they can prevent this forever. Let RS(G,m, r, s) denote this game played on the graph G by s spies and r revolutionaries with meeting size m.

The revolutionaries can form \floor(r/m) disjoint meetings (if G has at least this many vertices), so the spies need s at least \floor(r/m) to avoid losing immediately. For fixed G, r, m, let sigma(G,m,r) be the least s such that RS(G,m, r, s) is won by the spies. Say that G is spy-good if sigma(G,m,r) = \floor(r/m) for all m and r such that (r/m) < |V(G)|. We obtain a large class of spy-good graphs. A webbed tree is a graph G having a rooted spanning tree T such that every edge of G not in T joins vertices having the same parent in T.

Theorem: Every webbed tree is spy-good. Furthermore, all interval graphs and all graphs having a dominating vertex are webbed trees.

We also consider the game on bipartite graphs, hypercubes, unicyclic graphs, large k-partite graphs, and graphs with small domination number. This is joint work with Jane V. Butterfield, Gregory J. Puleo, Clifford D. Smyth, Douglas B. West, and Reza Zamani.

Dan Cranston is an invited speaker of the Student Colloquium Committee, which is funded by the VIGRE grant.

Tuesday, October 11, 2011

Posted October 11, 2011

3:40 pm – 4:30 pm Lockett 240

Jerome W. Hoffman, Mathematics Department, LSU
Galois representations and Humbert surfaces

Monday, October 17, 2011

Posted October 3, 2011

9:00 am – 10:30 am Johnston Hall 338

Luke Owens, Automated Trading Desk
Who Wants to be a Millionaire? A Path to Riches Through A Career in Quantitative Finance

Posted September 30, 2011

3:40 pm – 4:30 pm Lockett 233

Hanna Terletska, Department of Physics and Astronomy, LSU and Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory
Towards a multiscale formalism for disordered systems

Posted September 27, 2011

4:30 pm Keisler Lounge (Room 321 Lockett)

Actuarial Club Meeting

Wednesday, October 19, 2011

Posted August 31, 2011
Last modified September 22, 2011

3:30 pm – 4:30 pm 338 Johnston Hall

William Hager, University of Florida
Numerical Techniques In Optimal Control

Abstract: The talk gives an overview of some discrete approximation techniques that have been developed for optimal control problems. We focus in particular on Runge-Kutta discretizations and more recent work on pseudospectral schemes. The numerical paradigm consistency + stability => convergence is explained in the context of these discretizations. Gradient techniques for solving the discretized problems will also be discussed. Additional details can be found at http://www.cct.lsu.edu/events/talks/584

Posted September 11, 2011

3:40 pm – 4:30 pm Lockett 233

Eamonn Tweedy, Department of Mathematics, Rice University
Virtual Seminar: A filtration on the Heegaard Floer chain complex of a double branched cover

Abstract: Seidel and Smith defined their fixed-point symplectic Khovanov cohomology theory for links in the 3-sphere. For the case of a knot K, they described how to define a particular filtration on their complex. Via an observation of Manolescu, this filtration induces a spectral sequence from the Seidel-Smith theory to the Heegaard Floer hat theory for the double cover of the 3-sphere branched along K. This spectral sequence is itself a knot invariant, and has some nice properties. We also discuss how the construction leads to a family of rational-valued knot invariants.

Posted September 26, 2011
Last modified October 17, 2011

3:40 pm – 4:30 pm Lockett 244

Angela Pasquale, University of Metz and CNRS
Reductive dual pairs and orbital integrals on symplectic spaces

Abstract: We present a Weyl integration formula on the symplectic space for a real reductive dual pair. The formula is motivated by the study of the regularity properties of the intertwining distributions of irreducible admissible representations occurring in the Howe correspondence of a reductive dual pair. This is a joint work with M. McKee and T. Przebinda.

Thursday, October 20, 2011

Posted August 23, 2011
Last modified September 30, 2011

3:40 pm – 4:30 pm Lockett 284

Angela Pasquale, University of Metz and CNRS
Ramanujan's Master Theorem for Riemannian symmetric spaces

The abstract for this talk can be found at www.math.lsu.edu/~morales/colloquium/pasquale.pdf

Monday, October 24, 2011

Posted August 23, 2011
Last modified October 23, 2011

3:40 pm – 4:30 pm Lockett 233

Rustum Choksi, Department of Mathematics and Statistics, McGill University, Montréal, Canada
Self-assembly of Diblock Copolymers and Variational Problems with Long-Range Interactions

Energy-driven pattern formation induced by competing short and long-range interactions is common in many physical systems. This talk will address mathematical and physical paradigms for periodic pattern formation induced by these energetic competitions. The mathematical paradigm consists of nonlocal perturbations to the well-studied Cahn-Hilliard and isoperimetric problems. The physical paradigm is self-assembly of diblock copolymers. Via a combination of analysis and numerics, I will address the structure of minimizers across the phase diagram.

Tuesday, October 25, 2011

Posted October 3, 2011

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Johnston Hall 338

Georgios Veronis, Louisiana State University
Plasmonics For Controlling Light At The Nanoscale: Cavity And Slow-Light Enhanced Devices, And The Effect Of Disorder

Posted September 8, 2011
Last modified May 1, 2021

3:40 pm – 4:30 pm Lockett 240

Amber Russell, Mathematics Department, LSU
Graham's variety and perverse sheaves on the nilpotent cone: Results in type $A_n$

In recent work, Graham has constructed a variety with a map to the nilpotent cone that is similar to the Springer resolution. However, Graham's map differs from the Springer resolution in that it is not in general an isomorphism over the principal orbit, but rather the universal covering map. This map gives rise to a certain semisimple perverse sheaf on the nilpotent cone. In this talk, we discuss the problem of describing the summands of this perverse sheaf. For type $A$, a key tool is a description of the affine paving of Springer fibers given by Tymoczko that lends itself nicely to understanding the fibers of Graham's map.

Wednesday, October 26, 2011

Posted September 8, 2011
Last modified September 22, 2011

3:40 pm – 4:30 pm Lockett 233

Effie Kalfagianni, Michigan State University
Virtual Seminar: Polyhedral decompositions, essential surfaces and colored Jones polynomials.

Abstract: We generalize the checkerboard decompositions of alternating knots and links: For A- or B-adequate diagrams, we show that the checkerboard knot surfaces are incompressible, and we obtain an ideal polyhedral decomposition of their complement. In the talk I will describe these decompositions and give some of the applications, which include fibering knot criteria and relations between hyperbolic volume and colored Jones polynomials. The talk will be based on joint work with Dave Futer (Temple) and Jessica Purcell (BYU).

Posted October 23, 2011

3:40 pm – 4:30 pm Lockett 244

Benjamin Harris, LSU
Limit Formulas for Reductive Lie Groups.

Abstract: Limit formulas for reductive Lie groups were first studied by Gelfand-Graev and Harish-Chandra in connection with the Plancherel formula for reductive Lie groups. Limit formulas for nilpotent orbits are closely related to character theory and invariants of irreducible representations. In this talk, we will discuss some of the things that are known and some of the things that are not known about limit formulas for reductive Lie groups.

Thursday, October 27, 2011

Posted September 13, 2011
Last modified October 24, 2011

3:40 pm – 4:30 pm 235 Lockett

Effie Kalfagianni, Michigan State University
Geometric and combinatorial knot invariants

Abstract: It has been known since the 80's that knot complements admit geometric decompositions and that the class of hyperbolic knots is the richest class of knots. In practice, knots are often given in terms of combinatorial topological descriptions, and it is both natural to seek for ways to deduce geometric information from these descriptions. On the other hand, in the last couple of decades ideas from physics have led to powerful and subtle combinatorial knot invariants such as the Jones knot polynomials. Understanding the relation of the combinatorial knot descriptions and invariants to the detailed structures coming from the geometric picture is an important goal of low dimensional topology that received particular attention in recent years.

In this talk I will survey some conjectured and some established such relations.

Friday, October 28, 2011

Posted September 16, 2011
Last modified September 20, 2011

3:30 pm – 4:30 pm Locket 243

John Rhodes, University of California at Berkeley
Representing Matroids and Hereditary Collections by Boolean Matrices

We give the definition of representing a hereditary collection of sets on a finite set by a Boolean matrix and then prove all matroids have Boolean representations. We then talk about what other hereditary collections have Boolean representations. Though this research is new, the methods are elementary and should be understood by all. Joint work with Zur Izhakian.

Tuesday, November 1, 2011

Posted October 3, 2011
Last modified November 29, 2022

3:30 pm – 4:30 pm Johnston Hall 338

Jintao Cui, Institute for Mathematics and Its Applications
HDG Methods For The Vorticity-Velocity-Pressure Formulation Of The Stokes Problem

In this talk we discuss the hybridizable discontinuous Galerkin (HDG) method for solving the vorticity-velocity-pressure formulation of the three-dimensional Stokes equations of incompressible fluid flow. The idea of the a priori error analysis consists in estimating a projection of the errors that is tailored to the very structure of the numerical traces of the method. We show that the approximated vorticity and pressure, which are polynomials of degree k, converge with order k + 1/2 in L2-norm for any k ≥ 0. Moreover, the approximated velocity converges with order k + 1. This is joint work with Bernardo Cockburn from University of Minnesota. Further details at http://www.cct.lsu.edu/events/talks/579

Wednesday, November 2, 2011

Posted August 30, 2011

1:30 pm – 2:30 pm Conference Room - Lockett 301D

Final Event for MS Comprehensive Exam

Mathematics MS applicants for December 2011 graduation must meet with the following committee members:
William Adkins (Chair)
Leonard Richardson
Padmanaban Sundar
in order to complete the process that began with passing the written Comprehensive Examination at the MS Qualifying Level. Apply to the Graduate School to have the Final Exam at this date with the listed committee.

Posted October 12, 2011
Last modified March 2, 2021

3:40 pm – 4:30 pm Lockett 244

Boris Rubin, Louisiana State University
Philomena Mader's Inversion Formulas for Radon Transforms

In 1927 Philomena Mader derived elegant inversion formulas for the hyperplane Radon transform on $R^n$. These formulas differ from the original ones by Johann Radon (1917) and do not need Abel's integral equation or fractional powers of the minus-Laplacian. Surprisingly, these remarkable formulas have been forgotten. We generalize Mader's formulas to totally geodesic Radon transforms in any dimension on arbitrary constant curvature space. This is a joint work with Yuri Antipov.

Posted September 23, 2011
Last modified October 25, 2011

3:40 pm – 4:30 pm Lockett 233

Adam Lowrance, Department of Mathematics, Vassar College
Virtual Seminar: "A categorification of the Tutte polynomial"

Abstract: The Tutte polynomial is a graph and matroid polynomial which has a close relationship with the Jones polynomial. We construct a categorification of the Tutte polynomial for graphs and matroids. Our construction is modeled after the construction of odd Khovanov homology, which is a categorification of the Jones polynomial developed by Ozsvath, Rasmussen, and Szabo. Many properties of the Tutte polynomial lift to expected properties of our categorification. The deletion-contraction relation of the Tutte polynomial becomes an exact triangle in the categorification, and the formula for the Tutte polynomial of the dual matroid has an analog for our categorification. We will also present examples and an application that leads to an invariant of (mutation classes of) alternating links.

Friday, November 4, 2011

Posted October 31, 2011
Last modified November 2, 2011

Committee Meeting

8:30 am Lockett 301D (Conference Room)

Executive Committee Meeting

Agenda: Formulating a departmental Graduate Faculty policy.

Posted October 28, 2011
Last modified October 31, 2011

3:40 pm – 4:30 pm Lockett 243

Karl Mahlburg, Department of Mathematics, LSU
Enumeration of Non-crossing pairings on bit strings

A non-crossing pairing on a bit string is a matching of 1s and 0s in the string with the property that the pairing diagram has no crossings. This enumeration problem arises when calculating moments in the theory of random matrices and free probability, and the goal is to obtain useful formulas and/or asymptotic estimates. The main results include explicit formulas in the "symmetric" case where each run of 1s and 0s has the same length, as well as upper and lower bounds that are uniform across all words of fixed length and fixed number of runs. The results are proved through bijective mappings that relate the set of non-crossing pairings into certain generalized "Catalan" structures that include labelled trees and lattice paths.

Monday, November 7, 2011

Posted September 12, 2011
Last modified March 2, 2022

3:30 pm 233 Lockett

Itai Shafrir, Department of Mathematics, Technion - Israel Institute of Technology
On the distance between homotopy classes of maps taking values in manifolds

It is well known that for $p ≥ m$ the degree of maps in $W^{1,p}(S^m, S^m)$ is well defined and one has the following decomposition of this space as a disjoint union of homotopy classes: $W^{1,p}(S^m, S^m) = \bigcup_{d\in\mathbb{Z}}\mathcal{E}_d$. It is natural then to study the distance $δ_p(d_1, d_2)$ between each pair of distinct homotopy classes $\mathcal{E}_{d_1}$ and $\mathcal{E}_{d_2}$, defined by \[ δ_p^p(d_1, d_2) = \inf\bigl\{ \int_{S^m} |∇(u_1 − u_2)|^p : u_1 \in \mathcal{E}_{d_1},\ u_2\in \mathcal{E}_{d_2} \bigr\}. \] In the one dimensional case, $m = 1$, we find that the distance is given explicitly by the formula $δ_p(d_1, d_2) = \tfrac{2^{1+1/p}\,|d_2−d_1|}{π^{1−1/p}}$.

In higher dimensions, $m ≥ 2$, it turns out that in the limiting case $p = m$, the distance between the homotopy classes is always zero. On the other hand, when $p > m$, for $d_1 \ne d_2$ the distance is positive, but independent of $d_1$ and $d_2$, i.e., $δ_p(d_1, d_2) = c(m, p)$. Here $c(m, p)$ is a positive constant that had already been computed explicitly by Talenti (for $m = 2$) and Cianchi (for any $m$) in the context of Sobolev-type inequalities on spheres.

This talk is based on a work in progress with Shay Levy and on a earlier work with Jacob Rubinstein.

Posted November 7, 2011
Last modified February 20, 2022

3:40 pm – 4:30 pm Lockett 240

Benedykt Szozda, Department of Mathematics, LSU
Anticipative Stochastic Integral and Near-Martingales

In this talk, we present a new approach to stochastic integration based on the concept of instantaneous independence introduced by Ayed and Kuo in 2008. We compare the new integral to well known results by Itô, Hitsuda, and Skorokhod. We also discuss some properties of the instantly independent processes, the new integral and the stochastic processes associated with the new integral. Among the properties mentioned above are the Itô formula, isometry property and a near-martingale property that arises naturally in the study of the new integral. We also present numerous examples and evaluation formulas for the new integral. This is joint work with Hui-Hsiung Kuo and Anuwat Sae-Tang.

Tuesday, November 8, 2011

Posted November 1, 2011

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:30 pm 338 Johnston Hall

Xiaoliang Wan, Louisiana State University
Minimum Action Method And Dynamical Systems

In this work, we present an adaptive high-order minimum action method for dynamical systems perturbed by small noise. We use the hp finite element method to approximate the minimal action path and nonlinear conjugate gradient method to solve the optimization problem given by the Freidlin-Wentzell least action principle. The gradient of the discrete action functional is obtained through the functional derivative and the moving mesh technique is employed to enhance the approximation accuracy. Numerical examples are given to demonstrate the efficiency and accuracy of the proposed numerical method. We also discuss the application of the minimum action method to study the structure of the phase space and some open issues from the numerical point of view.

Wednesday, November 9, 2011

Posted October 25, 2011
Last modified October 26, 2011

1:30 pm – 2:30 pm Lockett 235

Loredana Lanzani, University of Arkansas
Practical Uses of Complex Analysis

This talk is primarily aimed at undergraduates.

In this talk I will quickly introduce the fundamental notion of conformal mapping for a planar (2-D) domain, which is one of the main ideas behind the classical subject of (one variable) complex analysis.

I will then proceed to present some of the applications of conformal mappings to real-life situations, including: cartography; airplane wing design (transonic flow); taxonomy; art (in particular, the work of M. C. Escher). No previous knowledge of complex analysis is required.

There will be a light lunch in the Keisler Lounge from 1:00-1:30.

Posted October 25, 2011
Last modified October 26, 2011

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:30 pm Lockett 235

Loredana Lanzani, University of Arkansas
Several Complex Variables: the many joys (and occasional pains) of multivariable complex calculus

This talk is primarily aimed at graduate students.

In this talk I will discuss some of the main ideas behind the (relatively recent) research area of Several Complex Variables, which in many ways is strikingly different from its one-variable counterpart -- that is the classical (and much older) subject of complex analysis. A basic knowledge of multivariable calculus will be the main prerequisite for this talk.

There will be refreshments in the Keisler Lounge from 3:00-3:30.

Posted November 4, 2011

3:40 pm – 4:30 pm In R^4

Scott Baldridge, Louisiana State University
Knotted embedded tori in R^4

Abstract: One of the barriers to studying knotted surfaces in R^4 has been that there are few ways to represent them that lead to powerful yet easy-to-compute invariants. In this talk we will describe a new way to represent 2-dimensional knotted tori in R^4 using 4n half-integer valued points in the cube [0,n]^4. We will illustrate why the construction represents knotted spun tori and discuss the ramifications of the representation to topics such as Heegaard Floer Homology and Contact Homology.

Friday, November 11, 2011

Posted August 29, 2011
Last modified February 2, 2022

3:30 pm – 4:30 pm 233 Lockett

Leonid V. Berlyand, Department of Mathematics, Pennsylvania State University
Modeling of collective swimming of bacteria.

Bacteria are the most abundant organisms on Earth and they significantly influence carbon cycling and sequestration, decomposition of biomass, and transformation of contaminants in the environment. This motivates our study of the basic principles of bacterial behavior and its control. We have conducted analytical, numerical and experimental studies of suspensions of swimming bacteria. In particular, our studies reveal that active swimming of bacteria drastically alters the material properties of the suspension: the experiments with bacterial suspensions confined in thin films indicate a 7-fold reduction of the effective viscosity and a 10-fold increase of the effective diffusivity of the oxygen and other constituents of the suspending fluid. The principal mechanism behind these unique macroscopic properties is self-organization of the bacteria at the microscopic level–a multiscale phenomenon. Understanding the mechanism of self-organization in general is a fundamental issue in the study of biological and inanimate system. Our work in this area includes

• Numerical modeling. Bacteria are modeled as self-propelled point force dipoles subject to two types of forces: hydrodynamic interactions with the surrounding fluid and excluded volume interactions with other bacteria modeled by a Lennard-Jones-type potential. This model, allowing for numerical simulations of a large number of particles, is implemented on the Graphical Processing Units (GPU), and is in agreement with experiments.

• Analytical study of dilute suspensions. We introduced a model for swimming bacteria and obtained explicit asymptotic formula for the effective viscosity in terms of known physical parameters. This formula is compared with that derived in our PDE model for a dilute suspension of prolate spheroids driven by a stochastic torque, which models random reorientation of bacteria (“tumbling”). It is shown that the steady-state probability distributions of single particle configurations are identical for the dilute and semi-dilute models in the limiting case of particles becoming spheres. Thus, a deterministic system incorporating pairwise hydrodynamic interactions and excluded volume constraints behaves as a system with a random stochastic torque. This phenomenon of stochasticity arising from a deterministic system is referred to as self-induced noise.

• Kinetic collisional model—work in progress. We seek to capture a phase transition in the bacterial suspension–an appearance of correlations and local preferential alignment with an increase of concentration. Collisions of the bacteria, ignored in most of the previous works, play an important role in this study.

Collaborators: PSU students S. Ryan and B. Haines, and DOE scientists I. Aronson and D. Karpeev (both Argonne Nat. Lab)

Tuesday, November 15, 2011

Posted November 1, 2011
Last modified November 29, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 338 Johnston Hall

Shawn Walker, LSU
Optimization Of Flapping Based Locomotion

Locomotion at the macro-scale is important in biology and industrial applications, such as for understanding the fundamentals of flight to enable design of artificial locomotors. We present an analysis of a fluid-structure interaction problem that models a rigid flapping body at intermediate Reynolds number (in 2-D). In particular, we have an energy estimate and a schur-complement method for solving the coupled system, which is valid for all mass densities of the body (even zero). We also describe an optimal control problem for the time-dependent actuation profile that drives the forward motion of the body. The actuation consists of a vertical velocity control attached to a pivot point of an elongated rigid body, which is allowed to rotate and is affected by a torsional spring; the spring acts as an elastic recoil. We then solve the time-dependent, PDE-constrained optimization problem (with appropriate constraints). Optimization results for certain parameter variations (relative mass density, spring constant, etc) will be shown. This work is joint with Michael Shelley at NYU. (Refreshments at 3pm. Further details at http://www.cct.lsu.edu/events/talks/596 )

Posted August 30, 2011

3:40 pm – 4:30 pm Lockett 240

Christopher Bremer, Mathematics Department, LSU
TBA

Wednesday, November 16, 2011

Posted September 23, 2011
Last modified November 3, 2011

3:40 pm – 4:30 pm Lockett 233

Heather Russell, USC
Virtual Seminar: Springer varieties and spider webs

Abstract: Springer varieties are certain flag varieties classically studied because their cohomology rings are Weyl group representations. Khovanov, Stroppel-Webster, Cautis-Kamnitzer, Seidel-Smith and others have studied the connections of Springer varieties to knot theory. In past work we built on ideas of Khovanov and Stroppel-Webster to give a diagrammatic framework enabling the study of Springer representations as well as the topology of certain Springer varieties via sl_2 webs. We will discuss recent work extending some of these results to other classes of Springer varieties using sl_3 webs.

Posted September 26, 2011
Last modified October 28, 2011

3:40 pm – 4:30 pm Lockett 244

Gestur Olafsson, Mathematics Department, LSU
Limits of spherical representations and spherical functions for inductive limits of compact symmetric spaces

Abstract: Spherical representations and functions are the building blocks for harmonic analysis on Riemannian symmetric spaces. We will give a short overview of injective limits of compact symmetric spaces $G_\infty/K_\infty = \varinjlim G_n/K_n$ and limits of spherical representations. We will then describe what happens to the limits of the related spherical $\varphi_n (x) = \langle e_n, \pi_n (x)e_n\rangle$ where $e_n$ is a $K_n$--fixed unit vector for $\pi_n$. The main result is that the limit $\lim_{n\to \infty} \varphi_n(x)$ defines a spherical function on $G_\infty /K_\infty$ if and only if the rank of $G_n/K_n$ is bounded.

Posted November 16, 2011

6:00 pm James E. Keisler Lounge (room 321 Lockett)

Guest: Paul Richmond from the Louisiana Legislative Auditor's Office

ASA president, Chen Liu, writes, \"Paul Richmond who works as a manager of Actuarial services at Louisiana legislator\'s auditor\'s office, will give us insights about the actuary advisory in Louisiana, He provides various actuarial consulting to legislature and public retirement system in Louisiana. There will be chat and question time followed.
It promises to be a good meeting and there will be refreshment served.\"

Friday, November 18, 2011

Posted November 16, 2011

2:00 pm Lockett 6

Faculty Meeting to discuss departmental graduate faculty policy

Posted November 11, 2011

3:40 pm – 4:30 pm Locket 243

Clifford Smyth, University of North Carolina at Greensboro
Correlation inequalities and the BKR inequality

Correlation inequalities are theorems giving conditions on when certain classes of events (or random variables) are positively (or negatively) correlated. Perhaps one of the most well-known is the FKG inequality which asserts the positive correlation of increasing random variables on finite distributive lattices as long as the probability measure obeys the positive lattice condition. The BKR inequality is another well-known correlation-type result with important applications in percolation. The BKR inequality is phrased on product spaces but recently we have found a generalization to finite distributive lattices.

Monday, November 21, 2011

Posted November 21, 2011

3:40 pm Lockett 240

Benedykt Szozda, Department of Mathematics, LSU
Anticipative Ito formula and linear Stochastic Differential Equations with anticipating initial conditions

Abstract: In this talk we present several Ito formulas for the new stochastic integral of instantly independent and adapted processes. We give numerous examples and apply the new Ito formula to solve stochastic differential equation with anticipating initial condition. Our approach is based on results of Ayed and Kuo. This is a joint work with Hui-Hsiung Kuo and Anuwat Sae-Tang.

Posted November 7, 2011

Algebra and Number Theory Seminar Questions or comments?

4:30 pm – 6:30 pm Lockett 321, Keisler Lounge

Actuarial Student Club

Tuesday, November 22, 2011

Posted November 21, 2011

3:40 pm – 4:30 pm Lockett 240

Christopher Bremer, Mathematics Department, LSU
Flat $G$-bundles and regular strata

Let $G$ be a reductive group over a Laurent series (or $p$-adic) field. Broadly speaking, a fundamental stratum is a pair $(K, b)$ consisting of a ``compact\'\' subgroup $K < G$ and a character $b$ of $K$ that satisfies a non-degeneracy condition. The theory of fundamental strata was originally developed by Bushnell, Howe, Moy, and Prasad to study wildly ramified representations of $p$-adic groups, and this theory plays an important role in the parameterization of admissible GL_n representations. In this talk I will describe recent work with Sage on applications of fundamental strata to the study of flat $G$-bundles. One of our primary innovations is the notion of a ``regular\'\' stratum, which satisfies a graded version of regular semi-simplicity. I will first discuss results on the Deligne-Simpson problem and isomonodromic deformations of irregular singular flat GL_n bundles, and then indicate how this theory generalizes to the reductive case.

Monday, November 28, 2011

Posted November 23, 2011

Algebra and Number Theory Seminar Questions or comments?

1:40 pm – 3:30 pm Lockett 240

Pramod Achar, Mathematics Department, LSU
Introduction to the Hitchin fibration, Part I

I will repeat a talk given by Olivier Schiffmann at the Université de Caen on November 15, 2011, in preparation for the virtual seminar on November 29. Please contact me for lecture notes.

Tuesday, November 29, 2011

Posted November 23, 2011

Algebra and Number Theory Seminar Questions or comments?

8:45 am – 10:45 am Lockett 233

Olivier Schiffmann, Université Paris-Sud
Introduction to the Hitchin fibration, Part II

This will be a virtual seminar, joint with the \"Groupe de travail en théorie de représentations\" at the Université de Caen.

Posted November 1, 2011

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 338 Johnston Hall

Hongchao Zhang, Louisiana State University
An Adaptive Preconditioned Nonlinear Conjugate Gradient Method With Limited Memory

Nonlinear conjugate gradient methods are an important class of methods for solving large-scale unconstrained nonlinear optimization. However, their performance is often severely affected when the problem is very ill-conditioned. In the talk, efficient techniques for adaptively preconditioning the nonlinear conjugate method in the subspace spanned by a small number of previous searching directions will be discussed. The new method could take advantages of both nonlinear conjugate methods and limited-memory BFGS quasi-Newton methods, and achieves significant performance improvement compared with CG\\_DESCENT conjugate gradient method and L-BFGS quasi-Newton method. (Refreshments at 3pm. Further details at http://www.cct.lsu.edu/events/talks/592 )

Posted November 28, 2011

3:40 pm – 4:30 pm Lockett Hall 240

Jorge Morales, Mathematics Department, LSU
Generic polynomials and Frobenius modules

I will begin by giving a brief historical introduction to the classical Noether problem on fields of invariants of finite groups and its relation with the inverse Galois problem. Then I will define the notion of generic polynomial and discuss some modern approaches to their construction, in particular the use of Matzat\'s \"lower bound\" theorem on Frobenius modules for the explicit construction of generic polynomials in characteristic p for groups of rational points of algebraic groups. This is (developing) joint work with REU student D. Tseng (MIT); it will be accessible to everyone.

Wednesday, November 30, 2011

Posted October 31, 2011
Last modified November 4, 2011

3:40 pm – 4:30 pm Lockett 233

Ben McCarty, LSU
Virtual Seminar: "On the rotation class of knotted Legendrian tori in R^5"

Abstract Legendrian knots in R^3 have been studied extensively in recent years. However, much less is known about Legendrian knots in higher dimensions. We present Lagrangian hypercube diagrams as a convenient tool to study knotted Legendrian tori in R^5 with the standard contact structure. In particular, we describe an easy way to compute a Legendrian invariant, the rotation class, from a Lagrangian hypercube diagram, and discuss applications to contact homology. (Joint work with S. Baldridge)

Thursday, December 1, 2011

Posted October 3, 2011
Last modified May 8, 2021

Controls Seminar

2:00 pm 117 Electrical Engineering Building

Aleksandra Gruszka, LSU Department of Mathematics PhD Student of Prof. Malisoff
Tracking and Robustness Analysis for UAVs with Bounded Feedbacks

Information on ECE Seminar Web Site.

Wednesday, December 7, 2011

Posted November 14, 2011

Party

12:00 pm 321 Lockett Hall, Keisler Lounge

Annual Holiday Party

This is a pot-luck luncheon, with the department supplying the turkeys. Side dishes, such as vegetables, desserts, or other meats or non-meats, would very much be appreciated, to make this a complete meal and hopefully, supply plenty for all to enjoy. Please feel free to share a dish from your native country. The sign-up list will be posted on the front door of Lockett 303. Thank you and happy holidays!

Friday, December 9, 2011

Posted November 30, 2011
Last modified March 2, 2022

3:40 pm – 4:30 pm Lockett 233

Michel Jabbour, University of Kentucky
On step dynamics and related morphological instabilities during epitaxial growth of thin crystalline films.

Thin crystalline films are often bounded by surfaces consisting of flat terraces separated by atomic steps. During epitaxial growth in the step-flow regime, adsorbed atoms (from a vapor or beams) diffuse on the terraces until they attach to steps, causing them to advance. For a train of steps, two modes of morphological instability can occur: bunching, which leads to regions of high step density separated by wide terraces, and meandering, whereby steps become wavy. Experiments indicate that bunching and meandering can coexist on some stepped surfaces, in contrast to the predictions of the standard Burton–Cabrera–Frank (BCF) model. In this talk, I will review the BCF theory and present a thermodynamically consistent (TC) generalization of it that resolves this apparent paradox. In particular, I will show that step bunching and meandering can occur simultaneously, provided that the adatom equilibrium coverage exceeds a critical value. I will also compare the TC model with various extensions of the BCF paradigm that attempt to reconcile theory with experiments.

Monday, January 9, 2012

Posted November 7, 2011
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 285

Comprehensive / PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, January 11, 2012

Posted November 7, 2011
Last modified December 13, 2022

1:00 pm – 4:00 pm 285 Lockett

Comprehensive / PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Posted December 21, 2011

3:40 pm – 4:30 pm Lockett 233

Benjamin Himpel, Centre for Quantum Geometry of Moduli Spaces, Aarhus, Denmark
tba

Friday, January 13, 2012

Posted November 7, 2011
Last modified December 13, 2022

1:00 pm – 4:00 pm 285 Lockett

Comprehensive / PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Thursday, January 19, 2012

Posted October 21, 2011
Last modified November 1, 2011

3:30 pm – 4:30 pm 338 Johnston Hall

Chi-Wang Shu, Brown University
Maximum-Principle-Satisfying And Positivity-Preserving High Order Discontinuous Galerkin And Finite Volume Schemes

When solving convection dominated partial differential equations, such as the incompressible and compressible Euler equations in fluid dynamics, it is a challenge to design numerical schemes which are both strongly stable and high order accurate, especially when the solution contains sharp gradient regions or discontinuities. Previous schemes satisfying strict maximum principle for scalar equations and positivity-preserving for systems are mostly first order, or at most second order accurate. We construct uniformly high order accurate discontinuous Galerkin (DG) and weighted essentially non-oscillatory (WENO) finite volume (FV) schemes satisfying a strict maximum principle for scalar conservation laws and passive convection in incompressible flows, and positivity preserving for density and pressure for compressible Euler equations. One remarkable property of our approach is that it is straightforward to extend the method to two and higher dimensions on arbitrary triangulations. We will also emphasize recent developments including arbitrary equations of state, source terms, integral terms, shallow water equations, high order accurate finite difference positivity preserving schemes for Euler equations, and a special non-standard positivity preserving high order finite volume scheme for convection-diffusion equations. Numerical tests demonstrating the good performance of the scheme will be reported. This is a joint work with Xiangxiong Zhang. (Additional details at http://www.cct.lsu.edu/events/talks/591)

Friday, January 20, 2012

Posted December 5, 2011

9:00 am – 10:30 am 338 Johnston Hall

A Conversation with Carol Woodward

This is breakfast event with Carol S. Woodward (Lawrence Livermore National Laboratory). Dr. Woodward received a B.S. in Mathematics from LSU in 1991 and a Ph.D. in Computational Science and Engineering from Rice University in 1996. Since June 1996, she has been a computational scientist with the Center for Applied Scientific Computing at Lawrence Livermore National Laboratory. This event is hosted by the SIAM Student Chapter and the VIGRE Program.

Posted September 22, 2011
Last modified September 17, 2021

1:00 pm – 4:00 pm Saturday, January 21, 2012 Louisiana State University

SCALA 2012 - Scientific Computing Around Louisiana

Wednesday, January 25, 2012

Posted January 11, 2012

3:40 pm – 4:30 pm Lockett 233

Yeonhee Jang, Hiroshima University
Virtual Seminar: Bridge presentations of links

Abstract: This talk will be devoted to introduce the speaker\'s works related to bridge presentations of links. In the first half of this talk, we introduce results on the classification or characterization of certain 3-bridge links and their 3-bridge presentations. In the last half, we introduce results on Cappell-Shaneson\'s question which asks whether the bridge numbers of links are equal to the minimal numbers of meridian generators of link groups.

Wednesday, February 1, 2012

Posted January 28, 2012
Last modified January 31, 2012

3:40 pm – 4:30 pm Lockett 233

Cody Armond, Department of Mathematics, LSU
"The colored Jones polynomial and adequate links"

Thursday, February 2, 2012

Posted December 5, 2011

3:30 pm – 4:30 pm 338 Johnston Hall

Ricardo Nochetto, University of Maryland
Modeling, Analysis And Computation Of Biomembranes

We present three models of biomembranes along with their numerical simulation. The first one is purely geometric since the equilibrium shapes are the minimizers of the Willmore (or bending) energy under area and volume constraints. The second model incorporates the effect of the inside (bulk) viscous incompressible fluid and leads to more physical dynamics. The third model describes the interaction of a director field with a membrane, giving rise to an induced spontaneous curvature. We propose a parametric finite element method for the discretization of these models and examine crucial numerical issues such as dealing with curvature and length constraints within a variational framework. We show several simulations describing the dynamics of purely geometric flows, membrane-fluid interaction, and the dramatic effect of defects of the director field on membrane shape. This work is joint with S. Bartels, A. Bonito, G. Dolzmann, M.S. Pauletti, and A. Raisch. Refreshments at 3pm. Further information at http://www.cct.lsu.edu/events/talks/600

Posted January 28, 2012
Last modified February 2, 2012

3:40 pm – 4:30 pm Lockett 277

David Vela-Vick, Columbia University
Contact structures, Legendrian and transverse knots, and Heegaard Floer homology

Abstract: The past decade has ushered in a number of major advances in the field of 3-dimensional contact geometry. Beginning with Ozsvath and Szabo's construction of an invariant of contact structures on closed 3-manifolds, a complex tapestry of generalizations and applications has emerged. In this talk, I plan to survey Heegaard Floer theory as it applies to the study of Legendrian and transverse knots. In doing so, I will discuss some surprising relationships between seemingly distinct specializations of this general theory.

Friday, February 3, 2012

Posted January 30, 2012

2:30 pm – 3:30 pm Lockett 239

Dennis Hall, Department of Mathematics, LSU Graduate Student
Unavoidable minors for connected 2-polymatroids.

Abstract: It is well known that, for any integer $n$ greater than one,
there is a number $r$ such that every $2$-connected simple graph with
at least $r$ edges has a minor isomorphic to an $n$-edge cycle or
$K_{2,n}$. This result was extended to matroids by Lov\\\'asz,
Schrijver, and Seymour who proved that every sufficiently large
connected matroid has an $n$-element circuit or an $n$-element
cocircuit as a minor. In this talk, we generalize these theorems by
providing an analogous result for connected $2$-polymatroids.

Monday, February 6, 2012

Posted January 31, 2012

3:40 pm – 4:30 pm Lockett 277

Jian Song, Rutgers University
Feynman-Kac formula

Abstract: In this talk, I will review the classical Feynman-Kac formula for partial differential equations (PDEs), and explain the Feynman-Kac formulas we have obtained for stochastic partial differential equations (SPDEs).

Tuesday, February 7, 2012

Posted February 5, 2012

3:30 pm – 4:30 pm 338 Johnston Hall

Tchavdar Marinov, Southern University at New Orleans
Solitary Wave Solutions As Inverse Problem

A special numerical technique has been developed for identification of solitary wave solutions of Boussinesq and Korteweg--de Vries equations. Stationary localized waves are considered in the frame moving to the right. The original ill-posed problem is transferred into a problem of the unknown coefficient from over-posed boundary data in which the trivial solution is excluded. The Method of Variational Imbedding is used for solving the inverse problem. The generalized sixth order Boussinesq equation is considered for illustrations. http://www.cct.lsu.edu/events/talks/605

Wednesday, February 8, 2012

Posted January 30, 2012
Last modified February 1, 2012

3:40 pm – 4:30 pm Lockett 244

Ricardo Estrada, Mathematics Department, LSU
Inversion Formulas for the Spherical Means in Constant Curvature Spaces

Abstract: This is a talk on recent work by Boris Rubin, Yuri Antipov and
Ricardo Estrada on inversion formulas for the spherical means. For details
see: arXiv:1107.5992

Monday, February 13, 2012

Posted February 1, 2012
Last modified February 7, 2012

LSU AWM Student Chapter LSU AWM Student Chapter Website

3:40 pm – 4:30 pm Lockett 277

Artem Pulemotov, University of Chicago
Geometric flows on manifolds with boundary

Abstract: Geometric flows are partial differential equations that describe evolutions of geometric objects. They are typically used to tackle problems in topology, mathematical physics, and several other fields. The canonical example of a geometric flow is the heat equation on a Riemannian manifold. In the first part of the talk, we will discuss the fundamental features of this equation. We will also speak about two estimates for its positive solutions on manifolds with boundary. A more contemporary example of a geometric flow is the Ricci flow for a Riemannian metric. It is mostly famous for its role in the proof of the Poincare conjecture. The second part of the talk will be devoted to the main features and the behavior of the Ricci flow on manifolds with boundary. Towards the end, we will give a brief overview of related problems.

Tuesday, February 14, 2012

Posted February 7, 2012

12:00 pm – 1:30 am Keisler Lounge, Lockett Hall

AWM Spring Welcome Event

Join us for pizza. Everyone is welcome! AWM@LSU webpage: https://www.math.lsu.edu/awm/

Posted February 6, 2012

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 277

Carl Mautner, Harvard University
Parity sheaves

One approach to Lie theory involves relating categories of representations to sheaves on singular algebraic varieties. This is advantageous in that sheaves can be studied locally. This technique has been quite successful in studying representations over fields of characteristic zero.

The usefulness of this approach often hinges on deep theorems about a class of objects called intersection cohomology sheaves. These theorems generalize classical results on the rational cohomology of smooth projective varieties.

One would like to be able to make use of this technique for representations over fields of positive characteristic. However, in this case, the theorems valid over characteristic zero no longer hold.

We consider a class of objects, parity sheaves, which tend to coincide with intersection cohomology sheaves in characteristic zero and have better behavior over fields of positive characteristic.

(Joint with D. Juteau and G. Williamson.)

Wednesday, February 15, 2012

Posted February 6, 2012
Last modified February 15, 2012

3:40 pm – 4:30 pm Lockett 244

Yongdo Lim, Kyungpook National University
Deterministic approaches to the Karcher mean on Hadamard spaces

Abstract: Means on positive matrices and operators have received considerable attention in recent years, particular multivariable and weighted means. Applications have arisen in a variety of areas: approximations, interpolation, filtering, estimation, and averaging, diffusion tensor-MRI, sensor networks, radar signal processing. It has become clear that geometric and metric notions are a vital tool, and the Cartan centroid (least squares mean) on non-positive curved metric spaces plays a key role in metric-based computational algorithms. We discuss some deterministic (i.e., probability-free) approaches to the Cartan centroid on Hadamard spaces.

Posted February 6, 2012

3:40 pm – 4:30 pm Lockett 233

Dan Rutherford, University of Arkansas
A combinatorial Legendrian knot DGA from generating families

Abstract: This is joint work with Brad Henry. A generating family for a Legendrian knot L in standard contact R^3 is a family of functions f_x whose critical values coincide with the front projection of L. Pushkar introduced combinatorial analogs of generating families which have become known as Morse complex sequences. In this talk, I will describe how to associate a differential graded algebra (DGA) to a Legendrian knot with chosen Morse complex sequence. In addition, I will discuss the geometric motivation from generating families and the relationship with the Chekanov-Eliashberg invariant.

Thursday, February 16, 2012

Posted January 31, 2012
Last modified February 7, 2012

3:40 pm – 4:30 pm Lockett 277

Betsy Stovall, University of California Los Angeles
Counteracting flatness with affine arclength measure

Abstract: There are many operators in harmonic analysis for which the curvature of some underlying manifold plays a significant role. We will discuss recent efforts to establish uniform estimates for such operators by compensating for degeneracies of curvature with an appropriate measure. We will focus on the case when the underlying manifolds are polynomial curves.

Friday, February 17, 2012

Posted February 13, 2012
Last modified February 15, 2012

2:30 pm – 3:30 pm Lockett 239

Daniel Guillot, Department of Mathematics, LSU Graduate Student
Coloring Graphs with Independent Crossings

There are many well known results regarding bounds for the chromatic number of a graph embedded in a particular surface. A related problem is considering graphs drawn on a surface with some crossings. Kral and Stacho showed that for planar graphs with independent crossings, the chromatic number is at most 5. We will consider graphs drawn on other surfaces and show that, with the possible exception of certain complete graphs, Heawood's number is the correct upper bound.

Wednesday, February 22, 2012

Posted January 25, 2012
Last modified March 3, 2021

VIGRE@LSU: Student Colloquium Questions or comments?

3:40 pm – 4:30 pm Lockett 244

Kubo Toshihisa, Oklahoma State University, Stillwater
Conformally Invariant systems of differential operators of non-Heisenberg parabolic type

The wave operator $\square$ in Minkowski space $\mathbf{R}^{3,1}$ is a classical example of a conformally invariant differential operator. The Lie algebra $\mathfrak{so}(4,2)$ acts on $\mathbf{R}^{3,1}$ via a multiplier representation $\sigma$. When acting on sections of an appropriate bundle over $\mathbf{R}^{3,1}$, the elements of $\mathfrak{so}(4,2)$ are symmetries of the wave operator $\square$; that is, for $X \in \mathfrak{so}(4,2)$, we have $$[\sigma(X), \square] = C(X) \square$$ with $C(X)$ a smooth function on $\mathbf{R}^{3,1}$.

The notion of conformal invariance for a differential operator appears implicitly and explicitly in the literature. The conformality of one operator has been generalized by Barchini-Kable-Zierau to systems of differential operators. Such systems yield homomorphisms between generalized Verma modules. In this talk we build such systems of first and second-order differential operators in the maximal non-Heisenberg parabolic setting. We also discuss the corresponding homomorphisms between generalized Verma modules.

Monday, February 27, 2012

Posted February 13, 2012
Last modified February 17, 2012

1:40 pm – 2:30 pm Lockett 112

Kevin Knudson, Florida University
Fujimoto Approximation

This talk is primarily aimed at undergraduates.

If I hand you a strip of paper and ask you to fold it in half, or fourths, or 128ths, you can do it very easily. But what if I ask you to fold it into fifths, or sevenths, or 31sts? In this talk I'll show you Fujimoto's approximation method for folding into nths, where n is any odd number. A surprising cast of mathematical characters will show up along the way - binary decimals, discrete dynamical systems, and primitive roots of unity modulo n.

There will be a light lunch in the Keisler lounge at 1:00pm preceding the talk.

Tuesday, February 28, 2012

Posted February 13, 2012
Last modified February 17, 2012

VIGRE@LSU: Student Colloquium Questions or comments?

11:40 am – 12:30 pm Himes 253

Kevin Knudson, Florida University
Topological Data Analysis

This talk is primarily aimed at graduate students.

In this talk I will introduce the concept of persistent homology, a method to use techniques from algebraic topology to find nonlinear structures in large data sets. Several examples will be discussed including the space of natural images (analysis due to Carlsson, et. al.) and data sets built from human speech signals (joint with K. Brown). No detailed knowledge of algebraic topology will be assumed.

There will be refreshments in the Keisler lounge at 11:00am preceding the talk.

Posted February 20, 2012
Last modified February 21, 2012

3:40 pm – 4:30 pm Lockett 277

Ling Long, Iowa State University
The arithmetic of modular forms for noncongruence subgroups

Abstract: Among all finite index subgroups of the modular group, majority of them are noncongruence, i.e. they cannot be described in terms of congruence relations. Compared to the classical theory of congruence modular forms, modular forms for noncongruence subgroups are more mysterious due to the lack of efficient Hecke theory. However, noncongruence modular forms exhibit some remarkable properties and are closely related to many topics in number theory. In this talk, we will introduce these functions and discuss some recent developments in this area. In particular, we will consider Galois representations attached to noncongruence modular forms constructed by Tony Scholl which are generalizations of Deligne's Galois representations attached to classical Hecke eigenforms. We will prove under special circumstances that these Scholl representations are automorphic in the sense that their L-functions agree with the L-functions of automorphic forms on reductive groups and then give some applications of such automorphic results.

Wednesday, February 29, 2012

Posted February 15, 2012

3:40 pm – 4:30 pm Lockett 244

Angela Pasquale, University of Metz and CNRS
Estimates for the hypergeometric functions associated with root systems

Friday, March 2, 2012

Posted February 27, 2012
Last modified February 29, 2012

2:40 pm – 3:30 pm Lockett 239

Jesse Taylor, Department of Mathematics, LSU Graduate Student
On a Class of Nearly Binary Matroids.

One of the most widely known excluded-minor characterizations of matroids is Tutte's characterization of the class of binary matroids. In this presentation, we look at a class of matroids which is nearly binary. Specifically, we give an excluded-minor characterization for the class of matroids M in which M\\e or M/e is binary for all e in E(M).

Monday, March 5, 2012

Posted February 29, 2012
Last modified March 5, 2012

4:30 pm Lockett 277

Meeting to discus hiring an associate professor

Tuesday, March 6, 2012

Posted March 5, 2012
Last modified March 2, 2021

CCT Lecture Events organized by the LSU Center for Computation and Technology

3:30 pm 338 Johnston Hall

Haijun Yu, Chinese Academy of Sciences
Chebyshev Sparse Grid Mehod for High-dimensional PDEs

Posted March 5, 2012

3:30 pm – 4:30 pm 338 Johnston Hall

Haijun Yu, Institute of Computational Mathematics, Chinese Academy of Sciences
Chebyshev Sparse Grid Method for High-dimensional PDEs

Sparse grid is a special discretization for high-dimensional problems.
It was first introduced by S.A. Smolyak in 1960s for the integration
and interpolation of tensor product functions. During the 1990s, C.
Zenger et al. extended it to solve high-dimensional PDEs. The commonly
used bases are Fourier bases for periodic problems and linear finite
element bases for non-periodic problems. In this talk, we introduce
Chebyshev sparse grid method for solving non-periodic PDEs and apply it
to solve the electronic Schrodinger equation.

Thursday, March 8, 2012

Posted February 27, 2012
Last modified March 5, 2012

3:40 pm – 4:30 pm Lockett 277

Christopher Bremer, Mathematics Department, LSU
A new perspective on flat G-bundles and the Stokes phenomenon

Let G/C be a reductive algebraic group and let X/C be a smooth (not necessarily compact) algebraic curve. Flat G-bundles on X are a natural generalization of differential equations with algebraic coefficients, where the latter are viewed as vector bundles (having structure group GL_n) equipped with an integrable connection that is meromorphic at infinity. When the connection has an irregular singular point, the asymptotic series of a fundamental solution jumps discontinuously as it is continued across sectors in a neighborhood of that point. This behavior is known as the Stokes phenomenon. The "jumps" are encoded by elements of the group G, so one might think of the Stokes data as being an enhancement of the monodromy representation associated to a meromorphic differential equation.
The wild ramification case of the geometric Langlands conjecture suggests that there should be a natural correspondence between Stokes data arising from the irregular monodromy map, and representation theoretic data associated to the Langlands dual of the loop group. I will discuss a new approach (based on joint work with D. Sage) to the study of irregular flat G-bundles, inspired by methods from p-adic representation theory. Specifically, we have developed a geometric version of the Moy-Prasad theory of fundamental strata (aka minimal K-types). In this talk I will explain how the theory of fundamental strata applies to the study of moduli spaces of flat G-bundles, allowing one to significantly generalize results of Boalch, Jimbo et al., and others on the Stokes map and the irregular isomonodromy equations.

Posted February 6, 2012

4:45 pm Lockett 277

Meeting of Associate and Full Professors (third-year review)

Tuesday, March 13, 2012

Posted December 5, 2011
Last modified March 5, 2012

3:30 pm – 4:30 pm 338 Johnston Hall

Guang Lin, Pacific Northwest National Laboratory
Uncertainty Quantification Algorithms and Applications for High Dimensional Stochastic PDE Systems

Experience suggests that uncertainties often play an important role in quantifying the performance of complex systems. Therefore, uncertainty needs to be treated as a core element in modeling, simulation and optimization of complex systems. In this talk, a new formulation for quantifying uncertainty in the context of subsurface flow and transport problem will be discussed. An integrated simulation framework will be presented that quantifies both numerical and modeling errors in an effort to establish "error bars" in CFD. In particular, stochastic formulations based on Galerkin and collocation versions of the generalized Polynomial Chaos (gPC), multi-output Gaussian process model, Multilevel Monte Carlo, scalable multigrid-based pre-conditioner for stochastic PDE, adaptive ANOVA decomposition, and some stochastic sensitivity analysis and Bayesian parameter estimation techniques will be discussed in some detail. Several specific examples on flow and transport in randomly heterogeneous porous media, Bayesian climate model parameter estimation will be presented to illustrate the main idea of our approach.

Wednesday, March 14, 2012

Posted February 26, 2012
Last modified March 14, 2012

3:40 pm – 4:30 pm Lockett 233

John Etnyre, Georgia Institute of Technology
Virtual Seminar: Open books decompositions and the geometry of contact structures

Abstract: Giroux's correspondence between open books decompositions and contact structures on 3-manifolds has been key to many advances in contact geometry and its application to topology. In this talk I will discuss several recent advances that describe how properties of a contact structure, such as tightness and fillability, are reflected in its associated open book decompositions and vice vera. In addition I will discuss how some operations on open books decompositions, such as cabling a binding component, affect the associated contact structure.

Thursday, March 15, 2012

Posted October 27, 2011
Last modified March 15, 2012

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 277

Abhinav Kumar, Massachusetts Institute of Technology
Lattices, sphere packings and spherical codes

Abstract: It is a classical problem in geometry to find the densest arrangement of non-overlapping spheres in Euclidean space. I will give a brief overview of sphere packing and related geometrical problems, like the kissing number problem. After surveying some of the known results, I'll describe recent approaches to these problems, involving linear programming bounds, numerical optimization using gradient descent, and deformations and the notion of rigidity. The talk will also focus on many concrete examples and explain what we are able to observe and prove using these techniques, as well as many natural open questions.

Friday, March 16, 2012

Posted February 8, 2012
Last modified March 2, 2012

3:40 pm – 4:30 pm Lockett 277

Abhinav Kumar, Massachusetts Institute of Technology
Hilbert modular surfaces and K3 surfaces

I will outline an approach to compute equations for Hilbert modular surfaces $Y_{-}(D)$, which are moduli spaces of principally polarized abelian surfaces with real multiplication by the full ring of integers of $Q(\sqrt{D})$, based on moduli spaces of elliptic K3 surfaces. Using it we are able to calculate these surfaces for all fundamental discriminants less than 100, and analyze various arithmetic properties, such as rational points and curves which we can use to produce explicit genus 2 curves (or 1-parameter families of these) whose Jacobians have real multiplication. This is joint work with Noam Elkies.

Saturday, March 17, 2012

Posted September 14, 2011

9:00 am – 4:00 pm Tureaud Hall

LSU High School Math Contest

Tuesday, March 20, 2012

Posted March 6, 2012

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm

Xiang Zhou, Brown University
The Study of Rare Events

Many methods for stochastic systems take into account only average behavior (or perhaps variance) of the model response. But this is often not enough as the performance is related to rare events with a small probability of occurring. In my talk, I will review the large deviation theory for analyzing rare events, introduce a minimum action method for small noise diffusion processes, and the recent importance sampling Monte Carlo method based on the large deviation. Throughout the talk, I will also stress the special features of noise-induced transition in non-gradient systems and how to understand subcritical instability in physics and fluid dynamics from perspective of noise-induced transition.

Posted March 12, 2012
Last modified March 19, 2012

3:40 pm – 4:30 pm Lockett 277

Laura Rider, Department of Mathematics, LSU Graduate Student
A derived Springer correspondence for mixed perverse sheaves

The simplest case of the Springer correspondence can be understood with linear algebra and knowledge of the representation theory of the symmetric group. We write down the correspondence in this case and then review a geometric method for realizing the relationship. In this setting, the Springer correspondence can be realized as an equivalence between a certain category of perverse sheaves and the category of representations of the Weyl group. We explain how to extend this to a derived equivalence between modules over a graded ring related to W and a certain category of mixed perverse sheaves on the nilpotent cone.

Wednesday, March 21, 2012

Posted March 7, 2012
Last modified March 14, 2012

3:40 pm – 4:30 pm Lockett 233

Matt Clay, Allegheny College
Virtual Seminar: The geometry of right-angled Artin subgroups of mapping class groups

Abstract: We describe sufficient conditions which guarantee that a finite set of mapping classes generate a right-angled Artin group quasi-isometrically embedded in the mapping class group. This is joint work with Chris Leininger and Johanna Mangahas.

Thursday, March 22, 2012

Posted January 29, 2012
Last modified February 8, 2012

3:40 pm – 4:30 pm Lockett 277

Kenneth Gross, University of Vermont
Special Functions of Matrix Argument

Classical special functions such as the gamma function, Bessel functions, and hypergeometric functions, to name a few, apply in many different contexts ranging from mathematical analysis to statistics and the physical sciences. Beginning over six decades ago, generalizations of such classical functions to spaces of matrices (and to symmetric cones more generally) arose in the context of harmonic analysis, multivariate statistics, number theory, and the representation theory of Lie groups. In this talk, expository in nature, we will discuss the origins of these generalizations, highlight the critical role of symmetry considerations, and touch upon applications which have appeared recently in multiple-input multiple-output (MIMO) models that form the basis of modern cell-phone transmission.

Friday, March 23, 2012

Posted March 13, 2012

2:40 pm – 3:30 pm Lockett 239

Charles Semple, University of Canterbury, New Zealand
Realizing phylogenies with local information

Results that say local information is enough to guarantee global information provide the theoretical underpinnings of many reconstruction algorithms in evolutionary biology. Such results include Buneman\'s Splits-Equivalence Theorem and the Tree-Metric Theorem. The first result says that, for a collection C of binary characters, pairwise compatibility is enough to guarantee compatibility for C, that is, there is a phylogenetic (evolutionary) tree that realizes C. The second result says that, for a distance matrix D, if every 4 by 4 distance submatrix of D is realizable by an edge-weighted phylogenetic tree, then D itself is realizable by such a tree. In this talk, we investigate these and other results of this type. Furthermore, we explore the closely related task of determining how much information is enough to reconstruct the correct phylogenetic tree.

Tuesday, March 27, 2012

Posted January 16, 2012
Last modified July 25, 2021

Algebra and Number Theory Seminar Questions or comments?

3:15 pm – 5:00 pm Conference Room - Lockett 301D

Final Event for MS Comprehensive Exam

Mathematics (non-thesis) MS applicants for May 2012 graduation must meet with committee members William Adkins (Chair), Leonard Richardson, and Stephen Shipman in order to complete the process that began with passing the written Comprehensive Examination at the MS Qualifying Level. Apply to the Graduate School to have the Final Exam at this date with the listed committee.

Posted February 1, 2012
Last modified March 20, 2012

3:40 pm – 4:30 pm Lockett 277

Inka Klostermann, University of North Carolina
Generalization of the Macdonald formula for Hall-Littlewood polynomials

Gaussent and Littelmann developed a formula for Hall-Littlewood polynomials in terms of one-skeleton galleries in the affine building. In type $A_n$, $B_n$ and $C_n$ these galleries can be described by using certain Young tableaux. In this talk I will explain how to translate the Gaussent-Littelmann formula into an easy purely combinatorial formula in terms of Young tableaux. It turns out that the resulting so-called combinatorial Gaussent-Littelmann formula coincides with the well-known Macdonald formula for Hall-Littlewood polynomials in type $A_n$.

Thursday, March 29, 2012

Posted February 23, 2012
Last modified March 7, 2012

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 277

Aaron Welters, LSU
Dissipative Properties of Systems Composed of High-Loss and Lossless Components

Abstract: We study energy dissipation features of a system composed from lossy and lossless components. One of the principal result is that the dissipation causes modal dichotomy, i.e., splitting of the eigenmodes into two distinct classes according to their dissipative properties: high-loss and low-loss modes. Interestingly, larger losses in the lossy component make the entire composite less lossy, the dichotomy more pronounced, low-loss modes less lossy, and high-loss modes less accessible to external excitations. We also have carried out an exhaustive analytical study of the system quality factor. This is joint work with Alexander Figotin.

Tuesday, April 3, 2012

Posted March 15, 2012
Last modified March 28, 2012

3:40 pm – 4:30 pm Lockett 277

Peter Fiebig, Universität Erlangen-Nürnberg
Periodic structures in the affine category O at positive level

The categorical structure of the affine category O at positive level can be described in terms of affine moment graphs. Recently, Martina Lanini exhibited a periodic structure on moment graphs associated to maximally singular affine blocks, which yields a categorification of the stabilization phenomenon of parabolic affine KL-polynomials. I will report on the representation theoretic implications of Lanini's result and, in particular, I will explain how it is connected to a still conjectural structure of the affine category O at the critical level.

Monday, April 16, 2012

Posted February 10, 2012
Last modified March 2, 2022

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett, 233

Michael Borden, Institute for Computational Engineering and Sciences, University of Texas at Austin
Isogeometric Analysis and Computational Fracture Mechanics

I will begin my presentation with an overview of isogeometric analysis, emphasizing its application to problems in nonlinear solid mechanics. The basic idea of the isogeometric concept is to use the same basis for analysis as is used to describe the geometry in, for example, a CAD representation. The smoothness of typical geometric representations (e.g., NURBS and T-splines) has been shown to have computational advantages over standard finite elements in many solid mechanics problems.

In the second part of my presentation I will discuss our recent work on the numerical implementation of variational, or phase-field, models of fracture. The phase-field approach to predicting fracture uses a scalar-valued field to indicate that the material is in some state between complete undamaged or completed fractured with a smooth transition between the two states. This allows cracks to be modeled without explicit tracking of discontinuities in the geometry or displacement fields. In this part of my presentation I will also discuss work in which we make use of the smoothness provided by isogeometric analysis to explore the effect of adding higher-order terms to the phase-field model. Several numerical examples will be shown for both two and three-dimensional problems that demonstrate the ability of these models to capture complex crack behavior.

Tuesday, April 17, 2012

Posted March 13, 2012
Last modified April 13, 2012

3:40 pm – 4:30 pm

Harold Williams, UC Berkeley
Loop Groups and Cluster Integrable Systems

While double Bruhat cells in simple algebraic groups have played a key role in the development of cluster algebras, their counterparts in general Kac-Moody groups have been less studied. In this talk I will explain how the double Bruhat decomposition of an affine Kac-Moody group can be used to construct a new class of completely integrable Hamiltonian systems. As an example we obtain the relativistic periodic Toda system, which we will see leads to a connection with recent work of Goncharov and Kenyon on integrable systems related to dimer models.

Thursday, April 19, 2012

Posted April 4, 2012
Last modified April 16, 2012

VIGRE@LSU: Student Colloquium Questions or comments?

1:30 pm – 2:30 pm Lockett 239

Benson Farb, University of Chicago
Topology, dynamics, and geometry of surfaces (and their remarkable relationships)

This talk is primarily aimed at undergraduate students.

Surfaces can be considered from many different viewpoints: their shape (i.e. topological structure), their geometry (e.g. curvature), and the behavior of fluid flows on them. In this talk I will describe three beautiful theorems, one for each of these aspects of surfaces. I will also try to explain the remarkable fact that these seemingly completely different perspectives are intimately related.

There will be a light lunch in the Keisler Lounge at 1:00pm.

Posted August 23, 2011
Last modified April 9, 2012

VIGRE@LSU: Student Colloquium Questions or comments?

3:40 pm – 4:30 pm Lockett 277

Benson Farb, University of Chicago
Permutations and polynomiality in algebra and topology

Abstract: Tom Church, Jordan Ellenberg and I recently discovered that each Betti number of the space of configurations on n points on any manifold is a polynomial in n. Similarly for the moduli space of n-pointed genus g curves. Similarly for the dimensions of various spaces of homogeneous polynomials arising in algebraic combinatorics. Why? What do these disparate examples have in common? The goal of this talk will be to answer this question by explaining a simple underlying structure shared by these (and many other) examples in algebra and topology.

Friday, April 20, 2012

Posted April 4, 2012
Last modified April 17, 2012

11:30 am – 12:30 pm Lockett 239

Benson Farb, University of Chicago
The Mostow Rigidity Theorem: topology vs. algebra vs. geometry

The Mostow Rigidity Theorem changed geometry and topology. This talk, aimed at graduate students, will attempt to explain how and why.

There will be refreshments in the Keisler Lounge at 11:00am.

Tuesday, April 24, 2012

Posted March 15, 2012

Algebra and Number Theory Seminar Questions or comments?

3:40 pm – 4:30 pm Lockett 277

James Madden, Mathematics Department, LSU
Sheaves of ratios

Book V of Euclid's Elements is said to be an exposition of Eudoxus theory of ratio. In 1900, Hölder wrote a paper analyzing Book V, and in this connection he proved the fundamental theorem that every archimedean totally-ordered group is isomorphic to a subgroup of the additive reals. A theorem of Yosida (1942) states that every archimedean vector-lattice is a vector lattice of almost-everywhere real functions on a compact space. We can recover Yosida's Theorem by viewing Hölder's Theorem in an appropriate topos. This point of view also leads to improved versions of Yosida's Theorem. The talk illustrates how ideas that are taught in elementary school may, if analyzed with sufficient depth, have a bearing on research questions.

Wednesday, April 25, 2012

Posted January 20, 2012
Last modified April 19, 2012

2:40 pm – 3:30 pm Lockett 244

Andreas Seeger, University of Wisconsin, Madison
Singular Integrals and a Problem on Mixing

Posted April 9, 2012
Last modified October 1, 2021

3:40 pm – 4:30 pm Lockett 233

Rafal Komendarczyk, Tulane University
Virtual Seminar: "Towards the $\kappa$-invariant conjecture"

A parametrization of an $n$-component link in $R^3$, produces a natural evaluation map from the $n$-torus to the configuration space of $n$ distinct points in $R^3$. Denote by $\kappa$ the map from homotopy links to the set of homotopy classes of evaluation maps. A natural conjecture arises, that $\kappa$ classifies homotopy links. Koschorke first proved that $\kappa$ has this property for homotopy Brunnian links. In this talk, I will show how to recast Koschorke's correspondence in the language of torus homotopy groups, which reveals an interesting algebraic structure. Further, time permitting, I will describe progress towards extending the result beyond the Brunnian case. This is joint work with Frederick Cohen at Rochester and Clayton Shonkwiler at UGA.

Monday, April 30, 2012

Posted March 14, 2012

3:30 pm Keisler lounge, third floor Lockett

Annual Math Awards Ceremony

Posted February 5, 2012
Last modified April 30, 2012

Algebra and Number Theory Seminar Questions or comments?

4:10 pm Lockett 233

Shari Moskow, Mathematics Department, Drexel University
Scattering and Resonances of Thin High Contrast Dielectrics

We study the scattered field from a thin high contrast dielectric volume of finite extent. We examine both the Helmholtz model and the full three dimensional time-harmonic equations. For the case of the Helmholtz model, we derive an asymptotic expansion and show error estimates. We also consider the problem of calculating resonance frequencies by using these asymptotics and compare it with using finite elements and perfectly matched layers. For Maxwell equations, we derive a formulation of Lippmann-Schwinger type which has an additional surface term to account for the discontinuities. We analyze this surface term and present the limiting equations that result.
(based on joint work with collaborators D. Ambrose, J. Gopalakrishnan, F. Santosa and J. Zhang)

Wednesday, May 2, 2012

Posted April 24, 2012

3:40 pm Lockett 277

Zhibin Liang, Capital Normal University, Beijing
The non-commutative Iwasawa theory of modular forms

In this talk, we will discuss some new conjectures on critical values of L-functions twisted by a non-commutative Artin representation. We talk about some explicit computations and how this may contribute to a non-commutative Iwasawa theory.

Thursday, May 3, 2012

Posted March 5, 2012
Last modified March 2, 2022

3:40 pm – 4:30 pm Lockett 233

Richard Lehoucq, Sandia National Laboratories
A new approach for a nonlocal, nonlinear conservation law

My presentation describes an approach to nonlocal, nonlinear advection in one dimension that extends the usual pointwise concepts to account for nonlocal contributions to the flux. The spatially nonlocal operators introduced do not involve derivatives. Instead, the spatial operator involves an integral that, in a distributional sense, reduces to a conventional nonlinear advective operator. In particular, we examine a nonlocal inviscid Burgers equation, which gives a basic form with which to characterize well-posedness. We describe the connection to a nonlocal viscous regularization, which mimics the viscous Burgers equation in an appropriate limit. We present numerical results that compare the behavior of the nonlocal Burgers formulation to the standard local case. The developments presented in this paper form the preliminary building blocks upon which to build a theory of nonlocal advection phenomena consistent within the peridynamic theory of continuum mechanics. This is joint work with Qiang Du (PSU), Jim Kamm (SNL) and Mike Parks (SNL)

Wednesday, May 9, 2012

Posted April 3, 2012
Last modified October 1, 2021

3:40 pm – 4:30 pm Lockett 233
(Originally scheduled for Wednesday, April 4, 2012)

Dennis Roseman
Small Lattice Surfaces in Four Dimensions

A lattice point is a point with integer coordinates. The standard p x q x r x s lattice box is all lattice points in R^4 within [0,p-1] x [0,q-1] x [0, r-1] x [0, s-1]. A lattice square in R^4 is a unit square whose vertices are lattice points. A lattice surface or lattice surface link is a finite union of lattice squares which is topologically is a closed two-dimensional manifold (perhaps not connected, perhaps not orientable).
We focus on the question: which surface link types can be represented as lattice surfaces in a given small lattice box? We show that any orientable surface link in a 3x3x3x3 lattice box is a pseudo-ribbon link, and discuss a new surface link invariant that can detect non-pseudo-ribbon links. We give a table of surface links that lie in a 3x3x3x2 lattice box and develop notations, terminology, mathematical strategies and visualization tools for investigating these and surface links in slightly larger boxes.

Tuesday, May 15, 2012

Posted March 27, 2012

3:30 pm – 4:30 pm 338 Johnston Hall

Guido Kanschat, Texas A&M University
Discontinuous Galerkin Methods for Diffusion-Dominated Radiative Transfer Problems

Abstract: While discontinuous Galerkin (DG) methods had been developed and analyzed in the 1970s and 80s with applications in radiative transfer and neutron transport in mind, it was pointed out later in the nuclear engineering community, that the upwind DG discretization by Reed and Hill may fail to produce physically relevant approximations, if the scattering mean free path length is smaller than the mesh size. Mathematical analysis reveals, that in this case, convergence is only achieved in a continuous subspace of the finite element space. Furthermore, if boundary conditions are not chosen isotropically, convergence can only be expected in relatively weak topology. While the latter result is a property of the transport model, asymptotic analysis reveals, that the forcing into a continuous subspace can be avoided. By choosing a weighted upwinding, the conditions on the diffusion limit can be weakened. It has been known for long time, that the diffusion limit of radiative transfer is a diffusion equation; it turns out, that by choosing the stabilization carefully, the DG method can yield either the LDG method or the method by Ern and Guermond in its diffusion limit. We will close discussing solution techniques for the resulting discrete problems.

Refreshments at 3pm.

Monday, August 13, 2012

Posted April 25, 2012
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 285

Comprehensive / PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Tuesday, August 14, 2012

Posted August 8, 2012
Last modified March 3, 2021

3:40 pm – 4:30 pm Lockett Hall 285

The Fourier and Gegenbauer analysis of fundamental solutions for Laplace's equation on Riemannian spaces of constant curvature

Due to the isotropy of $d$-dimensional hyperbolic and hyperspherical spaces, there exist spherically symmetric fundamental solutions for their corresponding Laplace-Beltrami operators. The $R$-radius hyperboloid model of hyperbolic geometry with $R>0$ represents a Riemannian manifold with negative-constant sectional curvature and the $R$-radius hypersphere embedded in Euclidean space represents a Riemannian manifold with positive-constant sectional curvature. We obtain spherically symmetric fundamental solutions for Laplace's equation on these manifolds in terms of their geodesic radii. We give several matching expressions for these fundamental solutions including definite integral results, finite summation expressions, Gauss hypergeometric functions, and associated Legendre and Ferrers function of the second kind representations. On the $R$-radius hyperboloid we perform Fourier and Gegenbauer analysis for a fundamental solution of Laplace's equation. For instance, in rotationally-invariant coordinate systems, we compute the azimuthal Fourier coefficients for a fundamental solution of Laplace's equation. For $d\ge 2$, we compute the Gegenbauer polynomial expansion in geodesic polar coordinates for a fundamental solution of Laplace's equation on the $R$-radius hyperboloid. In three-dimensions, an addition theorem for the azimuthal Fourier coefficients for a fundamental solution of Laplace's equation is obtained through comparison with its corresponding Gegenbauer expansion. Generalization of this work on the rank one symmetric spaces will be discussed.

Short Bio: Dr Howard Cohl obtained a B.S. in Astronomy and Astrophysics from Indiana University, a M.S. and Ph.D. in Physics from Louisiana State University, and a Ph.D. in Mathematics from the University of Auckland in New Zealand. He has worked as a research scientist at various research institutions including the National Solar Observatory in Sunspot, New Mexico; Naval Oceanographic Office Major Shared Resource Center in Stennis Space Center, Mississippi; Lawrence Livermore National Laboratory in Livermore, California; and the School of Physics, University of Exeter in Exeter, United Kingdom. Howard started in December 2010, as a National Research Council Postdoctoral Research Associate in the Applied and Computational Mathematics Division at the National Institute of Standards and Technology. Dr Cohl is currently interested in the special functions associated with fundamental solutions for linear partial differential equations on Riemannian manifolds.

Posted August 8, 2012

3:40 pm – 4:30 pm 233 Lockett

Raul Tempone, King Abdullah University of Science and Technology, KAUST
Strategies for Optimal Polynomial Approximation of Elliptic PDEs with Stochastic Coefficients

Partial differential equations with stochastic coefficients are a suitable tool to describe systems whose parameters are not completely determined, either because of measurement errors or intrinsic lack of knowledge on the system. In the case of elliptic PDEs, an effective strategy to approximate the state variables and their statistical moments is to introduce high order polynomial approximations like Stochastic Galerkin or Stochastic Collocation method, exploiting the fact that the state variables may exhibit high regularity in their dependence with respect to the random parameters. When the number of parameters is moderate, these methods can be remarkably more effective than classical sampling methods. However, contrary to the latter, the performance of polynomial approximations deteriorates as the number of random variables increases (\\emph{curse of dimensionality}); to prevent this, care has to be put in the construction of the approximating polynomial space. In this talk we will propose strategies to construct optimal spaces and propose some particular polynomial spaces and generalized sparse grids that are optimal for particular problems. We will also support our claims with some simple numerical examples. This work is a joint collaboration with J. Beck, F. Nobile and L. Tamellini.

Posted August 7, 2012
Last modified March 2, 2022

4:40 pm – 5:30 pm 233 Lockett Hall

Mohammad Motamed, Visiting Scholar, Institute for Engineering and Computational Science UT Austin
Analysis and Computation of Linear Hyperbolic Problems with Random Coefficients

In this talk, in particular, we consider the second-order acoustic and elastic wave equations. In the first part of this talk, we propose and analyze a stochastic collocation method for solving the acoustic wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and depends on a finite number of random variables. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. This approach leads to the solution of uncoupled deterministic problems as in the Monte Carlo method. We consider both full and sparse tensor product spaces of orthogonal polynomials. We demonstrate different types of convergence of the “probability error” with respect to the number of collocation points for full and sparse tensor product spaces and under some regularity assumptions on the data. In the second part of the talk, we present extensions to the elastic wave equation with random coefficients and random boundary conditions.

Wednesday, August 15, 2012

Posted April 25, 2012
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 285

Comprehensive / PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, August 17, 2012

Posted April 25, 2012
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 285

Comprehensive / PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Tuesday, August 21, 2012

Posted August 5, 2012
Last modified August 21, 2012

3:40 pm – 4:30 pm Lockett 240

Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Trotter Product Formula for Stochastic Evolutions in Fock space

Thursday, August 23, 2012

Posted May 3, 2012
Last modified August 11, 2012

3:30 pm – 4:30 pm 338 Johnston Hall

Carsten Carstensen, Humboldt Universität zu Berlin
Five Trends in the Mathematical Foundation of Computational PDEs

This presentation concerns five topics in computational partial differential equations: (1) equivalence of first-order methods for the Poisson problem, (2) nonconforming and mixed finite element methods for the Stokes equations and their adaptivity, (3) adaptive methods for elliptic eigenvalue problems, (4) adaptive error control for obstacle problems, and (5) computational microstructures with degenerate convex minimization. The overall goals for the work in these topics are reliable error control and efficient simulation. The presentation will also demonstrate the surprising advantages of nonstandard discretizations over conforming finite element schemes. (Additional details can be found at http://www.cct.lsu.edu/lectures/five-trends-mathematical-foundation-computational-pdes)

Wednesday, September 5, 2012

Posted August 21, 2012
Last modified March 3, 2021

3:30 pm – 4:20 pm Lockett 284

Boris Rubin, Louisiana State University
Weighted norm inequalities for $k$-plane transforms

We obtain sharp weighted norm inequalities for the $k$-plane transform, the “$j$-plane to $k$-plane” transform, and the corresponding dual transforms, acting on $L^p$ spaces with a radial power weight. These transforms are well known in integral geometry and harmonic analysis. The operator norms are explicitly evaluated. Some generalizations and open problems will be discussed. The paper is available in arXiv:1207.5180v1.

Posted August 26, 2012
Last modified September 3, 2012

3:30 pm – 4:20 pm

Anastasiia Tsvietkova, LSU
Virtual Seminar: "Hyperbolic structures from link diagrams"

W. Thurston demonstrated that every link in $S^3$ is a torus link, a satellite link or a hyperbolic link and these three categories are mutually exclusive. It also follows from work of W. Menasco that an alternating link represented by a prime diagram is either hyperbolic or a $(2,n)$--torus link. The talk will introduce an alternative method for computing the hyperbolic structure of the complement of a hyperbolic link. It allows computing the structure directly from the link diagram. Some of its consequences will be discussed, including a surprising rigidity property of certain tangles, and the formulas that allow one to calculate the exact hyperbolic volume, as well as complex volume, of hyperbolic 2--bridge links. This is joint work with M. Thistlethwaite.

Posted August 24, 2012
Last modified August 31, 2012

4:30 pm Lockett 05 (basement room)
(Originally scheduled for Wednesday, August 29, 2012, 4:30 pm)

Faculty Meeting

Wednesday, September 12, 2012

Posted September 7, 2012

3:30 pm – 4:30 pm Lockett 240

Habib Ouerdiane, University of Tunis El Manar
Unitarising measure for the representation of Lie group and associated invariant differential operators.

Posted August 20, 2012
Last modified August 31, 2012

4:30 pm James E. Keisler Lounge (room 321 Lockett)

meeting of student actuarial club

1. Welcome to new students and an introduction to being an actuary.

2. Options for actuarial students to get capstone credit.

3. Planning for exams.

4. Discussing possible visitors.

Thursday, September 13, 2012

Posted September 10, 2012
Last modified September 13, 2012

3:30 pm – 4:20 pm Lockett 277

Michael Malisoff, LSU Roy P. Daniels Professor
Adaptive Tracking and Parameter Identification for Nonlinear Control Systems

Given a control system that has a vector of unknown constant parameters and a reference trajectory for the system, the adaptive tracking and parameter identification problem is to find a dynamic controller that forces the system to track the reference trajectory and a parameter estimator that converges to the unknown parameter vector. In the first part of this talk, I will review the necessary background on control theory. Then I will discuss my research on adaptive tracking and parameter identification for systems with unknown control gains. In the last part, I will discuss an application to marine robots and open problems. This work is joint with Frederic Mazenc and Fumin Zhang. This talk will be understandable to anyone who knows all of the material in the basic graduate ODEs course Math 7320 at LSU.

Wednesday, September 19, 2012

Posted September 14, 2012
Last modified February 6, 2021

2:30 pm – 3:20 pm Lockett 284

Raul Quiroga, Centro de Investigacion en Matematicas (CIMAT)
Commutative C*-algebras of Toeplitz operators and their geometric aspects, Part 1

Our main object of interest are the Toeplitz operators on weighted Bergman spaces over complex bounded domains. Such operators are given by a multiplication operator (by a measurable bounded symbol) followed by the Bergman projection. These operators generalize those considered in Hardy spaces and also naturally appear in Berezin's quantization procedure. We will explain a rather unexpected fact: the existence of large and rich families of symbols that define commutative C*-algebras of Toeplitz operators on weighted Bergman spaces. It is also found that Berezin's quantization implies that any such commutative C*-algebra always carries a distinguished geometric structure. We will see how the use of such geometric structure allows to classify the symbols that define commutative C*-algebras on all weighted Bergman spaces on the unit disk. These geometric tools have also provided some interesting constructions for Reinhardt domains and the n-dimensional unit ball.

Posted August 21, 2012
Last modified September 3, 2012

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 233
(Originally scheduled for Sunday, September 2, 2012)

Shea Vela-Vick, Louisiana State University
Virtual Seminar: "The equivalence of transverse link invariants in knot Floer homology"

Abstract: The Heegaard Floer package provides a robust tool for studying contact 3-manifolds and their subspaces. Within the sphere of Heegaard Floer homology, several invariants of Legendrian and transverse knots have been defined. The first such invariant, constructed by Ozsvath, Szabo and Thurston, was defined combinatorially using grid diagrams. The second invariant was obtained by geometric means using open book decompositions by Lisca, Ozsvath, Stipsicz and Szabo. We show that these two previously defined invariant agree. Along the way, we define a third, equivalent Legendrian/transverse invariant which arises naturally when studying transverse knots which are braided with respect to an open book decomposition.

Tuesday, September 25, 2012

Posted September 20, 2012
Last modified September 24, 2012

3:30 pm – 4:30 pm Lockett 235

Greg Muller, Department of Mathematics, LSU
Superunital domains of cluster algebras

A cluster algebra is a type of commutative algebra with a set of distinguished generators, called cluster variables, with desirable combinatorial properties. For a given cluster algebra, we consider its cluster variables as functions on an octant in n-dimensions. The `superunital domain\' is the subset of this octant on which each cluster variable is greater than or equal to one. The topology of the boundary encodes many of the desirable properties of the cluster variables. When the cluster algebra is `finite-type\', the superunital domain is compact and possesses a natural volume form; I will mention some preliminary results with Joel Geiger and Karl Mahlburg on the integral of this form.

Wednesday, September 26, 2012

Posted September 14, 2012
Last modified March 3, 2021

2:30 pm – 3:20 pm Lockett 284

Raul Quiroga, Centro de Investigacion en Matematicas (CIMAT)
Commutative C*-algebras of Toeplitz operators and their geometric aspects, Part 2

Friday, September 28, 2012

Posted September 24, 2012
Last modified September 25, 2012

3:30 pm Lockett 241

Full Professors' Meeting

Wednesday, October 3, 2012

Posted September 26, 2012
Last modified March 3, 2021

2:30 pm – 3:20 pm Lockett 284

Moritz Egert, University of Darmstadt
Square roots of elliptic systems

We study a system $A$ of $2$nd-order elliptic differential equations on the whole space. We realize $A$ as a maximal-accretive operator on $L^2$. It turns out that in this setting, $A$ admits a unique maximal-accretive square root $A^{\frac{1}{2}}$ that shares an astonishing regularity property: Its domain allows for one weak derivative although the domain of the full operator $A$ does not allow for the expected two weak derivatives in general. As a consequence, the Riesz transform $\nabla A^{-\frac{1}{2}}$ is a bounded operator on $L^2$. Finally, we study the Riesz transform on the $L^p$-scale ($p \in (1,\infty)$) culminating in Auscher's characterization of those $p$ for which the Riesz transform extends to a bounded operator on $L^p$.

Posted September 1, 2012
Last modified September 14, 2012

3:30 pm – 4:20 pm

Ken Baker, University of Miami
Virtual Seminar: "Annular twists and Bridge numbers of knots"

Abstract: Performing +1/n and -1/n Dehn surgery on the boundary components of an annulus A in a 3-manifold M provides a homeomorphism of M similar to a Dehn twist. If a knot intersects the interior of A in an essential manner, then this twisting produces an infinite family of knots. In joint work with Gordon and Luecke, we show (under certain hypotheses) that if the bridge numbers of this family with respect to a given Heegaard surface of M are bounded, then the annulus may be isotoped to embed in the Heegaard surface. With this we construct genus 2 manifolds that each contain a family of knots with longitudinal surgeries to S^3 and unbounded genus 2 bridge number. In contrast, our earlier work gives an a priori upper bound on the bridge number of a knot in a genus g manifold with a non-longitudinal S^3 surgery.

Thursday, October 4, 2012

Posted August 22, 2012
Last modified October 1, 2012

3:30 pm – 4:20 pm Locket 277

Joseph Wolf, University of California, Berkeley
Infinite Dimensional Lie Groups

Abstract: I'll survey some analytic aspects of a class of infinite dimensional
Lie groups that have a lot of properties in common with their finite
dimensional counterparts. These include smoothness, the Borel-Weil
and Bott-Borel Weil theorems, and the possibility of extending some
of Harish-Chandra's constructions from the finite dimensional case.
This leads to a number of interesting open problems.

Friday, October 5, 2012

Posted October 1, 2012
Last modified October 3, 2012

3:30 pm – 4:20 pm Lockett 237

Moshe Cohen, Department of Mathematics, Bar-Ilan University, Israel
The graph of perfect matchings coming from knots: a formula for its diameter

The graph of perfect matchings has as its vertices the perfect matchings of a specific bipartite graph and as edges a flip move taking alternating edges of a face to the missing edges. We realize Kauffman's obscure vocabulary in his book on Formal Knot Theory as a result about the graph of perfect matchings coming from knots. In this case, the plane embedding of the bipartite graph gives a direction to the flip move edges which helps to answer one of the first questions in this combinatorial theory: what is the diameter of this graph?

We prove recursive structural properties of the bipartite graph and mention applications to grid graphs and to discrete Morse functions.

This is joint work with Mina Teicher.

Saturday, October 6, 2012

Posted September 19, 2012
Last modified February 11, 2022

9:00 am – 5:00 pm Sunday, October 7, 2012 241 Lockett Hall

Workshop on Lie Groups, Lie Algebras and Their Representations

During the weekend a workshop on "Lie groups, Lie algebras and their representations" will take place at LSU. Detailed information about the program, location, and the participants can be found at www.math.lsu.edu/~lie2012. The workshop is supported by an NSF grant and organized by G. Olafsson and M. Yakimov.

Monday, October 8, 2012

Posted October 1, 2012
Last modified October 8, 2012

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 240

Irina Craciun, Department of Mathematics, LSU Graduate Student
Gaussian Measure for Subspaces of a Banach Space

Tuesday, October 9, 2012

Posted October 5, 2012
Last modified May 8, 2021

3:30 pm – 4:30 pm Lockett 235

Pramod Achar, Mathematics Department, LSU
Schur-Weyl duality, nilpotent orbits, and tilting modules

This mostly expository talk will be about connections between the following four topics: (1) representations of the symmetric group $S_n$; (2) representations of the general linear group $GL_n$; (3) topology of the set of nilpotent matrices; (4) topology of the set of lattices in a vector space over the field of Laurent series. Some of these connections are very old: Issai Schur discovered a link between (1) and (2) more than 100 years ago. The topological aspects have been developed mostly since the mid-1970's, by Springer, Lusztig, Ginzburg, Mirković-Vilonen, and others; a nice unifying result has been proved by Carl Mautner. I will try to explain these ideas with concrete examples, and give one application: a new geometric proof, via Fourier transform on the nilpotent variety, of Ringel self-duality for Schur algebras. This last result is joint work of myself and C. Mautner.

Wednesday, October 10, 2012

Posted September 14, 2012
Last modified March 2, 2021

3:30 pm – 4:20 pm

Moshe Cohen, Department of Mathematics, Bar-Ilan University, Israel
Virtual Seminar: "Kauffman's clock lattice as a graph of perfect matchings: a formula for its height"

Kauffman gives a state sum formula for the Alexander polynomial of a knot using states in a lattice that are connected by his clock moves. We show that this lattice is more familiarly the graph of perfect matchings of a bipartite graph obtained from the knot diagram by overlaying the two dual Tait graphs of the knot diagram. Using a partition of the vertices of the bipartite graph, we give a direct computation for the height of Kauffman\'s clock lattice obtained from a knot diagram with two adjacent regions starred and without crossing information specified. We prove structural properties of the bipartite graph in general and mention applications to Chebyshev or harmonic knots (obtaining the popular grid graph) and to discrete Morse functions.

Thursday, October 11, 2012

Posted September 11, 2012
Last modified March 2, 2021

3:30 pm – 4:20 pm Lockett 277

Barbara Rüdiger, Bergische Universität Wuppertal - Germany
Stochastic (Partial) Differential Equations with Lévy noise: Existence, uniqueness and properties of solutions

In this talk we first analyze properties of integrands when integration is done with respect to Lévy processes or compensated Poisson random measures. Then we introduce SP(D)Es with Lévy noise and show the existence, uniqueness and continuous properties of the solutions.

Monday, October 15, 2012

Posted September 4, 2012
Last modified March 2, 2021

4:00 pm Lockett 233

Stephanos Venakides, Department of Mathematics, Duke University
Higher breaking in the focusing nonlinear Schrödinger equation

The focusing nonlinear Schrödinger equation iε du/dt + ε² d²u/dx² + 2|u|²u = 0 (NLS) appears dominantly in nonlinear optical transmission, together with its many variants. Mathematically, the initial value problem of the NLS on the line is integrable. It can be linearized with the aid of a Lax operator pair, produced by Zakharov and Shabat. Determining the evolution of an NLS waveform becomes possible with the aid of Riemann-Hilbert problems (RHP), the conceptual nature of which is simple and will be explained in the talk.
The development of the steepest descent method for oscillatory RHP provided rigorous asymptotic procedures, that make the solution of NLS and nonlinear integrable systems in general, explicit or nearly explicit. The method applies to asymptotics of RHP in the same spirit as the classic methods of stationary phase and steepest descent apply in the asymptotic evaluation of Fourier type integrals arising from the solution of linear differential equations. In both the linear and the nonlinear cases, there is a separation of space-time scales over similar parameter regimes.
Employing initial data of the form u(x,0)=A(x)exp(iS(x)/ε) in the asymptotic limit ε→0, we describe the solution over a large domain of space-time and the mechanism of the break-down of the method beyond this domain. Using a combination of analytic and numerical considerations, we establish the boundary beyond which the asymptotic solution is still unknown. The spatial component of this domain is bounded.

Tuesday, October 16, 2012

Posted October 1, 2012
Last modified October 9, 2012

3:30 pm – 4:30 pm 338 Johnston Hall

Duk-Soon Oh, Louisiana State University
A Balancing Domain Decomposition Method by Constraints for Raviart-Thomas Vector Fields

Balancing domain decomposition by constraints(BDDC) preconditioners consist of a coarse component, involving primal constraints across the interface between the subdomains, and local components related to the Schur complements of the local subdomain problems. A BDDC method for vector field problems discretized with Raviart-Thomas finite elements is introduced. The method is based on a new type of weighted averages developed to deal with more than one variable coefficient. Bounds on the condition number of the preconditioned linear system are also provided and the estimated condition number is quite insensitive to the values and jumps of the coefficients across the interface and has a polylogarithmic bound in terms of the number of degrees of freedom in the individual subdomains. Numerical experiments for 2D and 3D problems, which support the theory and show the effectiveness of our algorithm, are also presented.

Wednesday, October 17, 2012

Posted September 14, 2012
Last modified October 16, 2012

3:30 pm – 4:20 pm

Adam Lowrance, Department of Mathematics, Vassar College
Virtual Seminar: "Khovanov homology and oriented ribbon graphs"

Abstract: We define Khovanov homology of ribbon graphs and discuss how it ties together the Khovanov homology of both classical and virtual links. The spanning tree complex of Khovanov homology generalizes in the ribbon graph setting to a quasi-tree complex, which shows a relation between the Khovanov homology (of both classical and virtual links) and Turaev genus. We also discuss ribbon graph Reidemeister moves and discuss how they may be used to give distinct virtual links with isomorphic Khovanov homology.

Posted October 9, 2012

4:30 pm James E. Keisler Lounge (room 321 Lockett)

meeting of student actuarial club

1.Chen Liu will give a presentation on her work from her summer internship. She will discuss cash balance plan in the state-wide retirement system.
2. We will also discuss seeking an internship for this summer and getting capstone credit.
3. Planning for exams.

Monday, October 22, 2012

Posted October 19, 2012
Last modified March 3, 2021

3:30 pm – 4:20 pm Lockett 235

Clifford Smyth, University of North Carolina at Greensboro
Means and Row-Column Correlation

We prove generalized arithmetic-geometric mean inequalities for quasi-means arising from symmetric polynomials. The inequalities are satisfied by all positive, homogeneous symmetric polynomials, as well as a certain family of nonhomogeneous polynomials; this family allows us to prove the following combinatorial result. Suppose that a random subgraph is chosen from a complete bipartite graph G with an equal number of vertices in each part of the bipartition (A;B), where each edge is independently chosen with a probability that depends only on its intersection with A. Then for any m, the probability that the degree of each vertex in A is bounded by m is less than the probability that this is true of each vertex in B.

This talk is based on joint work with Karl Mahlburg

Posted October 7, 2012
Last modified May 5, 2020

3:40 pm – 4:30 pm Room 233 Lockett

Stewart Silling, Sandia National Laboratories
Multiscale Modeling of Fracture with Peridynamics

The peridynamic theory is an extension of traditional solid mechanics that treats discontinuous media, including the evolution of discontinuities such as fracture, on the same mathematical basis as classically smooth media. Since it is a strongly nonlocal theory, peridynamic material models contain a length scale that characterizes the interaction distance between material points. By changing this length scale in a way that preserves the bulk elastic properties, greater spatial resolution in a simulation can be focused on a growing crack tip or other evolving singularity. This leads to a consistent way to treat fracture at the smallest physically relevant length scale within a larger model, without remeshing or coupling dissimilar methods. The method works within a meshless discretization of the peridynamic equations similar to that used in the Emu code. The grid has multiple elves of resolution. The high resolution portions of the grid supply material properties, including damage, to the coarser levels. The displacement field in the coarsest level is determined by the equation of the motion at that level, using these coarse-grained material properties. The resulting coarse displacements are applied as boundary conditions on the finer levels of the grid. The equation of the motion in the finer levels is solved only where the damage is ongoing or large deformations are occurring. In this way, the greatest computational power is focused only on those parts of the region, such as growing crack tips, where it is required. This peridynamic multiscale method appears to provide a promising approach to understanding the evolution of material failure, including the interaction of small defects with each other and with heterogeneities. This talk will first review the basics of the peridynamic theory. The new multi scale method will then be discussed, with computational examples drawn from the mechanics of contact and from damage progression in heterogeneous media.

Tuesday, October 23, 2012

Posted September 8, 2012
Last modified November 29, 2022

3:00 pm – 4:00 pm 338 Johnston Hall

Klaus Boehmer, Philipps-Universität Marburg
Dew Drops on Spider Webs: A Symmetry Breaking Bifurcation for a Parabolic Differential-Algebraic Equation

Lines of dew drops on spider webs are frequently observed on cold mornings. In this lecture we present a model explaining their generation. Although dew is supposed to condense somehow evenly along the thread, only lines of drops are observed along the spider thread. What are the reasons for this difference? We try to give an explanation by concentrating on some essential aspects only. This everyday observation is an example of one of the fascinating scenarios of nonlinear problems, symmetry breaking bifurcation. Despite many simplifications the model still provides very interesting mathematical challenges. In fact the necessary mathematical model and the corresponding numerical methods for this problem are so complicated that in its full complexity it has never been studied before. We analyze and numerically study symmetry breaking bifurcations for a free boundary problem of a degenerate parabolic differential-algebraic equation employing a combination of analytical and numerical tools.

Posted October 19, 2012

4:10 pm 132 Prescott (NOTE: Prescott is the first building you pass when taking the shortest route from Lockett to the quadrangle.)

Faculty meeting to discuss changes to undergrad studies and also grad studies

Wednesday, October 24, 2012

Posted September 19, 2012
Last modified January 10, 2022

3:30 pm – 4:20 pm Lockett 233

Bulent Tosun, CIRGET (Montreal)
Virtual Seminar: "Cabling and Legendrian simplicity"

This talk will be about Legendrian and transverse knots in cabled knot types in standard contact three sphere and their classifications up to contact isotopy. We will be able to give structural theorems that ensure when cables a of a Legendrian simple knot type are Legendrian simple. We will then give complete classification in case of cables of positive torus knots. These results exhibits many new phenomena about structural understanding of Legendrian and transverse knot theory. The key ingredient of the proofs will be understanding of certain quantities associated to contact solid tori representing positive torus knots in standard contact three sphere. Part of the results are joint work with John Etnyre and Douglas LaFountain.

Thursday, October 25, 2012

Posted September 11, 2012
Last modified September 17, 2021

3:30 pm – 4:20 pm Lockett 277

Aderemi Kuku, Grambling State University William W.S. Clayton Endowed Professor of Mathematics
Higher Algebraic K-Theory and Representations of Algebraic Groups

In this talk, I at first discuss some features of K-theory as a multidisciplinary subject that classifies various mathematical structures and objects as well ramifies into and co-ordinates several areas of mathematics. Next, I present constructions and computations of equivariant higher K-theory and profinite (continuous) equivariant higher K-theory for the action of algebraic groups with applications to twisted flag varieties.

Monday, October 29, 2012

Posted September 10, 2012
Last modified March 3, 2021

2:30 pm – 3:20 pm Lockett 284

Angela Pasquale, University of Metz and CNRS
Resonances and meromorphic continuation of the resolvent of the Laplace operator on Riemannian symmetric spaces of the noncompact type

Let $\Delta$ be the Laplace-Beltrami operator on a symmetric space of the noncompact type $G/K$, and let $\sigma(\Delta)$ denote its spectrum. The resolvent $R(z)=(\Delta-z)^{-1}$ is a holomorphic function on $\mathbb C \setminus \sigma(\Delta)$, with values in the space of bounded operators on $L^2(G/K)$. We study the meromorphic continuation of $R$ as distribution valued map on a Riemann surface above $\mathbb C \setminus \sigma(\Delta)$. If such a meromorphic continuation is possible, then the poles of the meromorphically extended resolvent are called the resonances. If $\dim X$ is odd and all Cartan subgroups of $G$ are conjugate, then there are no resonances. This can be seen as a consequence of Huygens' principle for the modified wave equation on $X$. In other examples the resonances exist and can be explicitly determined. This is a work in progress with Joachim Hilgert and Tomasz Przebinda.

Posted September 19, 2012
Last modified March 2, 2022

3:00 pm Lockett 233

Anna Zemlyanova, Department of Mathematics, Texas A&M
Elimination of oscillating singularities at the crack-tips of an interface crack with a help of a curvature-dependent surface tension

A new model of fracture mechanics incorporating a curvature-dependent surface tension acting on the boundaries of a crack is considered. The model is studied on the example of a single straight interface crack between two elastically dissimilar semi-planes. Linear elasticity is assumed for the behavior of the material of the plate in a bulk. A non-linear boundary condition with a consideration for a curvature-dependent surface tension is given on the crack boundary. It is well known from linear elastic fracture mechanics (LEFM) that oscillating singularities exist at the crack tips and lead to non-physical interpenetration and wrinkling of the crack boundaries. Using the methods of complex analysis, such as Dirichlet-to-Neumann mappings, the problem is reduced to a system of six singular integro-differential equations. It is proved that the introduction of the curvature-dependent surface tension eliminates both classical power singularities of the order 1/2 at the tips of the crack and oscillating singularities, thus resolving the classical contradictions of LEFM. Numerical computations are presented.

Monday, November 5, 2012

Posted October 9, 2012
Last modified October 12, 2012

2:30 pm – 3:20 pm Lockett 284

Pierre Clare, Penn State University
C*-algebraic normalised intertwiners

Normalised intertwining integrals related to principal series are central objects in representation theory. The aim of this talk is to describe how to construct and study analogous objects at the level of Hilbert modules and C*-algebras that arise when considering the (reduced) dual of a Lie group from the point of view of noncommutative geometry. Some results appear to carry a similar flavour to recent advances in the classical geometric approach.

Tuesday, November 6, 2012

Posted November 1, 2012

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 338 Johnston Hall

Harbir Antil, George Mason University
Optimal Control of a Free Boundary Problem with Surface Tension Effects

We consider a PDE constrained optimization problem governed by a free boundary problem. The state system is based on coupling the Laplace equation in the bulk with a Young-Laplace equation on the free boundary to account for surface tension, as proposed by P. Saavedra and L.R. Scott. This amounts to solving a second order system both in the bulk and on the interface. Our analysis hinges on a convex constraint on the control such that the state constraints are always satisfied. Using only first order regularity we show that the control to state operator is twice Fr\'echet differentiable. We improve slightly the regularity of the state variables and exploit this to show existence of a control together with second order sufficient optimality conditions. Next we prove the optimal a priori error estimates for the control problem and present numerical examples. Finally, we give a novel analysis for a more practical model with Stokes equations in the bulk and slip boundary conditions on the free boundary interface. (Refreshments at 3pm)

Posted November 3, 2012
Last modified May 8, 2021

3:30 pm – 4:20 pm Lockett 235

Myron Minn-Thu-Aye, Department of Mathematics, LSU Graduate Student
Multiplicity formulas for perverse coherent sheaves on the nilpotent cone

Bezrukavnikov has shown that the category of perverse coherent sheaves on the nilpotent cone of a complex reductive algebraic group is quasi-hereditary. The Andersen-Jantzen sheaves play an important role, analogous to that of the Verma modules in category O. We describe progress towards computing multiplicities of simple objects in Andersen-Jantzen sheaves. The main tool is an equivalence between perfect complexes on the nilpotent cone and mixed sheaves on the affine Grassmannian.

Wednesday, November 7, 2012

Posted November 2, 2012

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm Lockett 10 (basement room)

Professorial Faculty Meeting to discuss pursuing a unique hiring opportunity

See the forum: https://www.math.lsu.edu/node/1869

Thursday, November 8, 2012

Posted October 24, 2012
Last modified October 30, 2012

1:30 pm – 2:20 pm Lockett 232

Debra Knisley, East Tennessee State University
Graph-theoretic measures of biomolecular structures

In this talk I will present an overview of graph-theoretic models in molecular biology. We will see how graphs can be used to represent DNA structure, secondary RNA structure and protein structures. Techniques that attempt to numerically characterize biomolecular structure and function, using concepts from chemical graph theory, combinatorial graph theory and network science will be compared. Recent projects that utilize ideas from all of the above to model RNA and proteins will be presented as examples and the future of such applications will be a discussed. This is joint work with a number of students at ETSU, both undergraduate and beginning graduate.

This talk is primarily aimed at undergraduate students.

There will be a light lunch from 1:00-1:30 in the Keisler Lounge.

Posted September 11, 2012
Last modified March 3, 2021

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:20 pm Locket 277

Yang Tonghai, University of Wisconsin
The Gross-Zagier formula — history, application, and development

How do you know whether a cubic equation like $y^2 =x^3 -n^2 x$ have infinitely many solutions or not (for a fixed integer $n$)? How do you find them? The Birch and Swinnerton-Dyer conjecture would tell you that some analysis ($L$-function) would tell you a lot about this kind of questions. The Gross-Zagier formula gives a deep and direct relation between the arithmetic and analysis. In this talk, I will briefly talk about this beautiful formula, some of its significant applications, and its generalizations.

Friday, November 9, 2012

Posted October 24, 2012
Last modified October 30, 2012

2:30 pm – 3:20 pm Lockett 232

Debra Knisley, East Tennessee State University
Vertex-weighted graph models of protein structure

In this talk I will present several graph based models of proteins. Our previous work on predicting changes in protein binding affinity due to mutations shows that graphical invariants coupled with data mining tools inherently combine primary sequential information, structural information and amino acid motif recognition. Misfolded proteins are responsible for a number of diseases, among them cystic fibrosis. The misfolding of a critical protein, the Cystic Fibrosis Transmembrane Conductance Regulator (CFTR) membrane protein, is the result of a single point mutation in the gene that encodes CFTR. We extend our previous findings to model CFTR with a nested vertex-weighted graph approach, defining novel measures of graphs from combinatorial concepts which we use as biomolecular descriptors. Our model is then used to perform virtual mutations of CFTR in order to numerically characterize the
consequences of each mutation on the structural features of the protein. We compare the results of eight of the most commonly occurring mutations of CFTR. This work is in progress and the findings are preliminary.

This talk is primarily aimed at graduate students.

There will be refreshments in the Keisler Lounge from 2:00-2:30.

Tuesday, November 13, 2012

Posted November 8, 2012
Last modified February 20, 2022

3:30 pm James E. Keisler Lounge (room 321 Lockett)

meeting of student actuarial club

1. Kayla Lato and Blake Winchell from LSU career services will give a presentation. 2. Mel Lazo, ASA member and Ourso college graduate student will discuss the how to set up a LinkedIn profile and the benefits of doing so.

Posted November 1, 2012

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 338 Johnston Hall

Shawn Walker, LSU
A New Mixed Formulation For a Sharp Interface Model of Stokes Flow and Moving Contact Lines

Two phase fluid flows on substrates (i.e. wetting phenomena) are important in many industrial processes, such as micro-fluidics and coating flows. These flows include additional physical effects that occur near moving (three-phase) contact lines. We present a new 2-D variational (saddle-point) formulation of a Stokesian fluid with surface tension that interacts with a rigid substrate. The model is derived by an Onsager type principle using shape differential calculus (at the sharp-interface, front-tracking level) and allows for moving contact lines and contact angle hysteresis through a variational inequality. We prove the well-posedness of the time semi-discrete and fully discrete (finite element) model and discuss error estimates (ongoing). Simulation movies will be presented to illustrate the method. We conclude with some discussion of a 3-D version of the problem as well as future work on optimal control of these types of flows. (Refreshments at 3pm.)

Posted October 24, 2012
Last modified October 26, 2021

3:30 pm – 4:30 pm Lockett 235

Joel Geiger, Department of Mathematics, LSU Graduate Student
Noncommutative prime spectra of quantum Schubert cell algebras

The quantum Schubert cell algebras defined by De Concini, Kac, and Procesi and independently by Lusztig comprise a large and versatile collection of subalgebras of the positive part of the quantized universal enveloping algebras. In this talk I will outline two major approaches to understanding the noncommutative prime spectra of the quantum Schubert cell algebras—a ring theoretic approach due to Gerard Cauchon and a representation theoretic approach due to Milen Yakimov. We answer two questions of Cauchon and Mériaux, thereby unifying the two seemingly disparate approaches. Time permitting we will also investigate a result relating this unified approach to the theory of quantum cluster algebras. This work is joint with Milen Yakimov.

Monday, November 19, 2012

Posted November 14, 2012

VIGRE@LSU: Student Colloquium Questions or comments?

2:30 pm – 3:20 pm Lockett 235

Renzo Cavalieri, Colorado State University
Counting factorizations in the symmetric group using graphs

Given a permutation x in the symmetric group and an integer r, we want to investigate the following question:

How many ways can I write x as a product of r transpositions?

This is a group theoretic question that can be answered in terms of representation theory of the symmetric group. In this talk I want to present a combinatorial approach, which provides the answer in terms of an appropriate weighted sum over certain decorated graphs which I suggestively call \"tropical covers\". This method comes from the study of an equivalent geometric question... but this is another story...

This talk is primarily aimed at undergraduate students.

There will be refreshments in the Keisler lounge from 2:00-2:30pm.

Posted October 29, 2012
Last modified March 2, 2022

VIGRE@LSU: Student Colloquium Questions or comments?

3:40 pm – 4:30 pm Room 233 Lockett

Michael Malisoff, LSU Roy P. Daniels Professor
Asymptotic Stabilization for Feedforward Systems with Delayed Feedbacks

We study a problem of state feedback stabilization of time-varying feedforward systems with a pointwise delay in the input. Our approach relies on a time-varying change of coordinates and Lyapunov-Krasovskii functionals. Our result applies for any given constant delay, and provides uniformly globally asymptotically stabilizing controllers of arbitrarily small amplitude. The closed-loop systems enjoy input-to-state stability properties with respect to additive uncertainty on the controllers. We illustrate our work using a tracking problem for a model for high level formation flight of unmanned air vehicles. We will review all of the necessary background on control theory, so no prior exposure to controls will be needed to understand this talk. This work is joint with Frederic Mazenc from INRIA in France.

Tuesday, November 20, 2012

Posted November 14, 2012

1:30 pm – 2:20 pm Lockett 235

Renzo Cavalieri, Colorado State University
A tale of Hurwitz theory

Hurwitz theory studies covers of algebraic curves by algebraic curves. It has been used as a tool for the study of the geometry of the moduli space of curves, and has appeared in the construction of toy models in string theory. Because of the \"multiple identities\" of algebraic curves (they are geometric objects, but they also are purely algebraic objects if you identify a curve with its field of functions), Hurwitz theory is by nature interdisciplinary.

In this talk I would like to present some aspects of Hurwitz theory, specifically the study of simple and double Hurwitz numbers, the connections to the geometry of the moduli space of curves, and the remarkable combinatorial structure that these numbers have.

This talk is primarily aimed at graduate students.

There will be a light lunch in the Keisler lounge from 1:00-1:30pm.

Posted November 12, 2012

3:30 pm – 4:20 pm Lockett 277

Renzo Cavalieri, Colorado State University
Polynomiality and Wall Crossings in Hurwitz Theory

Abstract: in this talk I will present a story that began with the observation of Goulden-Jackson-Vakil that families of Hurwitz numbers tend to have interesting polynomiality or piecewise-polynomiality aspects. Cavalieri-Johnson-Markwig subsequently exploited the combinatorics suggested by tropical geometry in order to gain a good understanding of this phenomena, and to be able to describe wall crossings. The story is now evolving with an attempt of lifting these observations from the level of \"numbers\" to the level of \"cycles\". Again, the parallel with tropical geometry helps shed light on the combinatorial features of certain families of Hurwitz classes. The story is understood so far in genus 0 and becomes substantially more complicated in higher genus. The most recent work discussed is joint work with Aaron Bertram and Hannah Markwig.

Wednesday, November 28, 2012

Posted September 19, 2012
Last modified November 20, 2012

4:00 pm Lockett 15

Faculty meeting: meet the Provost; visit from Dean Carman

Monday, January 7, 2013

Posted October 30, 2012
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 285

Comprehensive / PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, January 9, 2013

Posted October 30, 2012
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 285

Comprehensive / PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, January 23, 2013

Posted December 3, 2012
Last modified January 22, 2013

3:30 pm – 4:20 pm Lockett 233

Doug LaFountain, Western Illinois University
Virtual Seminar: "Links and doubling branched surfaces"

Abstract: We consider oriented links in the 3-sphere which are braided positively with respect to two different braid fibrations, and hence represent two different braid conjugacy classes for the link type. Following work of Morton, we show that these two braid fibrations may be assumed to be mutually braided with respect to each other; furthermore, after isotopies of the link which are non-increasing on braid index, the link projects onto one of a family of well-defined branched surfaces in the complement of the braid axes. Time permitting we discuss potential applications; this is joint work with Bill Menasco and Hiroshi Matsuda.

Thursday, January 24, 2013

Posted December 22, 2012
Last modified January 24, 2013

3:30 pm – 4:20 pm 277 Lockett

Tai Melcher, University of Virginia
Smoothness properties for some infinite-dimensional heat kernel measures

Abstract: Smoothness is a fundamental principle in the study of measures on
infinite-dimensional spaces, where an obvious obstruction to overcome is
the lack of an infinite-dimensional Lebesgue or volume measure. Canonical
examples of smooth measures include those induced by a Brownian motion,
both its end point distribution and as a real-valued path. Heat kernel
measure is the law of a Brownian motion on a curved space, and as such is
the natural analogue of Gaussian measure there. We will discuss some
recent smoothness results for these measures on certain natural classes of
infinite-dimensional groups, including in some degenerate settings. This
is joint work with Fabrice Baudoin, Daniel Dobbs, and Masha Gordina.

Tuesday, January 29, 2013

Posted October 9, 2012

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 338 Johnston Hall

Brittany Froese, University of Texas at Austin
Numerical Solution of the Optimal Transportation Problem Via Viscosity Solutions of the Monge-Ampere Equation

Despite the importance of optimal transportation in both theoretical and applied mathematics, the computation of solutions remains an extremely challenging problem. We describe a numerical method for the widely-studied case when the cost is quadratic and mass is being mapped onto a convex set. The solution is obtained by solving the Monge-Ampere equation, a fully nonlinear elliptic partial differential equation (PDE), coupled to a non-standard implicit boundary condition. First, we describe a variational formulation of the PDE operator, which enables us to construct a monotone finite difference discretisation. This is used as the foundation of a more accurate, almost-monotone discretisation. Next, we re-express the transport condition as a Hamilton-Jacobi equation on the boundary. We construct an upwind discretization of this equation that only requires data inside the domain. Using the theory of viscosity solutions, we prove convergence of the resulting method. A range of challenging computational examples demonstrate the effectiveness and efficiency of this method.

Posted January 21, 2013
Last modified January 28, 2013

3:30 pm – 4:30 pm Lockett 277

Christopher Dodd, University of Toronto
Modules over algebraic quantizations and representation theory

Recently, there has been a great deal of interest in the theory of modules over algebraic quantizations of so-called symplectic resolutions. In this talk I'll discuss some new work—joint, and very much in progress—that open the door to giving a geometric description to certain categories of such modules; generalizing classical theorems of Kashiwara and Bernstein in the case of D-modules on an algebraic variety.

Wednesday, January 30, 2013

Posted December 3, 2012
Last modified January 25, 2013

3:30 pm – 4:20 pm Lockett 233

Steven Sivek, Harvard
Virtual Seminar: "Donaldson invariants of symplectic manifolds"

Abstract: Donaldson proved in the late 80s that his polynomial invariants of smooth 4-manifolds are nonzero for Kaehler surfaces, and this was only recently extended to symplectic manifolds by Kronheimer and Mrowka. In this talk, we will give a new proof that symplectic 4-manifolds have nonzero Donaldson invariants. Our proof will rely on Kronheimer and Mrowka's structure theorem for manifolds of "simple type" together with some known cases of Witten's conjecture relating the Donaldson and Seiberg-Witten invariants.

Tuesday, February 5, 2013

Posted January 29, 2013

5:00 pm James E. Keisler Lounge (room 321 Lockett)

Meeting of student actuarial club

Wednesday, February 6, 2013

Posted December 3, 2012
Last modified January 28, 2013

3:30 pm – 4:20 pm Lockett 233

Tye Lidman, UT Austin
Virtual Seminar: "Left-orderability and Floer homology"

Abstract: We will study the seemingly unnatural question of when the fundamental group of a three-manifold can be given a left-invariant order. This is related to the existence of taut foliations on the manifold as well as the structure of its Heegaard Floer homology groups.

Wednesday, February 13, 2013

Posted January 22, 2013
Last modified March 2, 2021

3:30 pm – 4:20 pm Lockett 233

Anne Thomas, University of Sydney
Virtual Seminar: "Infinite reduced words and the Tits boundary of a Coxeter group"

Let (W,S) be a Coxeter system with W infinite. An infinite reduced word of W is an infinite sequence of elements of S such that each finite subsequence is a reduced word. We prove that the limit weak order on the blocks of infinite reduced words of W is encoded by the topology of the Tits boundary of the Davis complex of W. We consider many special cases, including W word hyperbolic and X with isolated flats. This is joint work with Thomas Lam.

Friday, February 15, 2013

Posted October 9, 2012
Last modified January 4, 2013

12:00 pm – 5:00 pm Saturday, February 16, 2013 Tulane University

SCALA 2013

Scientific Computing Around Louisiana 2013 Registration at http://tulane.edu/sse/ccs/news/scala-2013.cfm

Monday, February 18, 2013

Posted February 13, 2013
Last modified March 11, 2021

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:30 pm Lockett 237

Bruce Richter, University of Waterloo
On Zarankiewicz' conjecture: the crossing number of $K_{m,n}$

The problem of determining the crossing number of $K_{m,n}$ dates back at least to the Second World War. The conjectured value of $$\left\lfloor \mathstrut\frac{\mathstrut m}{\mathstrut 2}\right\rfloor \left\lfloor \frac{m-1}2\right\rfloor \left\lfloor \frac{\mathstrut n}{\mathstrut 2}\right\rfloor \left\lfloor \frac{n-1}2\right\rfloor$$ is achievable by a drawing. Two proofs that the conjecture is right were published in the early 1950's, but recognized in the 1960's to have fatal gaps. Kleitman showed in 1970 that the conjecture holds when $\min(m,n)\le 6$. More recent computer work with a related convex program has verified the conjecture for the pairs $(m,n)$ with $m=7,8$ and $n=7,8,9,10$ and provided improved lower bounds for the crossing number of $K_{m,n}$.

This talk takes the convex program approach one step further and shows that, for each $m$, either the conjecture is correct for $m$ or there is an explicit function $f(m)$ so that a counterexample exists with $n \le f(m)$.

Tuesday, February 19, 2013

Posted January 22, 2013
Last modified January 25, 2013

1:30 pm – 2:30 pm Lockett 237

Sylvester's 4-point problem and straight line drawings of the complete graph $K_n$

Abstract: In the 1880's, Sylvester raised the following question: if we pick 4 points at random from the Euclidean plane, what is the probability that they make a convex quadrilateral? Equivalently, what is the probability that one point is inside the triangle formed by the other three? We will make this question more precise in the talk.

A problem in graph theory is to determine, over all sets of $n$ points in the plane, no three collinear, the smallest number $f(n)$ of crossings of the $\binom n2$ straight line segments joining all pairs of these $n$ points. It is easy to see that no crossings are required for $n\le 4$, $f(5)=1$, $f(6)=3$, $f(7)=9$.

In a beautiful paper, Scheinerman and Wilf show that the answer to Sylvester's question is $\lim_{n\to\infty} f(n)/\binom n4$. This will be the main content of this talk.

This talk is primarily aimed at undergraduate students. There will be a light lunch before the talk at 1:00pm in the Keisler Lounge.

Wednesday, February 20, 2013

Posted January 22, 2013
Last modified January 25, 2013

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:30 pm Lockett 237

Bruce Richter, University of Waterloo
Embedding a Peano continuum in a surface

Abstract: It has been known since the 1930's that a Peano continuum (that is, a connected, compact, metric space) embeds in the sphere if and only if it does not contain the finite graphs $K_{3,3}$ and $K_5$ and two other particular continua $\mathfrak T_1$ and $\mathfrak T_2$. The spaces $\mathfrak T_i$ are closely related to the ``thumbtack space" consisting of a closed disc together with an line segment having one end at the centre of the disc, but otherwise disjoint from the disc. In this talk, we consider the same question for embedding a Peano continuum into a surface (that is, a connected, compact, 2-dimensional manifold).

The main result is that a Peano continuum $C$ embeds in a surface $\Sigma$ unless it contains one of:

1. A finite graph that does not embed in $\\Sigma$;

2. A surface of smaller genus than $\Sigma$;

3. The disjoint union of $\Sigma$ and a point; and

4. The continua $\mathfrak T_1$ and $\mathfrak T_2$.

This talk is primarily aimed at graduate students. There will be refreshments before the talk at 3:00pm in the Keisler Lounge.

Monday, February 25, 2013

Posted November 26, 2012
Last modified March 2, 2022

3:30 pm – 4:30 pm Lockett 233

Timothy Healey, Cornell University Professor of Mathematics and Mechanical and Aerospace Engineering
Nonlinear problems for thin elastic structures and the ubiquitous isola bifurcation

We begin with a simple 1-dimensional, 2-phase solid under "hard" tensile end loading in the presence of inter-facial effects. This is equivalent to a phase-field model, of the van der Waals-Cahn-Hilliard type, that illustrates well the concept of an isola bifurcation. Roughly speaking, the latter corresponds to the nucleation, growth, decay and eventual disappearance of a stable, inhomogeneous solution (representing here a phase mixture) as the loading parameter is monotonically increased. We then present results for three ostensibly distinct problems (models) - all exhibiting this same isola-bifurcation phenomenon: (i) twining in shape-memory solids; (ii) two-phase configuration of GUV's (fluid-elastic shell models of lipid-bilayer vesicles); (iii) wrinkling of highly stretched, finely thin rectangular sheets.

Wednesday, February 27, 2013

Posted February 26, 2013

2:30 pm – 3:20 pm Lockett 285

Simon Pfeil, Louisiana State University
Unbreakable Matroids

A matroid M is unbreakable if M/F is connected for all flats F of M. It is not difficult to show that M is unbreakable if and only if M* has no two skew circuits. This talk will discuss some properties of unbreakable matroids and, in particular, will describe all regular unbreakable matroids.

Saturday, March 2, 2013

Posted October 10, 2012

9:00 am Turead Hall

LSU Math High School Contest

Tuesday, March 5, 2013

Posted November 30, 2012
Last modified January 4, 2013

3:30 pm – 4:30 pm 338 Johnston Hall

Weinan E, Princeton University
Modeling Rare Events

Many important dynamic processes in physics, biology, chemistry and material science can be viewed as being rare events. These events are difficult to model due to the disparity of the time scales involved. From an abstract viewpoint, this can be formulated as the problem of navigating a system over its energy landscape. We will discuss the theoretical framework for describing such events, as well as the numerical algorithms that have been developed. We will discuss applications to problems that arise in material science, chemistry and fluid mechanics.

Wednesday, March 6, 2013

Posted August 24, 2012
Last modified February 25, 2013

4:00 pm Lockett 232

Tenured Faculty Meeting

Thursday, March 7, 2013

Posted September 11, 2012
Last modified February 25, 2013

3:30 pm – 4:20 pm Lockett 277

Nicholas Ercolani, University of Arizona
Conservation Laws in Random Matrix Theory

ABSTRACT: Analytical Combinatorics is an old subject (going back at least to Euler) which has received renewed impetus from several directions including complex systems theory, large scale computation, quantum gravity and non-equilibrium statistical mechanics. In particular methods from nonlinear PDE theory, both deterministic and stochastic, have begun to play a significant role in advancing this classical subject. In this talk we will discuss some very recent developments that bring to bear methods for studying systems of conservation laws on the asymptotic analysis of generating functions for "maps". A "random map" is a random topological tessellation of a Riemann surface. These are combinatorial objects that first arose in attempts to solve the four color problem but soon thereafter took on a life of their own. Subsequently, physicists working on the unification of the "strong" and "weak" forces discovered that generating functions for maps emerge naturally in the enumeration of Feynman diagrams for random unitary matrix ensembles. Our recent work provides the means for the explicit evaluation of map generating functions in terms of closed form solutions of the aforementioned conservation laws. These conservation laws are certain continuum limits of the Toda lattice differential equations in which the time variables are coupling coefficients of the random matrix ensembles. This topic brings together many areas of pure and applied mathematics and we will describe some of these bridges.

Posted February 24, 2013

4:30 pm James E. Keisler Lounge (room 321 Lockett)

Meeting of student actuarial club

The meeting will include a short talk about life tables and Exam MLC/3L by Professor Larry Smolinsky.

Friday, March 8, 2013

Posted May 3, 2012
Last modified January 4, 2013

Algebra and Number Theory Seminar Questions or comments?

12:30 pm – 6:00 pm Saturday, March 9, 2013 Energy, Coast & Environment Building, Dalton J. Woods Auditorium, Rotunda.

Spring 2013 Finite Element Circus and Rodeo

Details and registration at: http://www.cct.lsu.edu/events/finite-element-circus-rodeo

Tuesday, March 12, 2013

Posted March 5, 2013

3:30 pm – 4:20 pm Lockett 277

Ulrica Wilson, Morehouse College
Noncommutative division rings from Hamiliton to Albert to now

Thanks in large part to Galois, much is known about commutative division rings (aka fields). In this talk we will present some of the history, recent results, and open problems in the study of noncommutative division rings.

Wednesday, March 13, 2013

Posted March 5, 2013
Last modified March 3, 2021

2:30 pm – 3:20 pm Lockett 235

Luke Postle, Emory University
Linear Isoperimetric Bounds for Graph Coloring

We will discuss how linear bounds in graph coloring lead to new and interesting results. To that end, we say a family F of graphs embedded in surfaces is hyperbolic if for every G in F and for every closed curve Y that intersects G only in vertices and bounds an open disk D, we have that |V(G) (intersect) D| <= O(|V(G) (intersect) Y|). This says that the number of vertices inside such an open disk is linear in the number of vertices on the boundary of that disk (counted with multiplicities). Similarly we say that a family F is strongly hyperbolic if the same holds for every annulus D. Being strongly hyperbolic has a number of interesting consequences. Foremost is the fact that the number of vertices of a graph in a strongly hyperbolic family is linear in the Euler genus of the surface. This gives rise to a linear-time algorithm for testing whether a graph on a fixed surface contains a member of F.

The concept of hyperbolicity unifies and simplifies a number of known results about coloring graphs on surfaces while resolving some open conjectures. Robin Thomas and I recently proved that the family of 6-list-critical graphs is strongly hyperbolic. In particular, the theory of strongly hyperbolic families then implies that the number of 6-list-critical graphs on a fixed surface is finite, resolving a conjecture of Thomassen from 1997. It also follows that locally planar graphs with distant precolored vertices are 5-choosable. For the plane, this was conjectured by Albertson in 1999 and recently resolved by Dvorak, Lidicky, Mohar and Postle. Furthermore, we can prove that locally planar graphs drawn in a surface with crossings far apart are 5-choosable which generalizes a result of Dvorak, Lidicky and Mohar for the plane. We also resolve a conjecture of Thomassen that a 5-list-colorable graph has exponentially many 5-list-colorings which he proved for planar graphs.

I have also recently proved that the family of 4-list-critical graphs of girth at least five is strongly hyperbolic. This implies a few interesting results, and provides a simplified proof of Havel's conjecture that a planar graph with triangles far enough apart is 3-colorable.

Based on joint work with Robin Thomas.

Posted January 22, 2013
Last modified March 5, 2013

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 233

Clayton Shonkwiler, University of Georgia
Virtual Seminar: "The geometry and topology of random polygons"

Abstract: What is the expected shape of a random closed curve in space? For example, what is the expected radius of gyration or expected total curvature? What is the likelihood that the curve is knotted? As a first step, what are the corresponding answers when I restrict to closed n-gons in space? Aside from purely mathematical interest, such questions are natural in the context of statistical physics since n-gons in space are simple models for ring polymers with n monomers in solution. When we restrict attention to equilateral n-gons such questions become quite challenging, even numerically: current algorithms for sampling equilateral n-gons use a Markov process which "folds" polygons while preserving closure and edgelengths and are only expected to converge in O(n^3) time. The main point of this talk is that a much better sampling algorithm and indeed much better answers are available if we widen our view to the space of n-gons in three dimensional space of fixed total length (rather than with fixed edgelengths). I will describe a natural probability measure on n-gons of total length 2 which is pushed forward from the standard measure on the Stiefel manifold of 2-frames in complex n-space using methods from algebraic geometry. We can directly sample the Stiefel manifold in O(n) time, which gives us a fast, direct sampling algorithm for closed n-gons via the pushforward map. We can also explicitly compute the expected radius of gyration and expected total curvature and even recover some topological information. This talk describes joint work primarily with Jason Cantarella (University of Georgia) and Tetsuo Deguchi (Ochanomizu University).

Thursday, March 14, 2013

Posted March 6, 2013

3:30 pm – 4:20 pm Lockett 277

Amber Russell, University of Georgia
Cuspidal local systems and a decomposition involving perverse sheaves on the nilpotent cone

In a recent paper, Achar uses hyperbolic localization to give an orthogonal decomposition of the category of constructible sheaves on the nilpotent cone. In particular, he decomposes this category into those arising from the Springer sheaf and those not. In this talk, I will discuss the ongoing project to refine this decomposition using central character properties and Lusztig\'s cuspidal local systems. This is joint work with Laura Rider.

Friday, March 15, 2013

Posted December 22, 2012
Last modified March 15, 2013

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:20 pm Lockett 285

Julian Hook, Indiana University, Bloomington
Graph Theory and the Musical Tonnetz

Note: This colloquium is held on a Friday.

Monday, March 18, 2013

Posted March 12, 2013
Last modified March 14, 2013

12:30 pm – 1:20 pm Lockett 285

Michael Orrison, Harvey Mudd College
Generalizing the Condorcet Criterion

There will be a light lunch in the Keisler lounge from 12:00-12:30.

The Condorcet Criterion is relatively straightforward: In an election, if there is a candidate who would beat every other candidate in a head-to-head race, then that candidate should be declared the winner. In this talk, I\'ll describe a natural family of generalizations of the Condorcet Criterion that led us to some unexpected questions and answers concerning forbidden \"words of generalized Condorcet winners.\" This is joint work with Aaron Meyers, Jen Townsend, Sarah Wolff, and Angela Wu.

This talk is primarily aimed at undergraduate students.

Tuesday, March 19, 2013

Posted March 12, 2013
Last modified March 14, 2013

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:20 pm Lockett 285

Michael Orrison, Harvey Mudd College
Doubly Adapted Bases for the Symmetric Group

There will be refreshments in the Keisler lounge from 3:00-3:30.

Abstract: Adapted bases play an important computational role in many applications of the representation theory of finite groups. In this talk, I will describe an interesting \"doubly adapted\" (with respect to the usual left action and right action) basis for the regular representation of the symmetric group. I will then explain why we think such bases might be the key to a new approach to creating fast Fourier transforms for finite groups. This is joint work with Mike Hansen and Masanori Koyama.

This talk is primarily aimed at graduate students.

Wednesday, March 20, 2013

Posted January 29, 2013
Last modified March 21, 2013

3:30 pm – 4:20 pm Lockett 233

Margaret Doig, Indiana University
Virtual Seminar: "Obstructing finite surgery"

Abstract: We will discuss using Heegaard Floer invariants towards a partial classification of Dehn surgery on knots $K$ in $S^3$ which give elliptic manifolds $Y$ other than the lens spaces, sometimes called \emph{finite, non-cyclic surgeries}. Recent results using these techniques include: if $p<10$ and $K$ is hyperbolic, there are no such $Y$; for any fixed $p$, there are at most finitely many $Y$ given by any $p/q$-surgery; if $p\leq4$, there is a unique $p/q$-surgery (up to orientation) that gives an elliptic manifold, other than a lens space (for $g=1$, this was previously proved by Ghiggini: the surgery is $+1$ on the right-handed trefoil, and the manifold is the Poincar\'e homology sphere).

Thursday, March 21, 2013

Posted February 27, 2013
Last modified March 11, 2013

3:30 pm – 4:20 pm Lockett 277

Ilya Spitkovsky, College of William and Mary
The current state of the almost periodic factorization

Factorization of matrix functions (that is, their representation as products of multiples analytic inside and outside the given closed curve) arises naturally in many applications, including those to convolution type equations on a half-line (the classical Wiener-Hopf method). As it happens, the equations on finite intervals also can be treated via the factorization method. The resulting matrix functions, however, are of oscillating type, which has not been treated until recently. The general case can be boiled down to the situation when the matrix is almost periodic, that is, its elements belong to the algebra generated by exp(iax) with real values of the parameter a. We will discuss the current state of the factorization problem for such matrices. A special attention will be paid to a (seemingly narrow) case of 2-by-2 triangular matrix functions, but even for them the factorability properties remain a mystery. in striking difference with both the scalar almost periodic case and the classical Wiener-Hopf setting.

Posted March 15, 2013
Last modified March 18, 2013

4:30 pm Lockett 9

Meeting to discuss hiring

Monday, March 25, 2013

Posted March 19, 2013
Last modified March 3, 2021

3:30 pm – 4:20 pm Lockett 284

Karl Heinrich Hofmann, Darmstadt University, Germany Professor Emeritus
Transitive actions of a compact group on a locally contractible space: a Theorem by Janos Szenthe revisited and recast

In 1974, J. Szenthe published a theorem according to which a compact group which acts faithfully and transitively on a locally contractible space is a Lie group. This theorem was widely used in the sequel. In 2011, Sergey Antonyan discovered that one lemma claimed and essentially used in the original presentation was irretrievably false. So Szenthe's important theorem was open again. I shall report how in a joint paper with Linus Kramer of the University of Münster (Germany) a proof of Senthe's theorem recovers the result as originally stated. Antonyan and Dobrowolski submitted a paper a few days ago which presents a proof different from ours. A preprint of A. A George Michael surfaced in November of last year with another proof similar to theirs.

Wednesday, April 3, 2013

Posted January 24, 2013
Last modified March 2, 2021

3:30 pm – 4:20 pm tba

Matthew Dawson, Centro de Investigacion en Matematicas
TBA

Wednesday, April 10, 2013

Posted March 20, 2013
Last modified April 8, 2013

2:30 pm – 3:20 pm Lockett 235

Kimberly D'souza, Louisiana State University
Excluding the Pyramid

A very important problem in graph minors research is to characterize Petersen-free and $K_6$-free graphs, both of which are graphs on 15 edges. These two problems have remained unsolved using current methods. Study of smaller graphs produces new methods for approaching this type of problem. This talk looks at the Pyramid graph, a graph on 12 edges. This graph has a special connectivity, namely the graph is (4,4)-connected. We exploit this property of the graph to develop a means of characterizing all Pyramid-free graphs.

Posted April 8, 2013
Last modified March 2, 2021

3:30 pm – 4:20 pm Lockett 233

Sam Nelson, Claremont McKenna College
Virtual Seminar: "Rack and Birack Module Invariants"

In 2002, Andruskiewitsch and Graña defined an algebra $R[x]$ associated to a rack $X$ and used it to generalize rack homology. In recent work we have extended the rack algebra to the cases of biracks and twisted virtual biracks. In this talk we will see new invariants of knots and links defined from modules over these algebras.

Posted January 24, 2013
Last modified April 10, 2013

3:30 pm – 4:20 pm Lockett 284

Joachim Hilgert, Paderborn University
Fock spaces and small representations

Thursday, April 11, 2013

Posted December 22, 2012
Last modified March 14, 2013

3:30 pm – 4:20 pm Lockett 277

Sam Nelson, Claremont McKenna College
Enhancements of Counting Invariants

Abstract: Counting invariants are among the simplest computable invariants of knots and links. In this talk we will see various strategies for enhancing and strengthening counting invariants and some connections between these invariants and other knot and link invariants.

Monday, April 15, 2013

Posted March 8, 2013
Last modified March 2, 2022

Student Combinatorics Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 233
(Originally scheduled for Monday, March 11, 2013)

Stefan Llewellyn Smith, University of California, San Diego
Hollow Vortices

Hollow vortices are vortices whose interior is at rest. They posses vortex sheets on their boundaries and can be viewed as a desingularization of point vortices. After giving a history of point vortices, we obtain exact solutions for hollow vortices in linear and nonlinear strain and examine the properties of streets of hollow vortices. The former can be viewed as a canonical example of a hollow vortex in an arbitrary flow, and its stability properties depend. In the latter case, we reexamine the hollow vortex street of Baker, Saffman and Sheffield and examine its stability to arbitrary disturbances, and then investigate the double hollow vortex street. Implications and extensions of this work are discussed.

Wednesday, April 17, 2013

Posted April 15, 2013

2:30 pm – 3:20 pm Lockett 235

Dennis Hall, Department of Mathematics, LSU Graduate Student
An Introduction to Tangle Matroids

Posted October 2, 2012
Last modified April 3, 2013

Pasquale Porcelli Lecture Series Special Lecture Series

4:30 pm – 5:20 pm Design Building, Room 103

S. R. S. Varadhan, Courant Institute National Medal of Science (2010), Abel Prize (2007)
What is large deviations?

Thursday, April 18, 2013

Posted October 2, 2012
Last modified April 3, 2013

Pasquale Porcelli Lecture Series Special Lecture Series

4:30 pm – 5:20 pm Design Building, Room 103

S. R. S. Varadhan, Courant Institute National Medal of Science (2010), Abel Prize (2007)
Scaling limits of large systems

Friday, April 19, 2013

Posted October 2, 2012
Last modified April 3, 2013

Pasquale Porcelli Lecture Series Special Lecture Series

4:30 pm – 5:20 pm Design Building, Room 103

S. R. S. Varadhan, Courant Institute National Medal of Science (2010), Abel Prize (2007)
Counting Graphs

Monday, April 22, 2013

Posted April 18, 2013

Harmonic Analysis/Representation Theory Student Seminar

2:30 pm – 3:30 pm Lockett 235

Lucius Schoenbaum, LSU
Influence of the Murray von-Neumann Classification on Harmonic Analysis

Abstract: During the 1930\'s Murray and von Neumann published a reduction and classification theory for rings of operators now usually known as von Neumann algebras. In this talk we will discuss how this work influenced subsequent developments in harmonic analysis, specifically on theorems of Plancherel type for noncommutative groups. This talk may continue on Monday 4/29 (same time and place).

Posted February 23, 2013
Last modified April 9, 2013

3:30 pm Lockett 233

Daniel Onofrei, University of Houston
Active control of acoustic and electromagnetic fields

The problem of controlling acoustic or electromagnetic fields is at the core of many important applications such as, energy focusing, shielding and cloaking or the design of supper-directive antennas. The current state of the art in this field suggests the existence of two main approaches for such problems: passive controls, where one uses suitable material designs to control the fields (e.g., material coatings of certain regions of interest), and active control techniques, where one employs active sources (antennas) to manipulate the fields in regions of interest. In this talk I will first briefly describe the main mathematical question and its applications and then focus on the active control technique for the scalar Helmholtz equation in a homogeneous environment. The problem can be understood from two points of view, as a control question or as an inverse source problem (ISP). This type of ISP questions are severely ill posed and I will describe our results about the existence of a unique minimal energy solution. Stability of the solution and extensions of the results to the case of nonhomogeneous environment and to the Maxwell system are part of current work and will be described accordingly.

Posted April 18, 2013

Algebra and Number Theory Seminar Questions or comments?

4:30 pm – 5:30 pm Keisler Lounge, Lockett Hall 321

Richard Frnka, Department of Mathematics, LSU Graduate Student
Programming In Python

Abstract: Don\'t have any programming experience? Python is perfect for you! Have lots of programming experience? Python is perfect for you! This talk will introduce the language and highlight the advantages of using Python. Some basic concepts and math examples will be shown, along with a demonstration of some interesting algorithms.

Tuesday, April 23, 2013

Posted March 12, 2013
Last modified January 10, 2022

3:30 pm – 4:20 pm Lockett 277

Peter Samuelson, University of Toronto
Skein modules and the double affine Hecke algebra

The Kauffman bracket skein module is a vector space $K_q(M)$ associated to a 3-manifold $M$ and a parameter $q\in C^*$. We recall an old theorem which states that the colored Jones polynomials $J_n(q, K)\in C[q,q^{-1}]$ of a knot $K$ in $S^3$ can be computed from $K_q(S^3\setminus K)$. We also describe a theorem of Frohman and Gelca which shows that $K_q(S^3\setminus K)$ is a module over the $Z_2$-invariant subalgebra of the quantum torus $A_q$. This subalgebra is the specialization at $t=1$ of the double affine Hecke algebra $H(q,t)$, which is a 2-parameter family of algebras. We discuss deformations of $K_q(S^3\setminus K)$ to a 2-parameter family of modules over $H(q,t)$. Conjecturally, these lead to 2-variables polynomials $J_n(q,t,K)$ which specialize to the colored Jones polynomials when $t=1$. (All terms in this abstract will be defined, and this is work in progress with Yuri Berest.)

Wednesday, April 24, 2013

Posted March 21, 2013

2:30 pm – 3:20 pm Lockett 235

Trevor McGuire, Louisiana State University
The Combinatorics of Ideals with Binomial and Monomial Generators

For nearly 200 years, invariant theory has had some place in mathematics; sometimes it has been at the forefront, and other times it was nearly forgotten. Since Kung and Rota said, "Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics" in 1984, new tools have been applied to the field and it is strong once again. In particular, much research has been done in applying tools from commutative algebra and combinatorics to the theory of monomial and binomial ideals. In fact, in their 2005 book, Combinatorial Commutative Algebra, Miller and Sturmfels put the new branch of math on firm footing, and extensively outlined the combinatorial theory behind free resolutions of monomial ideals and binomial ideals.

When one reads the separate theories, though, it is clear that they are distantly related, but the current literature does not outline the connection between the two. In this talk, we will give exactly the relation between the two, and in particular, we will discuss free resolutions of ideals that have monomial and binomial generators, and show that the new theory reduces to the two known theories. We will begin with an overview of resolutions and primarily discuss concrete examples on our way to the statement of the overarching theorem.

Posted April 15, 2013

4:30 pm James E. Keisler Lounge - 321 Lockett

Actuarial Student Association Meeting

We have a guest speaker, David Ellsworth from Startmount Insurance Co.

Thursday, April 25, 2013

Posted April 12, 2013
Last modified April 18, 2013

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm Lockett B9

Faculty meeting to approve changes to the catalog, affecting both UG and Grad courses

Wednesday, May 1, 2013

Posted April 17, 2013
Last modified April 19, 2013

12:30 pm – 1:30 pm Lockett 277

Mihaela Dobrescu, Christopher Newport University
Bee Hives, Pennies, Needles, and Harmonic Analysis - Part I

There will be a light lunch at 12:00 before the talk in the Keisler Lounge.

Analysis problems in general, and harmonic analysis problems in particular can lead to purely geometric problems, while geometric questions are often tackled via analytic methods. In these two talks, we will investigate some older and newer problems, some closed, some still open, in geometrical analysis and their connections with analysis and harmonic analysis, and other branches of mathematics.

This talk is primarily aimed at undergraduates. Prerequisites are only some multivariable calculus and geometric intuition.

Posted April 15, 2013
Last modified April 29, 2013

VIGRE@LSU: Student Colloquium Questions or comments?

2:30 pm – 3:20 pm Lockett 235

Kwang Ju Choi, LSU
A characterization of almost all minimal not nearly planar graphs

In this work, we define nearly planar graphs G to be planar graphs or have an edge e such that G\\e is planar. The class of nearly planar graphs is not minor-closed, but is closed under topological minors. Since we can make a trivial infinite series of planar graphs using parallel subdivision, we define a relation between two graphs which is an extension of the topological minor relation. We define M to be the minimal excluded class of nearly planar graphs under our relation. We prove that all members of M, except finitely many, contain a Mobius ladder and are made by three blocks.

Posted March 30, 2013

Spring Awards Ceremony

3:30 pm Keisler Lounge, third floor Lockett

Departmental Spring Awards Ceremony

Thursday, May 2, 2013

Posted April 17, 2013
Last modified April 19, 2013

3:30 pm – 4:20 pm Lockett 285

Mihaela Dobrescu, Christopher Newport University
Bee Hives, Pennies, Needles, and Harmonic Analysis - Part II

There will be refreshments at 3:00pm before the talk in the Keisler lounge.

Analysis problems in general, and harmonic analysis problems in particular can lead to purely geometric problems, while geometric questions are often tackled via analytic methods. In these two talks, we will investigate some older and newer problems, some closed, some still open, in geometrical analysis and their connections with analysis and harmonic analysis, and other branches of mathematics.

This talk will be primarily aimed at graduate students. However, undergraduates or anyone with a geometrical intuition are encouraged to attend.

Posted March 18, 2013

Memorial celebration for Charlie Egedy

5:19 pm Lockett 2

A celebratioin of the life of Charlie Egedy

Monday, May 13, 2013

Posted May 8, 2013
Last modified October 1, 2021

3:30 pm Lockett 233

Guillermo Ferreyra, Mathematics Department, LSU
The Future of Analysis at LSU

SCI Data [PDF]
Letter from Provost [DOCX]

Tuesday, May 14, 2013

Posted May 7, 2013
Last modified May 13, 2013

3:30 pm Lockett 277

Arithmetic invariants: From finite groups to modular categories

Richard Ng, Iowa State University, visiting Cornell University

Thursday, May 16, 2013

Posted May 10, 2013
Last modified May 13, 2013

Algebra and Number Theory Seminar Questions or comments?

8:30 am Johnston Hall 338 (Training Room)

Around Lusztig's conjecture: Arithmetic problems in representation theory, combinatorics and geometry.

Peter Fiebig, Erlangen University, Germany will present a \"virtual colloquium\"

The early time 8:30 AM is to accommodate the 7-hour time difference between here and Germany.

Monday, June 3, 2013

Posted May 17, 2013
Last modified September 17, 2021

2:00 pm – 3:00 pm Lockett 277

Daniel Sternheimer, Rikkyo University & Institut de Mathématiques de Bourgogne
Altneuland in mathematical particle physics: back to the drawing board??

We describe work in progress and outline a "framework for conjectural frameworks" based on Flato's deformation philosophy, on joint works with or by Flato and coworkers (especially Fronsdal) since the 60's, and on discussions with many mathematicians and physicists in the past years. Namely we return to the old problem of connection between external (Poincaré group) and internal (unitary) symmetries of elementary particles but with a (Drinfeld) twist, suggesting that the internal symmetries might emerge from deforming to Anti de Sitter SO(2,3) and quantizing that (possibly in a new generalized manner) at root of unity. That raises challenging problems, both on the mathematical part and for particle physics.

There is also a longer version of the abstract.

Monday, July 15, 2013

Posted June 20, 2013

3:30 pm Lockett 381

Toshihisa Kubo
Construction of explicit homomorphisms between generalized Verma modules

Abstract: In this talk we study constructions of explicit homomorphisms between generalized Verma modules(equivalently, to construct explicit covariant differential operators between homogeneous vector bundles). We in particular show that there is a certain connection between constructions of such homomorphisms and a classic work of Wallach on the analytic continuation of holomorphic discrete series representations.

Monday, August 19, 2013

Posted October 30, 2012
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 284

Comprehensive / PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Posted August 11, 2013

3:30 pm Keisler Lounge

Welcome tea for new graduate students

Wednesday, August 21, 2013

Posted August 13, 2013
Last modified August 16, 2013

1:00 pm Keisler Lounge

Dan Linville, WebAssign
All your WebAssign questions answered

Posted May 1, 2013
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 284

Comprehensive / PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, August 23, 2013

Posted May 1, 2013
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 284

Comprehensive / PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Tuesday, September 3, 2013

Posted August 28, 2013
Last modified March 2, 2021

3:30 pm – 4:20 pm Lockett 285

Phuc Nguyen, Department of Mathematics, Louisiana State University
Capacities, nonlinear Calderón-Zygmund theory, and PDEs with power nonlinearities

We discuss the solvability of fully nonlinear and quasilinear equations of Lane-Emden type, quasilinear equations of Riccati type, and stationary Navier-Stokes equations with strongly singular external forces. Complete characterizations of existence will be given in connection with the theory of capacities, weighted norm inequalities, and a nonlinear version of Calderón-Zygmund theory for singular integrals. Removable singularities of Lane-Emden type equations will be described along with the stability of the stationary Navier-Stokes equation. This talk is based on joint work with Igor E. Verbitsky, Tadele Mengesha, and Tuoc Van Phan.

Thursday, September 5, 2013

Posted August 4, 2013
Last modified August 29, 2013

Student Harmonic Analysis/Representation Theory Seminar

4:00 pm Lockett 005

faculty meeting with dean

Wednesday, September 11, 2013

Posted September 6, 2013

3:30 pm Lockett 235

Matthew Dawson, Centro de Investigacion en Matematicas
Introduction to invariant means and applications to harmonic analysis, Part I

The study of harmonic analysis and representation theory on locally compact groups depends heavily on the existence of translation-invariant measures, called Haar measures, for such groups. Unfortunately, many interesting topological groups (e.g., infinite-dimensional Lie groups) are not locally compact and do not possess Haar measures. In this talk we discuss an alternate structure, called an invariant mean, which in some ways forms as a replacement for Haar measure. Groups which possess invariant means are called ``amenable\'\' and have many interesting properties related to such varied topics as the Banach-Tarski paradox, fixed point theorems, and the existence of a sort of ``Plancherel Theorem\'\' for some infinite-dimensional Lie groups.

Posted September 3, 2013

3:30 pm James E. Keisler Lounge (room 321 Lockett)

meeting of student actuarial club

Semester activities will be discussed including forming study groups and finding internships. Advice for students in the Actuarial Concentration. Selection of a new vice president. Pizza will be served.

Posted July 25, 2013
Last modified August 27, 2013

3:30 pm Lockett 277

Troy Schaudt, Wolfram Research
New Features in Computing and Teaching with Mathematica

Thursday, September 12, 2013

Posted August 27, 2013
Last modified September 7, 2013

3:30 pm Lockett 285

Oliver T. Dasbach, Mathematics Department, LSU
Knots, hyperbolic volume, and q-series

There will be refreshments in the Keisler lounge at 3 pm

Monday, September 16, 2013

Posted September 11, 2013
Last modified September 13, 2013

Kenilworth Math Club

3:30 pm – 6:30 pm James E. Keisler Lounge (room 321 Lockett)

Kenilworth Science and Technology Charter School

Tuesday, September 17, 2013

Posted August 27, 2013
Last modified September 16, 2013

3:30 pm Lockett 285

Stephen Shipman, Mathematics Department, LSU
Embedded Eigenvalues and Resonance in Quantum Graphs

A locally perturbed periodic graph operator admits bands of continuous spectrum as well as discrete eigenvalues corresponding to defect states. Under generic conditions, the eigenvalues lie in the gaps between the spectral bands. The obstruction to eigenvalues embedded in the continuous spectrum is algebraic--namely, that a generic polynomial in several variables does not factor. The polynomial in question comes from the Floquet transform of the operator; its zero set, called the Fermi surface, describes the admissible quasi-momenta for a given energy. I will show that there is an interesting class of quantum graphs possessing symmetries that allow the Fermi surface to separate for all frequencies. This separation allows one to construct embedded eigenvalues that result in complex resonant scattering when excited by radiation states of the surrounding continuous spectrum.

There will be refreshments in the Keisler lounge at 3 pm.

Wednesday, September 18, 2013

Posted September 10, 2013
Last modified September 11, 2013

3:30 pm – 4:20 pm Lockett 235

Matthew Dawson, Centro de Investigacion en Matematicas
Conical Representations of Direct-Limit Groups

Abstract: Motivated in part by physics, infinite-dimensional Lie groups have been studied more deeply over the past few decades. Due partially to the fact that they are not locally compact and thus do not possess Haar measures, there is currently no general theory of representations and harmonic analysis for infinite-dimensional Lie groups. However, much progress has been made in specific cases. In particular, direct limits of (finite-dimensional) Lie groups provide the simplest examples of infinite-dimensional Lie groups. We overview of some of some of the surprising properties of direct-limit groups and present some recent results related to the classification of conical and spherical representations for direct limits of compact Riemannian symmetric spaces.

Thursday, September 19, 2013

Posted August 27, 2013
Last modified September 10, 2013

3:30 pm Lockett 285

Hongchao Zhang, Louisiana State University
Recent Advances on Gradient Methods in Nonlinear Optimization

Abstract: In this talk I would briefly talk about some recently developed gradient-based algorithms for smooth unconstrained optimization, for smooth and nonsmooth composite optimization, for optimization with inexact gradients, and for general smooth nonlinear programming. The convergence properties as well as practical performance of some of these algorithms will be discussed in this talk.

There will be refreshments in the Keisler lounge at 3pm

Monday, September 23, 2013

Posted September 23, 2013

Kenilworth Math Club

3:30 pm – 5:30 pm James E. Keisler Lounge (room 321 Lockett)

Kenilworth Science and Technology Charter School

Tuesday, September 24, 2013

Posted August 27, 2013
Last modified September 13, 2013

3:30 pm Lockett 285

Blaise Bourdin, Department of Mathematics, Louisiana State University
The variational approach to fracture: recent developments and extensions.

Most models for the fracture of brittle materials rely on an energetic argument, the celebrated Griffith criterion, combined with ad-hoc branching criteria. In addition, such models rely heavily on smoothness and regularity assumptions whose validity is debatable. The variational approach to fracture was developed as an extension of Griffith criterion preserving its essence, competition between surface and volume energy, while avoiding any ad-hoc branching criterion or regularity hypothesis of fracture sets, in space or time. It is formulated as a sequence of unilateral global minimization problems of a free discontinuity energy. I will first recall some elements of the mathematical analysis of this approach. I will then describe its numerical implementation, focusing on methods based on elliptic regularization. I will finally show how this approach can be used in many applications, including transverse fracture and debonding of thin films, drying of colloidal suspension, thermal shocks of glass and ceramics, dynamic fracture and hydraulic stimulation. I will describe the mathematical and algorithmic tools developed for each specific problem, and present validation and verification experiments.

There will be refreshments in the Keisler lounge at 3 pm

Wednesday, September 25, 2013

Posted September 18, 2013

3:30 pm James E. Keisler Lounge (room 321 Lockett)

meeting of student actuarial club

Presentations by Adam Burmaster and Nick Crifasi.

Posted September 19, 2013

4:30 pm – 5:20 pm Lockett 235

Dillon Mayhew, Victoria University of Wellington, NZ
Characterizing representable matroids

Matroids abstract the notions of linear/geometric/algebraic dependence. More specifically, a matroid consists of a finite collection of points, and a distinguished family of dependent subsets. If we take a finite collection of vectors from a vector space, and distinguish the linearly dependent subsets, then the result is a matroid, and we say that such a matroid is representable. The original motivating problem in matroid theory involves deciding which matroids are representable and which are not. A large fraction of the research in the area has been driven by this problem.

This talk will be an introduction to matroid theory, and a survey of recent developments in the characterization of representable matroids. The focus will be on excluded-minor characterizations and formal languages. No knowledge of matroids will be assumed.

Thursday, September 26, 2013

Posted August 27, 2013
Last modified September 23, 2013

Student Harmonic Analysis/Representation Theory Seminar

Lockett 285

Pallavi Dani, Department of Mathematics, LSU
Filling invariants for groups

Any finitely generated group can be endowed with a natural metric which is unique up to maps of bounded distortion, i.e. quasi-isometries. A central question in geometric group theory is to classify finitely generated groups up to quasi-isometry. I will talk about recent work on understanding quasi-isometry invariants for groups in various settings, with an emphasis on filling invariants, a class of invariants that are motivated by classical isoperimetric inequalities.

There will be refreshments in the lounge at 3 pm

Monday, September 30, 2013

Posted September 23, 2013

Kenilworth Math Club

3:30 pm – 5:30 pm James E. Keisler Lounge (room 321 Lockett)

Kenilworth Science and Technology Charter School

Wednesday, October 2, 2013

Posted September 6, 2013
Last modified September 30, 2013

3:30 pm Lockett 235

Benjamin Harris, LSU
What is microlocal analysis? Part I

It had long been realized that continuous or measurable functions were not large enough collections of functions to solve many classical analysis questions so in the mid 20th century analysts sought to formalize definitions of generalized functions. Of course, analysts also needed new ways of studying these new generalized functions. Perhaps the most important of these theories is called microlocal analysis. Roughly speaking, there are two schools of microlocal analysis, sometimes called ``algebraic microlocal analysis'' and ``analytic microlocal analysis''. The so-called algebraic school began with two papers by Sato in 1958 and 1959. Sato quickly gained many collaborators in Japan, and his theory was already quite well developed when the so-called analytic school was begun by a paper of Hormander in 1971 (Hormander was aware of Sato's earlier work). Sato's ideas also inspired Kashiwara, who was Sato's student in the early years of the theory, to work on the theory of D-modules. In this series of two talks, we will give a brief and rough overview of Sato's theory of microlocal analysis. This series is really a tale of three sheaves on an analytic manifold: the sheaf of analytic functions, the sheaf of hyperfunctions, and the sheaf of microfunctions. Roughly speaking, this is a sheaf of classical functions, a sheaf of generalized functions, and a sheaf to help us study the differences between the two (that is where the microlocal analysis comes in). If time permits, we will show how to use this theory to say (more or less) concrete things about linear partial differential equations on analytic manifolds.

Posted October 1, 2013

3:30 pm – 4:20 pm Lockett 233

Juanita Pinzon-Caicedo, Indiana University
Traceless SU(2) representations of 2-stranded tangles

Abstract: Given a codimension 2 submanifold A⊂X define R(X,A) as the space of traceless SU(2) representations of π_1(X\\A) modulo conjugation. For Y a 3-manifold and K⊂Y a knot, Kronheimer-Mrowka defined the Instanton Knot Homology of (Y,K) as the homology of a chain complex whose groups are generated by the elements of R(Y,K). In the talk we describe a method to determine R(S^3,K) whenever K is a torus or pretzel knot.

Friday, October 4, 2013

Posted August 8, 2013
Last modified October 2, 2013

3:30 pm Lockett 112

Meeting of tenured faculty

Monday, October 7, 2013

Posted August 8, 2013
Last modified October 2, 2013

3:30 pm Lockett 112

Meeting of Full Professors

Tuesday, October 8, 2013

Posted September 11, 2013
Last modified September 15, 2013

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 5:00 pm Lockett 285

Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Stopping CCR-flows

Posted September 25, 2013
Last modified October 7, 2013

3:30 pm – 4:20 pm Lockett 243

Jacob Matherne, Department of Mathematics, LSU
Computing Upper Cluster Algebras

Cluster algebras are commutative unital domains generated by distinguished elements called cluster variables. These generators are grouped into sets called clusters, and a process called mutation allows movement between the clusters. Many notable varieties (Grassmannians, partial flag varieties, and others) are equipped with cluster structures where certain regular functions play the role of cluster variables.

From a geometric perspective, there is a more natural algebra to consider: the upper cluster algebra. In this talk, we study cluster algebras and upper cluster algebras using algebraic geometry, which leads to an algorithm for producing presentations of upper cluster algebras in terms of generators and relations.

This is joint work with Greg Muller.

Wednesday, October 9, 2013

Posted September 6, 2013
Last modified September 30, 2013

Student Harmonic Analysis/Representation Theory Seminar

3:30 pm Lockett 235

Benjamin Harris, LSU
What is microlocal analysis? Part II

Posted September 30, 2013
Last modified October 2, 2013

4:30 pm James E. Keisler Lounge (room 321 Lockett)

Discussion of job search

We will discuss job searches and have a guest: Kayla Kucharchuk from career services.

Posted September 19, 2013
Last modified October 4, 2013

Algebra and Number Theory Seminar Questions or comments?

4:30 pm – 5:20 pm Lockett 243

Carolyn Chun, Brunel University, London Former LSU graduate student
Delta-matroids, partial duality, and ribbon graphs

In this talk, I define delta-matroids and discuss their relationship with partial duality and ribbon graphs.

Tuesday, October 15, 2013

Posted September 25, 2013
Last modified March 2, 2021

3:30 pm – 4:20 pm Lockett 243

Holly Swisher, Oregon State University
Modularity of $k$-rank difference functions

Rank difference functions were used by Atkin and Swinnerton-Dyer to prove the well-loved Ramanujan congruences for the partition function modulo 5 and 7. In 2008, Ahlgren and Treneer recognized rank difference functions for partitions as modular or mock modular objects. Here, we similarly investigate k-component multipartitions (also called k-colored partitions). Ultimately, we relate restricted k-rank generating functions and k-rank difference functions to weakly holomorphic modular forms.

Posted October 1, 2013

3:30 pm – 4:30 pm Lockett 233

Hyea Hyun Kim, Kyung Hee University, South Korea
A Staggered Discontinuous Galerkin Method for the Stokes System and its Fast Solvers by Domain Decomposition Methods

https://www.cct.lsu.edu/lectures/staggered-discontinuous-galerkin-method-stokes-system-and-its-fast-solvers-domain-decomposi

Posted September 25, 2013

GEAUX committee meeting

5:00 pm James E. Keisler Lounge (room 321 Lockett)

GEAUX committee

Students from the 2013 GEAUX program and students interested in participating in the coming year.

Thursday, October 17, 2013

Posted August 7, 2013
Last modified October 15, 2013

3:30 pm Lockett 16 (in basement)

Faculty meeting with provost

Monday, October 21, 2013

Posted October 15, 2013
Last modified October 17, 2013

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett Hall 233

Stephen Shipman, Mathematics Department, LSU
Efficient Evaluation of 2D-periodic Green functions in 3D

I will describe the analytical basis behind a fast method of computing periodic Green functions, ultimately for the purpose of efficiently solving problems of scattering by periodic structures. The Poisson summation formula provides super-algebraic convergence away from frequencies for which one of the Rayleigh-Bloch modes is grazing. At grazing (cutoff) frequencies, the periodic Green function ceases to exist, and a more complicated method is needed. This involves introducing several sheets of periodic sources to create a half-space Green function. This is work with Oscar Bruno, Catalin Turc, and Stephanos Venakides.

Tuesday, October 22, 2013

Posted September 25, 2013
Last modified October 16, 2013

3:30 pm – 4:20 pm Lockett 243

Simon Riche, Université Clermont Auvergne
Perverse sheaves on affine Grassmannians, asymptotic Verma modules, and differential operators on the basic affine space

The Geometric Satake equivalence is an equivalence of categories between certain perverse sheaves on the affine Grassmannian of a reductive algebraic group and representations of the dual reductive group (in the sense of Langlands). The general philosophy underlying this equivalence is that representation theoretic properties of a representation are reflected in topological properties of the corresponding perverse sheaf. In this talk we will explain how one can describe equivariant cohomology of the costalks of these perverse sheaves, together with their natural symmetries, in terms of morphisms between universal Verma modules for the dual Lie algebra, and also in terms of differential operators on the basic affine space of the dual group. This is joint work with Victor Ginzburg.

Posted October 1, 2013
Last modified October 4, 2013

3:30 pm – 4:30 pm Lockett 233

Michael Friedlander, University of British Columbia
Gauge Optimization, Duality, and Applications

Gauge functions significantly generalize the notion of a norm, and gauge optimization is the class of problems for finding the element of a convex set that is minimal with respect to a gauge. These conceptually simple problems appear in a remarkable array of applications. Their gauge structure allows for a special kind of duality framework that may lead to new algorithmic approaches. I will illustrate these ideas with applications in signal processing and machine learning.
https://www.cct.lsu.edu/lectures/gauge-optimization-duality-and-applications

Wednesday, October 23, 2013

Posted October 9, 2013
Last modified October 10, 2013

3:30 pm – 4:20 pm Lockett 233

Susan Abernathy, Louisiana State University
Virtual Seminar: "The Kauffman bracket ideal for genus-1 tangles"

Abstract: A genus-1 tangle is a 1-manifold with two boundary components properly embedded in the solid torus. A genus-1 tangle G embeds in a link L if we can complete G to L via a 1-manifold in the complement of the solid torus containing G. A natural question to ask is: given a tangle G and a link L, how can we tell if G embeds in L? We define the Kauffman bracket ideal, which gives an obstruction to tangle embedding, and outline a method for computing a finite list of generators for this ideal. We also give an example of a genus-1 tangle with non-trivial Kauffman bracket ideal and discuss how the concept of partial closures relates to this ideal.

Thursday, October 24, 2013

Posted October 14, 2013
Last modified October 20, 2013

3:30 pm Lockett 285

Siu-hung (Richard) Ng, LSU
Frobenius-Schur indicators and exponents

ABSTRACT: Frobenius-Schur indicators were introduced a century ago for the representations of finite groups. It has been proved recently that these indicators are invariants of tensor categories, and so are the exponents of finite groups. In this talk, we will discuss dimensions, exponents and indicators for finite groups, and their generalizations in the settings of Hopf algebras as well as tensor categories.

There will be refreshments in the Keisler lounge at 3 PM

Friday, October 25, 2013

Posted October 23, 2013

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett 16 (in basement)

Meeting to discuss making an offer

Tuesday, October 29, 2013

Posted September 25, 2013
Last modified October 18, 2013

3:30 pm – 4:20 pm Lockett 243

Matt Papanikolas, Texas A&M University
Special points and L-values in positive characteristic

Going back to Dirichlet and Kummer one knows that special values of Dirichlet L-functions at s=1 can be expressed in terms of logarithms of circular units in cyclotomic fields and Gauss sums, and moreover these identities can be used to show that the group of circular units is of finite index in full group of units. The aim of the present talk is to investigate analogues of these results in positive characteristic for Goss L-functions of Dirichlet type, which take values in function fields of characteristic p. Anderson showed that values of these L-functions at s=1 are found from Carlitz logarithms of special points on the Carlitz module and investigated their properties. We will consider extensions of these results to s > 1, which involve modules of special points on tensor powers of the Carlitz module and log-algebraicity identities.

Wednesday, October 30, 2013

Posted October 15, 2013
Last modified September 17, 2021

VIGRE@LSU: Student Colloquium Questions or comments?

12:30 pm – 1:20 pm Lockett 113

Tadeusz Iwaniec, Syracuse University and the University of Helsinki
Harmonic Mappings

There will be a light lunch before the talk from 12:00-12:30 in the Keisler lounge.

This talk is primarily aimed at undergraduate students.

Posted April 3, 2013
Last modified June 8, 2020

3:30 pm – 4:20 pm Lockett 233

Peter Horn, Syracuse University
Virtual Seminar: "Computing higher-order Alexander polynomials of knots"

Abstract: The classical Alexander polynomial of a knot can be defined in several ways, one of which is via covering spaces. Using higher covering spaces, Cochran defined the higher-order Alexander polynomials. It is known that the degree of the classical Alexander polynomial gives a lower bound for the genus of a knot, and so do the degrees of the higher-order Alexander polynomials. These higher-order bounds are known to be stronger than the classical bound for satellite knots, but little is known about low crossing knots. We will present an algorithm to compute the degree of the first higher-order Alexander polynomial of any knot, and we will discuss some interesting computations.

Thursday, October 31, 2013

Posted October 14, 2013
Last modified September 17, 2021

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:20 pm Lockett 285

Tadeusz Iwaniec, Syracuse University
Sobolev mappings and energy integrals in nonlinear elasticity

Friday, November 1, 2013

Posted October 15, 2013
Last modified September 17, 2021

3:30 pm – 4:20 pm Lockett 239

Tadeusz Iwaniec, Syracuse University and the University of Helsinki
p-Harmonic Equation

There will be refreshments in the Keisler lounge from 3:00-3:30 preceding the talk.

This talk is primarily aimed at graduate students.

Wednesday, November 6, 2013

Posted August 29, 2013
Last modified November 5, 2013

3:30 pm – 4:30 pm Lockett 233

Ina Petkova, Rice University
Virtual Seminar: "Bordered Floer homology and decategorification"

Abstract: Bordered Floer homology is a TQFT-type generalization of Heegaard Floer homology to 3-manifolds with boundary, which satisfies a nice gluing formula. I will give a brief description of this generalized theory, and discuss some applications to topology. For example, bordered Floer homology categorifies the kernel of the homology map induced by the inclusion of the boundary into the 3-manifold.

Monday, November 11, 2013

Posted October 24, 2013

3:30 pm – 4:20 pm Room 233 Lockett Hall

Robert Lipton, Mathematics Department, LSU
Dynamics in Materials Far From Equilibrium

In this talk we address the role of local instability in the precipitation and propagation of failure in macroscopic samples of material. We work with non-locally interacting systems, eg. peridynamics. A class of scaled nonlinear interaction potentials are identified for which dynamic instability localizes and fracture surfaces appear in the scaling limit.

Tuesday, November 12, 2013

Posted October 15, 2013
Last modified November 9, 2013

3:30 pm – 4:30 pm Lockett 381

Jimmie Lawson, Mathematics Department, LSU
Random Variables with Values In Nonpositively Curved Metric Spaces

Algebra and Number Theory Seminar Questions or comments?

Posted October 14, 2013
Last modified November 5, 2013

3:30 pm – 4:20 pm Lockett 243

Ling Long, LSU
On p-adic analogues of Ramanujan type formulae for 1 over pi

In this talk, we will give some general backgrounds of hypergeometric series, elliptic curves, and Ramanujan type formulae for 1 over pi. Then we will discuss some p-adic analogues of these formulae which was conjectured by van Hamme for special cases and by Zudilin more generally. This is a joint work with Sarah Chisholm, Alyson Deines, Gabriele Nebe, and Holly Swisher.

Wednesday, November 13, 2013

Posted November 5, 2013

3:30 pm Keisler Lounge (321 Lockett)

student actuarial club meeting

Nathan White will give a presentation about his summer and ongoing internship.

Thursday, November 14, 2013

Posted October 9, 2013

3:30 pm – 4:20 pm Lockett 285

Gregor Masbaum, CNRS, Institut de Mathematiques de Jussieu, Paris, France
All finite groups are involved in the mapping class group

Abstract: A (finite) group G is said to be involved in an (infinite) group Gamma if G is isomorphic to a quotient of a subgroup of Gamma of finite index. I will discuss examples and non-examples of groups Gamma with the property that every finite group is involved in Gamma. I will then describe my joint work with A. Reid where we show that mapping class groups of surfaces have this property. A remarkable feature of the proof is that it involves quantum topology. In fact, the proof uses precisely the Integral TQFT-representations of mapping class groups that P. Gilmer and I constructed some years ago. However, no previous knowledge of quantum topology will be assumed in this talk.

Friday, November 15, 2013

Posted November 15, 2013

3:30 pm Lockett Hall 233

Materials science in electronics: an overview.

The contribution of traditional and modern day materials science research has ushered in unprecedented success in state-of-the-art electronics and device applications. From sustaining the Moore\'s law in integrated circuits (ICs) to the recent innovations in plastic and printed electronics, the interdisciplinary amalgamation of physics, chemistry, mathematics and engineering with materials science has steered informed and judicious manipulation of existing and new materials in their nanoscale dimensions. In this presentation, we would briefly discuss about the current trends in Fin-field effect transistors (FETs), quantum dot FETs and carbon nanomaterials (carbon nanotubes and graphene) based thin film transistors (TFTs). The invention of novel materials and their processing techniques in these technologies are believed to benefit incredibly from the ever evolving and reliable mathematical models, statistical and pattern- analysis techniques.

Monday, November 18, 2013

Posted October 25, 2013

3:30 pm – 4:20 pm Lockett Hall 233

Yaniv Almog, Department of Mathematics, LSU
Global stability of the normal state of superconductors under the effect of strong electric current

Consider a superconducting wire whose temperature is lower than the critical one. When one flows a sufficiently strong current through the wire, it is well known from experimental observation that the wire becomes resistive, behaving like a normal metal. We prove that the time-dependent Ginzburg-Landau model anticipates this behaviour. We first prove that, for sufficiently strong currents, the semi-group associated with the model, becomes a contraction semi-group. Then, we obtain an upper bound for the critical current where the semi-group becomes stable. We relate this current to the resolvent of the linearized elliptic operator. Joint work with Bernard Helffer

Tuesday, November 19, 2013

Posted November 13, 2013
Last modified July 26, 2015

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 381

Jimmie Lawson, Mathematics Department, LSU
Random Variables with Values In Nonpositively Curved Metric Spaces

Metric spaces of nonpositive curvature (also known as CAT-0 spaces) are metric generalizations of Riemannian manifolds and have been widely studied in recent years. We review how
significant parts of the basic theory of real random variables have have
been extended to the setting of RVs with values in such spaces. Recently
Y. Lim and the presenter have used this machinery to solve a basic open
problem about matrix means of positive definite matrices.

Posted September 30, 2013
Last modified November 5, 2013

3:30 pm – 4:20 pm Lockett 243

Ravi Ramakrishna, Cornell University
Hida Families of modular forms

The basic idea of Hida theory is that certain modular forms live in p-adic analytic families where all the forms are congruent mod p. Even though they have been studied for some 30 years, much remains mysterious Hida theory. This talk will recall relevant aspects of the theory, raise some (hopefully!) interesting and fundamental questions and explain work in progress towards answering some of these.

Wednesday, November 20, 2013

Posted August 29, 2013
Last modified November 14, 2013

3:30 pm – 4:20 pm Lockett 233

Eamonn Tweedy, Department of Mathematics, Rice University
Virtual Seminar: tba

Posted August 29, 2013
Last modified January 10, 2022

Student Combinatorics Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 233

Eamonn Tweedy, Department of Mathematics, Rice University
Virtual Seminar: "Positive Links"

Cochran and Gompf defined a notion of positivity for concordance classes of knots that simultaneously generalizes the usual notions of sliceness and positivity of knots. Their positivity essentially amounts to the knot being slice in a positive-definite simply-connected four manifold. I'll discuss an analogous property for links, describe a concrete characterization of positivity up to concordance, and give some obstructions to positivity.

Posted November 19, 2013

4:30 pm – 5:20 pm Lockett 243

Graph Discharging Techniques

The proof of the Four Color Theorem relies heavily on the use of the discharging method. This technique is useful when examining the structure of a graph embedded in a surface. In this talk we will discuss how the discharging method works and when it can be useful by examining several examples.

Posted October 21, 2013

6:00 pm Keisler Lounge (321 Lockett)

student actuarial club sponsored visitor

Sam Broussard, Pan-American Life Insurance Co, will be the guest speaker. Pizza will be served.

Thursday, November 21, 2013

Posted October 24, 2013

3:00 pm – 4:00 pm Lockett Hall 233

Amit Acharya, Carnegie Melon University
PDE dynamics of dislocations

The talk will describe a PDE framework to deal with the dynamics of dislocations leading to plasticity in solids. Dislocations are defects of deformation compatibility/integrability in elastic response. The presented framework will be shown to be capable of representing discrete defect dynamics as well as present a natural setting for asking questions related to macroscopic plasticity arising from the underlying dislocation dynamics.

Posted October 24, 2013

3:00 pm – 4:00 pm Lockett Hall 233

Amit Acharya, Carnegie Melon University
PDE dynamics of dislocations

Posted October 9, 2013
Last modified November 20, 2013

3:30 pm Lockett 285

Ravi Rau, Department of Physics and Astronomy, LSU
Quantum spins, real rotations, and a 1913 Ramanujan conjecture

Abstract: Quantum states are defined as complex variables and their time evolution is given by unitary transformations. For a quantum spin-1/2 or qubit of the field of quantum information, an equivalent picture of the Bloch sphere and real rotations of a unit vector from the origin to a point on the sphere has proved enormously useful. Extension of this nice geometrical view is also possible for a pair of qubits, such pairs being the fundamental objects of interest for entanglement and other quantum correlations that are used in quantum computing, key distribution and teleportation. The above results rest on the homeomorphism of SU(2)-SO(3) and SU(4)-SO(6) group pairs. These will be discussed and a hundred-year old conjecture of number theory (later the Ramanujan-Nagell Theorem) used to show that no such correspondence between unitary evolution and real rotations is available for systems of more qubits. However, the general construction of the evolution operator for SU(N) and of some of its sub-groups are likely to be of interest throughout the field of quantum information.

Monday, December 2, 2013

Posted November 12, 2013
Last modified November 20, 2013

2:30 pm – 3:30 pm Lockett 233

Neela Nataraj, Indian Institute of Technology Bombay
A C0 interior penalty method for an optimal control problem governed by the biharmonic operator

Abstract: In the recent past, C0 interior penalty methods have been attractive for solving the fourth order problems. In this talk, a C0 interior penalty method is proposed and analyzed for distributed optimal control problems governed by the biharmonic operator. The state equation is discretized using continuous piecewise quadratic finite elements while piecewise constant approximations are used for discretizing the control variable. *A priori *and *a posteriori *error estimates are derived for both the state and control variables under minimal regularity assumptions. Theoretical results are demonstrated by numerical experiments. The * a posteriori *error estimators are useful in adaptive finite element approximation and the numerical results indicate that the sharp error estimators work efficiently in guiding the mesh refinement and saving the computational effort substantially.

Wednesday, December 4, 2013

Posted November 19, 2013

3:30 pm – 4:20 pm Lockett 235

Boris Rubin, Louisiana State University
On the Overdeterminicity in Integral Geometry

Abstract: A simple example of an $n$-dimensional admissible complex of planes is given for the overdetermined $k$-plane transform in $\\bbr^n$. Existence of the corresponding restricted $k$-plane transform on $L^p$ functions and explicit inversion formulas are discussed. Similar questions are studied for overdetermined Radon type transforms on the sphere and the hyperbolic space. A theorem describing the range of the restricted $k$-plane transform on the space of rapidly decreasing smooth functions is proved.

Wednesday, December 11, 2013

Posted November 25, 2013

12:00 pm Keisler lounge

Math Department Holiday Party

Everyone is invited! Please bring some food to share with others. International students are encouraged to bring some food from their country of origin, if they wish. At noon there will be a short awards ceremony, followed by food and friendship.

Wednesday, January 8, 2014

Posted September 6, 2013
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive / PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, January 10, 2014

Posted September 6, 2013
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive / PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Monday, January 13, 2014

Posted September 6, 2013
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive / PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, January 22, 2014

Posted January 9, 2014
Last modified January 20, 2014

3:30 pm – 4:20 pm Lockett 235

Palle Jorgensen, University of Iowa
Cross roads of stochastic processes, representations of Lie groups, and their applications in physics

Thursday, January 23, 2014

Posted January 9, 2014
Last modified January 15, 2014

3:30 pm – 4:20 pm Lockett 285

Karl-Hermann Neeb, Universität Erlangen-Nürnberg
Reflection positivity and unitary Lie group representations

Reflection positivity (sometimes called Osterwalder-Schrader positivity) was introduced by Osterwalder and Schrader in the context of axiomatic euclidean field theories. On the level of unitary representations, it provides a passage from representations of the euclidean isometry group to representations of the Poincaré group. In our talk we shall explain how these ideas can be used to obtain a natural context for the passage from representations of Lie groups with an involutive automorphism (symmetric Lie groups) to representations of their dual Lie group. Already the case of one-parameter groups is of considerable analytic interest.

Thursday, January 30, 2014

Posted January 9, 2014
Last modified January 15, 2014

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 285

Tom Lenagan, University of Edinburgh
Totally nonnegative matrices

A real matrix is totally nonnegative if each of its minors is nonnegative, and is totally positive if each minor is greater than zero. We will outline connections between the theory of total nonnegativity and the torus invariant prime spectrum of the algebra of quantum matrices, and will discuss some new and old results about total nonnegativity which may be obtained using methods derived from quantum matrix methods. Most of the material is joint work with Stephane Launois and Ken Goodearl. (You don't need to know anything about quantum matrices to follow this talk.)

Friday, January 31, 2014

Posted January 9, 2014
Last modified January 31, 2014

3:30 pm – 4:20 pm Lockett 285
(Originally scheduled for Tuesday, January 28, 2014, 3:30 pm)

Tom Lenagan, University of Edinburgh
Algebras with restricted growth

We survey recent and not-so-recent results on growth of algebras, with special emphasis on small values.

Tuesday, February 4, 2014

Posted February 3, 2014

3:15 pm – 4:15 pm Lockett 233

Christopher Davis, LSU
Partition of Unity Methods for Fourth Order Problems

Thursday, February 6, 2014

Posted February 3, 2014

4:00 pm Lockett 285

Meeting to discuss 5-year professorial hiring plan

Tuesday, February 11, 2014

Posted February 6, 2014

5:00 pm James E. Keisler Lounge (room 321 Lockett)

Meeting of student actuarial club

Monday, February 17, 2014

Posted February 5, 2014
Last modified January 24, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 233

Itai Shafrir, Department of Mathematics, Technion - Israel Institute of Technology
Asymptotics of eigenstates of elliptic problems with mixed boundary data in domains tending to infinity

We analyze the asymptotic behavior of eigenvalues and eigenfunctions of an elliptic operator with mixed boundary conditions on cylindrical domains when the length of the cylinder goes to infinity. We identify the correct limiting problem and show, in particular, that in general the limiting behavior is very different from the one with Dirichlet boundary conditions. This is a joint work with Michel Chipot and Prosenjit Roy from the University of Zurich.

Tuesday, February 18, 2014

Posted January 31, 2014
Last modified March 2, 2021

3:30 pm – 4:20 pm Lockett 285

Ivan Dimitrov, Queen's University (Canada)
Integrable weight modules of gl(∞)

I will present a theorem classifying the irreducible integrable weight modules with finite dimensional weight spaces over the Lie algebra gl(∞) consisting of finitary infinite matrices. Every such module belongs to one of the following three classes: highest weight modules, infinite symmetric powers of the natural representations, and modules which are not highest weight but whose weights are dominated by a single weight. For the modules in the new third class I will present different realizations and will provide explicit parametrization. I will define all necessary terms and will state the problem and the main result.

Posted February 8, 2014

3:30 pm – 4:30 pm Lockett 233

Peter Minev, University of Alberta
A Fast Parallel Algorithm for Direct Simulation of Particulate Flows Using Conforming Grids

Friday, February 21, 2014

Posted February 11, 2014

9:30 am – 10:30 am Lockett Hall Keisler Lounge

A Conversation with Dr. Pavel Bochev

Posted October 15, 2013
Last modified November 19, 2013

1:00 pm – 5:00 pm Saturday, February 22, 2014 Digital Media Center Theatre

SCALA 2014 (Scientific Computing Around Louisiana)

https://www.cct.lsu.edu/events/scientific-computing-around-louisiana-workshop-scala

Tuesday, February 25, 2014

Posted February 19, 2014

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett Hall Room 233

Michael Mascagni, Department of Computer Science, Florida State University
Random Number Generation Using Normal Numbers

Normal numbers are irrationals with perfect digit distribution, and thus they are potentially sources of computational random numbers. Among provably normal numbers are the Stoneham numbers, which are special not only in their digit distribution, but in the fact that finite segments of the digits can be quickly computed. Thus, we examine random numbers produced by periodic sections of the digits of Stoneham numbers. We show how they are equivalent to a linear congruential generator with special parameters, and we investigate this generator as a linear congruential generator. This is joint work with Steve F. Brailsford.

Posted January 31, 2014
Last modified February 21, 2014

3:30 pm – 4:20 pm Lockett 285

Peter Schauenburg, Université de Bourgogne
Module categories of finite Hopf algebroids, and self-duality

The notion of Hopf algebroid generalizes that of a Hopf algebra; the key property the former shares with the latter is that modules over a Hopf algebroid admit a tensor product, much like representations of a group or a Lie algebra. Put in more abstract terms, the module category over a Hopf algebroid is a tensor category. There is already a long list of results going in the other direction: Given a category with an abstract tensor product, the aim is to reconstruct a Hopf algebra (or a more general object such as a quasi-Hopf algebra, or a weak Hopf algebra, or a Hopf algebroid) whose module category is equivalent (or at least closely related) to that category. Many variants exist according to the properties required of the category one starts with, the closeness of the relation obtained between the category and the (co)module category of the reconstructed Hopf-like object, and the properties one can obtain for the latter. I will present a version that gives a completely intrinsic characterization of the module categories of suitably "finite" Hopf algebroids, and which, moreover, admits a rather simple proof. Then I will show that in many situations the Hopf algebroid thus attached to a tensor category is self-dual (after suitably clarifying what self-duality might mean for a Hopf algebroid); this generalizes a result of Pfeiffer on self-duality of certain fusion categories.

Posted February 17, 2014

VIGRE@LSU: Student Colloquium Questions or comments?

5:00 pm James E. Keisler Lounge (room 321 Lockett)

Meeting of student actuarial club

presentations by Nick Crifasi and Nick Klinka.

Wednesday, February 26, 2014

Posted February 19, 2014

2:30 pm – 3:20 pm Lockett 285

Satyan Devadoss, Williams College and Stanford University
Packings and partitions

This talk is primarily aimed at undergraduates.

Motivated by Kepler's study of cannonball packing, and Lord Kelvin's study of ether and foam, the quest to understand the packing and partitioning of space have lead to some of the most remarkable ideas in mathematics. We look at these puzzles, in 2D, 3D, and beyond, and show their stunning appearance in nature, architecture, and current unsolved problems.

There will be refreshments at 2:00pm in the Keisler lounge before the talk.

Thursday, February 27, 2014

Posted February 19, 2014

VIGRE@LSU: Student Colloquium Questions or comments?

12:30 pm – 1:20 pm Lockett 241

Satyan Devadoss, Williams College and Stanford University
World of particle collisions

This talk is primarily aimed at graduate students.

Configuration spaces are not only fundamental objects in mathematics, but appear in numerous areas such as robot motion planning, DNA sequencing, sensor networks, surface reconstruction, and origami designs. Our story is motivated by the shape of the configuration space of particles moving and colliding on a circle, which is far more complicated than it seems. These novel spaces now appear across a broad spectrum of research, including geometric group theory, combinatorics, phylogenetics, and statistics. The entire talk is heavily infused with visual imagery.

There will a light lunch at noon in the Keisler lounge preceding the talk.

Posted January 9, 2014
Last modified February 24, 2014

3:30 pm – 4:20 pm Lockett 285

Satyan Devadoss, Williams College and Stanford University
Combinatorics of Surface Deformations

In the 1970s, Deligne and Mumford constructed a way to keep track of particle collisions using Geometric Invariant Theory. These spaces were then utilized by Gromov and Witten as invariants arising from string field theory and quantum cohomology. Later, Kontsevich and Fukaya generalized these ideas when studying deformation quantization to include surfaces with boundary and marked points. Such spaces appear in open-closed string theory, particularly with respect to holomorphic curves with Lagrangian submanifolds.

We consider a combinatorial framework to view the compactification of this space based on the pair-of-pants decomposition of the surface, relating it to the well-known phenomenon of bubbling. Our main result classifies all such spaces that can be realized as convex polytopes. A new polytope is introduced based on truncations of cubes, and its combinatorial and algebraic structures are related to generalizations of the classical associahedron.

Monday, March 3, 2014

Posted February 5, 2014
Last modified February 2, 2022

Student Harmonic Analysis/Representation Theory Seminar

3:30 pm – 4:20 pm Lockett 233

Bernard Helffer, University of Paris South, Orsay
Introduction to spectral minimal partitions, Aharonov-Bohm's operators and Pleijel's theorem

Given a bounded open set $Ω$ in $\mathbb{R}^n$ (or in a Riemannian manifold) and a partition $\mathcal{D}$ of $Ω$ by $k$ open sets $D_j$ , we can consider the quantity $Λ(\mathcal{D}) := \text{max}_j λ(D_j)$ where $λ(D_j)$ is the ground state energy of the Dirichlet realization of the Laplacian in $D_j$. If we denote by $\mathfrak{L}_k(Ω)$ the infimum over all the $k$-partitions of $Λ(\mathcal{D})$ a minimal $k$-partition is then a partition which realizes the infimum. Although the analysis is rather standard when $k = 2$ (we find the nodal domains of a second eigenfunction), the analysis of higher $k$’s becomes non trivial and quite interesting.

Wednesday, March 5, 2014

Posted February 14, 2014

3:30 pm Lockett 235

Ambar Sengupta, Mathematics Department, LSU
Representing the Heisenberg Group

In his foundational 1925 paper on quantum mechanics Heisenberg introduced a relation that was later formulated in the form PQ-QP=icI, where P and Q are infinite matrices corresponding to momentum and position, c is a positive physical constant, and I is the infinite identity matrix. This canonical commutation relation (CCR) led to a great journey, continuing today, involving the study of unbounded operators, the spectral theorem, and much else. In this talk we will explore some of these ideas, focusing on Weyl\'s reformulation of the CCR in terms of unitary operators and how this can be viewed as a representation of a group, called the Heisenberg group, that encodes the essential structure of the CCR. We will also look at von Neumann\'s formulation and proof of the equivalence of the CCR method with the wave mechanics introduced by Schroedinger in 1926.

Thursday, March 6, 2014

Posted September 30, 2013
Last modified February 24, 2014

7:00 pm Lod Cook Conference Center

MAA La-Miss Section Meeting

Info here: http://sections.maa.org/lams/meeting/index.php

Friday, March 7, 2014

Posted February 24, 2014

Lod Cook Conference Center

MAA La-Miss Section Meeting

Saturday, March 8, 2014

Posted February 12, 2014

primary and middle school teachers

9:00 am – 11:30 am James E. Keisler Lounge (room 321 Lockett)

primary and middle school Atari-Go

Posted February 24, 2014

until 1:00 pm Lod Cook Conference Center

MAA La-Miss Section Meeting

Tuesday, March 11, 2014

Posted February 19, 2014

Student Harmonic Analysis/Representation Theory Seminar

3:30 pm – 4:30 pm Lockett 233

Jiguang Sun, Michigan Technological University
Numerical Methods for Transmission Eigenvalues

Wednesday, March 12, 2014

Posted March 7, 2014

3:30 pm Lockett 235

Ambar Sengupta, Mathematics Department, LSU
Representing the Heisenberg Group (Part II)

Tuesday, March 18, 2014

Posted February 11, 2014

3:30 pm – 4:30 pm Lockett 233

Jichun Li, University of Nevada Las Vegas
Mathematical study and finite element modeling of invisibility cloaks with metamaterials

Posted March 5, 2014
Last modified March 6, 2014

5:00 pm James E. Keisler Lounge (room 321 Lockett)

Meeting of student actuarial club

Presentations by Nick Crifasi and Nick Klinka. Note the date was changed because of a conflicting statistics exam.

Wednesday, March 19, 2014

Posted March 17, 2014

3:30 pm – 4:20 pm Lockett 235

Raul Quiroga, Centro de Investigacion en Matematicas (CIMAT)
Commutative algebras generated by Toeplitz operators

Abstract: For a bounded symmetric domain $D$ we define the (weighted) Bergman spaces and their Toeplitz operators. The latter are given by multiplication operators followed by an orthogonal projection. We will also exhibit non-trivial and large commutative algebras generated by spaces of Toeplitz operators. All our examples will be seen to be closely related to the geometry of $D$ and to the holomorphic discrete series of the group of biholomorphisms of $D$.

Posted March 13, 2014
Last modified March 2, 2021

3:30 pm – 4:20 pm Lockett 233

Olga Plamenevskaya, SUNY Stony Brook
Virtual Topology Seminar: "Looking for flexibility in higher-dimensional contact manifolds"

Contact manifolds are odd-dimensional cousins of symplectic manifolds; a contact structure on a smooth manifold is a hyperplane field given as a kernel of a "non-degenerate" 1-form. Locally, all contact structures look the same, but globally, a lot of interesting topological phenomena arise. By a classical result of Eliashberg, contact manifolds in dimension 3 come in two flavors: tight (rigid) and overtwisted (flexible). While the tight ones are quite subtle, overtwisted contact structures are completely described by their algebraic topology. In higher dimensions, a class of flexible contact structures is yet to be found. We will describe some conjectural "overtwisted pieces" (due to Niederkruger et al.) and an important flexibility principle for certain Legendrian knots discovered by Murphy. Then, we will present some results (joint with E. Murphy, K. Niederkruger, and A. Stipsicz) showing that in the presence of an "overtwisted piece", all Legendrian knots are "flexible", and demonstrating some flexibility phenomena for contact manifolds in higher dimensions.

Thursday, March 20, 2014

Posted March 17, 2014
Last modified March 19, 2014

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm Keisler Lounge, 3rd Floor, Lockett Hall

Simon Pfeil, Louisiana State University
Remote Access and the Command Line

Abstract: Imagine you are at a conference as speaker, and your laptop goes missing! Without your slides and TeX files, what can you do? Come to this talk, and find out how you could recover your documents from the servers on campus, transfer files, and make changes remotely with a basic knowledge of the command line.

Tuesday, March 25, 2014

Posted March 24, 2014

2:30 pm – 3:20 pm Lockett 232

Arkady Berenstein, University of Oregon
Cluster recursions

This talk is primarily aimed at undergraduate students. There will be refreshments in the Keisler lounge at 2:00pm preceding the talk.

In my lecture I will discuss a class of rational recursions that, rather surprisingly, turn out to be integer sequences. For example, the rational recursion

x_{k+1}=(x_k^2+1)/x_{k-1}

with x_1=x_2=1 gives x_3=2, x_4=5, x_5=13, x_6=34, ... (this is a half of the Fibonacci sequence).

The ultimate reason for the integrality is that each x_n is a Laurent polynomial over integers in x_1 and x_2. For instance,

x_5=x_1/x_2^2 + 2/x_1 + 2/(x_1^2 x_2^2) + x_2^4/x_1^3 + 3 x_2^2/x_1^3 + 3 x_2^4/x_1^3 + 1/(x_1^3 x_2^2)

which gives x_5=13 when x_1=x_2=1. This is an example of what cluster recursions are: rational recursions of order n with the property that each member of the sequence is a Laurent polynomial in x_1,...x_n with integer coefficients.

I will provide more examples of \"one-dimensional\" cluster recursions such as

x_{k+1}=(x_k^b+1)/x_{k-1}, where b is a positive integer,

x_{k+1}x_{k-3}=x_k x_{k-2}+x_{k-1}^2 (Somos-4 sequence),

some \"two-dimensional\" recursions like:

x_{i,j+1}x_{i,j-1} = x_{i+1,j}x_{i-1,j} + x_{ij}^2 (Q-system of type A)

and many others. The explanation of the integrality of these sequences and of the underlying Laurent Phenomenon is in the theory of cluster algebras introduced by S. Fomin and A. Zelevinsky in 2001. I will conclude the lecture with appropriate definitions of cluster mutations and will demonstrate how the above examples fit to the general cluster framework.

Posted January 21, 2014

3:30 pm – 4:30 pm Digital Media Center

Randy Bank, University of California San Diego
Some Algorithmic Aspects of hp-Adaptive Finite Elements

Abstract: We will discuss our on-going investigation of hp-adaptive finite elements. We will focus on a posteriori error estimates based on superconvergent derivative recovery. Besides providing both global error estimates and local error indicators, this family of error estimates also provides information that forms the basis of our hp-adaptive refinement and coarsening strategies. In particular, these a posteriori error estimates address in a cost efficient and natural way the critical issue of deciding between h or p refinement/coarsening. Some numerical examples will be provided.

Wednesday, March 26, 2014

Posted March 14, 2014

3:30 pm – 4:30 pm Lockett 233

Arkady Berenstein, University of Oregon
Equivariant Littlewood-Richardson coefficients

ABSTRACT. The goal of my talk (based on joint work with Edward Richmond) is to compute all equivariant Littlewood-Richardson (LR) coefficients for semisimple and Kac-Moody groups G, that is, the structure constants of the equivariant cohomology algebra H_B(G/B), where B is the Borel subgroup of G. These coefficients are of importance in enumerative geometry, algebraic combinatorics and representation theory. Our formula for the LR coefficients is purely combinatorial and is given in terms of the Cartan matrix and the Weyl group of G. In particular, our formula gives a combinatorial proof of positivity of the equivariant LR coefficients in the cases when all off-diagonal Cartan matrix entries are less than or equal to -2.

Thursday, March 27, 2014

Posted March 25, 2014

VIGRE@LSU: Student Colloquium Questions or comments?

10:30 am – 11:30 am Lockett 276

Arkady Berenstein, University of Oregon
Quantum cluster characters of Hall algebras

The goal of my talk (based on a recent joint paper with Dylan Rupel) is to introduce a generalized quantum cluster character, which assigns to each object V of a finitary Abelian category C over a finite field F_q and any sequence ii of simple objects in C an element X_{V,ii} of the corresponding algebra P_ii of q-polynomials. If C is hereditary, then the assignment V--> X_{V,ii} is an algebra homomorphism from the Hall-Ringel algebra of C to the q-polynomial algebra P_ii, which generalizes the well-known Feigin homomorphisms from the upper half of a quantum group to various q-polynomial algebras.

If C is the representation category of an acyclic quiver Q and ii is the twice repetition-free source-adapted sequence for Q, then we construct an acyclic quantum cluster algebra on P_ii and prove that the quantum cluster characters X_{V,ii} for exceptional representations Q give all (non-initial) cluster variables in P_ii. This, in particular, settles an important case of a conjecture by A. Zelevinsky and myself on quantum unipotent cells.

Posted March 24, 2014

2:30 pm – 3:20 pm Lockett 232

Arkady Berenstein, University of Oregon
Quantum cluster algebras

This talk is primarily aimed at graduate students. There will be refreshments in the Keisler lounge at 2:00pm preceding the talk.

Cluster algebras have been introduced by Fomin and Zelevinsky in 2001 as an algebraic framework for total positivity and canonical bases in representations of reductive groups. Now the theory of cluster algebras is connected to many different areas of mathematics, for example, representation theory of finite dimensional algebras, Poisson geometry and Teichmuller Theory.

The goal of my talk (based on joint work with A. Zelevinsky) is to present the theory of quantum deformations of cluster algebras. While a cluster algebra corresponds to an integer skew-symmetrizable matrix B, its quantum version corresponds to a compatible pair of B with a skew-symmetric matrix Lambda responsible for the q-commutation relations and is, in many respects, a more natural algebraic object.

It turns out that all \"classical\" cluster structures can be carried over (sometimes conjecturally) to the quantum world. For instance we conjectured 10 years ago that each quantum reductive or Kac-Moody group admits a quantum cluster structure. This has been recenly confirmed by Kenneth Goodearl and Milen Yakimov.

Ultimately, I will explain how to fulfill one of the original goals of the cluster project: construction of the canonical triangular basis in acyclic case.

Posted March 19, 2014

3:30 pm – 4:20 pm Lockett 285

Stefan van Zwam, LSU
Beyond Total Unimodularity

A matrix is totally unimodular if the determinant of each square submatrix is in {-1, 0, 1}. Such matrices are a cornerstone of the theory of integer programming, and they have been studied extensively. In the late \'90s, Whittle introduced several classes of matrices with similar properties: the determinants of the submatrices are restricted to a certain set. In this talk I will discuss some results from the theory of totally unimodular matrices, and outline which of those results will, won\'t, or might generalize to Whittle\'s classes. The natural context for these problems is matroid theory, but prior knowledge of matroids is not required for this talk.

Friday, March 28, 2014

Posted March 26, 2014

1:30 pm Keisler Lounge, 3rd floor, Lockett Hall

Ben Warren, Department of Mathematics, LSU Graduate Student
Getting Started with Project Euler

Project Euler is an online repository of mathematical puzzles. Learn how Project Euler can help teach you how to improve your programming skills and impress your friends!

Monday, March 31, 2014

Posted March 31, 2014

1:30 pm – 2:20 pm Lockett 112

Irina Holmes, LSU
The Gaussian Radon transform and machine learning

Abstract: In this talk we investigate possible applications of the infinite dimensional Gaussian Radon transform for Banach spaces to machine learning. Specifically, we show that the Gaussian Radon transform offers a valid stochastic interpretation to the ridge regression problem in the case when the reproducing kernel Hilbert space in question is infinite-dimensional.

Tuesday, April 1, 2014

Posted March 21, 2014

5:00 pm Keisler Lounge (321 Lockett)

Meeting of the Actuarial Student Association

Yihua Sun will report on her internship in actuarial valuation in Taiwan Life.
Nick Crifasi will continue with his lessons in Excel.
Pizza will be served.

Wednesday, April 2, 2014

Posted March 30, 2014

Student Harmonic Analysis/Representation Theory Seminar

3:30 pm – 4:30 pm Lockett 233

Chris Cornwell, Duke University
Virtual Seminar: Knot contact homology, knot group representations, and the A-polynomial

Abstract: In the knot contact homology of a knot K there are augmentations that may be associated to a flat connection on the complement of K. We show that all augmentations arise this way. As a consequence, a polynomial invariant of K called the augmentation polynomial represents a generalization of the classical A-polynomial. A recent conjecture, similar to the AJ conjecture concerning the A-polynomial, relates a 3-variable augmentation polynomial to colored HOMFLY-PT polynomials. Our results can be seen as motivation for this conjecture having an augmentation polynomial in place of the A-polynomial.

Posted March 16, 2014
Last modified March 31, 2014

4:30 pm Lockett 235

Doug Pickrell, University of Arizona
Factorization in Lie groups

A periodic function can be decomposed into a Fourier series (which has many applications). In this talk I will present a somewhat analogous product factorization for a periodic function with values in a compact Lie group, such as SU(2) (and some of its applications, which are more specialized). At the end I will also briefly describe an analogous factorization for homeomorphisms of a circle.

Friday, April 4, 2014

Posted April 4, 2014

Algebra and Number Theory Seminar Questions or comments?

1:30 pm Keisler Lounge, 3rd floor, Lockett Hall

Jessica Bass, Department of Mathematics, LSU Graduate Student
An Introduction to Mathematica 9

Wolfram Mathematica is a great program to use for various mathematical computations. This talk will feature an introduction to using Mathematica and highlight features that are new to version 9. We will also discuss the compatibility of the Combinatorica package with Mathematica 9.

Tuesday, April 8, 2014

Posted March 25, 2014

3:30 pm – 4:20 pm Lockett 285

Atul Dixit, Tulane University
Some identities of Ramanujan in connection with the circle and divisor problems

On page 336 in his lost notebook, S. Ramanujan proposes an identity that may have been devised to attack a divisor problem. Unfortunately, the identity is vitiated by a divergent series appearing in it. We prove here a corrected version of Ramanujan\'s identity. While finding a plausible explanation for what may have led Ramanujan to consider a series that appears in this identity, we are led to a connection with a generalization of the famous summation formula of Voronoï. One of the ramifications stemming from this work allows us to obtain a one-variable generalization of two double Bessel series identities of Ramanujan, intimately connected with the circle and divisor problems, and which were proved only recently. This is work in progress and is joint with Bruce C. Berndt, Arindam Roy and Alexandru Zaharescu.

Wednesday, April 9, 2014

Posted April 8, 2014

2:30 pm Keisler Lounge, 3rd floor, Lockett Hall

Matt Barnes, Department of Mathematics, LSU Graduate Student
Sage Advice

Have you ever performed tedious calculations on your own personal computer? Would you much rather our computers do your work for you? Come learn how Sage, and our own math department computation servers, can save you time and resources. No prior experience with Sage is required or assumed.

Thursday, April 10, 2014

Posted February 25, 2014
Last modified April 5, 2014

3:30 pm Business Education Complex (BEC) 1510

Jean-Pierre Serre, College de France, emeritus Fields Medal recipient, Abel Prize recipient, and many more
Trace Forms

Refreshments will be served in the Keisler lounge from 2:45 to 3:15 pm. It takes approximately ten minutes to walk from Lockett Hall to BEC where the colloquium will be given.

Saturday, April 12, 2014

Posted February 24, 2014
Last modified February 11, 2022

9:00 am – 5:00 pm Business Education Complex (BEC) 1510

Automorphic Forms and Applications in Number Theory and Combinatorics

See the conference website: https://www.math.lsu.edu/nt2014/

Sunday, April 13, 2014

Posted February 24, 2014
Last modified April 9, 2014

9:00 am – 5:00 pm Business Education Complex (BEC) 1510 (excursion after morning lectures)

Automorphic Forms and Applications in Number Theory and Combinatorics

See conference website https://www.math.lsu.edu/nt2014/

Monday, April 14, 2014

Posted February 24, 2014
Last modified April 9, 2014

9:00 am – 5:00 pm Business Education Complex (BEC) 1510

Automorphic Forms and Applications in Number Theory and Combinatorics

See website https://www.math.lsu.edu/nt2014/

Tuesday, April 15, 2014

Posted February 24, 2014
Last modified April 9, 2014

9:00 am – 5:00 pm Business Education Complex (BEC) 1510

Automorphic Forms and Applications in Number Theory and Combinatorics

See website https://www.math.lsu.edu/nt2014/

Monday, April 21, 2014

Posted April 3, 2014
Last modified April 21, 2014

3:30 pm – 4:30 pm 233 Lockett Hall

Yuri Antipov, Mathematics Department, LSU
Diffraction of an obliquely incident electromagnetic wave by an impedance wedge

Tuesday, April 22, 2014

Posted February 23, 2014
Last modified November 29, 2022

3:30 pm – 4:30 pm Lockett 233

Eun-Jae Park, Yonsei University, South Korea
Recent Progress in Hybrid Discontinuous Galerkin Methods

A new family of hybrid discontinuous Galerkin methods is studied for second-order elliptic equations. Our approach is composed of generating PDE-adapted local basis and solving a global matrix system arising from a flux continuity equation. Our method can be viewed as a hybridizable discontinuous Galerkin method using a Baumann-Oden type local solver. A priori and a posteriori error estimates are derived and applications to the Stokes equations and Convection-Diffusion equations are discussed. Numerical results are presented for various examples.

Wednesday, April 23, 2014

Posted April 21, 2014

3:00 pm Lockett 009

Meeting of tenured faculty

Posted April 21, 2014
Last modified March 2, 2021

3:30 pm – 4:20 pm Lockett 233

Mustafa Hajij, Department of Mathematics, LSU Graduate Student
Virtual Topology Seminar: "Skein Theory and q-Series"

We study the tail a q-power series invariant of a sequence of admissible trivalent graphs with edges colored n or 2n. We use local skein relations to understand and compute the tail of these graphs. This allows us to understand the tail of the colored Jones polynomial for a large class of knots and links. For many quantum spin networks they turn out to be interesting number-theoretic q-series. In particular, certain quantum spin networks give a skein theoretic proof for the Andrews-Gordon identities for the two variable Ramanujan theta function as well to corresponding identities for the false theta function. Finally, we give product formula that the tail of such graphs satisfies.

Friday, April 25, 2014

Posted February 26, 2014

Pasquale Porcelli Lecture Series Special Lecture Series

3:00 pm Lockett 009

Faculty meeting

Monday, April 28, 2014

Posted March 12, 2014
Last modified February 6, 2021

3:30 pm – 5:30 pm Digital Media Center "Theatre" (Lecture Hall)

Susan Murphy, University of Michigan; H.E. Robbins Professor of Statistics & Professor of Psychiatry, Research Professor, Institute for Social Research 2013 MacArthur Fellow
L1: Getting SMART about Adapting Interventions L2: Adaptive Confidence Intervals for Non-smooth Parameters

Refreshments at 3pm in foyer by Digital Media Center Lecture Hall

Lecture 1 for General Audience (3:30-4:20)

Getting SMART about Adapting Interventions

Abstract: Imagine you are a child with ADHD. Wouldn't you like your doctors to periodically adapt your treatment to your unique—and ever-changing—condition? And wouldn't you be excited to learn that an algorithm used to analyze your medical data was originally developed for applications in robotics and artificial intelligence? This lecture will explain how a randomized clinical trial design (Sequential Multiple Assignment Randomized Trial or SMART) is being used to develop adaptive interventions—protocols that systematize sequential decision-making that is key to effective treatment of health problems. Examples include a study of children with ADHD and an ongoing study to improve care at mental health clinics.

Lecture 2 for more specialized audience (4:30-5:20)

Adaptive Confidence Intervals for Non-smooth Parameters

Abstract: Non-regular, aka "non-smooth" parameters are of scientific interest occur frequently in modern day inference. In particular when scientific interest centers on a non-smooth function of regular parameters such as in the assessment of a machine learning classifier's performance, in the estimation of multistage decision making policies and in the use of methods that use assumptions of sparsity to threshold estimators. If confidence intervals are considered at all, most research assumes potentially implausible "margin-like" conditions in order to justify the proposed confidence interval method. We describe a different approach based on constructing smooth upper and lower bounds on the parameter and then basing the confidence interval on the smooth upper and lower bounds. In particular two settings will be discussed and contrasted, that of a confidence interval for the misclassification rate and a confidence interval for a parameter in multistage decision making policies.

Tuesday, April 29, 2014

Posted March 26, 2014
Last modified April 21, 2014

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 233

Mark Wilde, LSU Department of Physics/CCT
Renyi generalizations of the conditional quantum mutual information

Abstract: The conditional quantum mutual information I(A;B|C) of a tripartite quantum state on systems ABC is an information quantity which lies at the center of many problems in quantum information theory. Three of its main properties are that it is non-negative for any tripartite state, that it decreases under local operations applied to systems A and B, and that it obeys the duality relation I(A;B|C)=I(A;B|D) for a four-party pure state on systems ABCD. It has been an open question to find Renyi generalizations of the conditional mutual information, that would allow for a deeper understanding of the original quantity and find applications beyond the traditional memoryless setting of quantum information theory. The present paper addresses this question, by defining different Renyi generalizations of the conditional mutual information that all converge to the conditional mutual information in a limit. Furthermore, we prove that many of these generalizations satisfy the aforementioned properties. As such, the quantities defined here should find applications in quantum information theory and perhaps even in other areas of physics, but we leave this for future work. We also state a conjecture regarding the monotonicity of the Renyi conditional mutual informations defined here with respect to the Renyi parameter. We prove that this conjecture is true in some special cases and when the Renyi parameter is in a neighborhood of one. Finally, we discuss how our approach for conditional mutual information can be extended to give Renyi generalizations of an arbitrary linear combination of von Neumann entropies, particular examples including the multipartite information and the topological entanglement entropy. This is joint work with Mario Berta (Caltech) and Kaushik Seshadreesan (LSU). This is based on the recent paper http://arxiv.org/abs/1403.6102

Posted April 24, 2014
Last modified April 27, 2014

3:30 pm – 4:20 pm Lockett 285

Fang-Ting Tu, National Center for Theoretical Sciences, Taiwan
Automorphic Forms on Shimura Curves of Genus Zero

Our aim is to study the arithmetic properties of automorphic forms on Shimura curves. Recently, Yifan Yang proposed a new method for studying automorphic forms on Shimura curves of genus zero, in which automorphic forms are expressed in terms of solutions of Schwarzian differential equations. We then can use the solutions to study the arithmetic properties of automorphic forms on Shimura curves. In this talk, we will give a quick overview of Yang's results, some applications, and a method to determine Schwarzian differential equations for certain Shimura curves.

Posted March 21, 2014
Last modified April 22, 2014

5:00 pm Keisler Lounge (321 Lockett)

Actuarial Student Association sponsored visitor

Our guest, Shelley Johnson (Foster & Foster Inc), is the consulting actuary to both the Louisiana State Employees\' Retirement System (LASERS) and the Teachers Retirement System of Louisiana (TRSL).

Thursday, May 1, 2014

Posted January 13, 2014
Last modified April 21, 2014

3:30 pm – 4:20 pm Lockett 285

Melvin Leok, University of California, San Diego
Lie group and homogeneous variational integrators and their applications to geometric optimal control theory

The geometric approach to mechanics serves as the theoretical underpinning of innovative control methodologies in geometric control theory. These techniques allow the attitude of satellites to be controlled using changes in its shape, as opposed to chemical propulsion, and are the basis for understanding the ability of a falling cat to always land on its feet, even when released in an inverted orientation.

We will discuss the application of geometric structure-preserving numerical schemes to the optimal control of mechanical systems. In particular, we consider Lie group variational integrators, which are based on a discretization of Hamilton's principle that preserves the Lie group structure of the configuration space. In contrast to traditional Lie group integrators, issues of equivariance and order-of-accuracy are independent of the choice of retraction in the variational formulation. The importance of simultaneously preserving the symplectic and Lie group properties is also demonstrated.

Recent extensions to homogeneous spaces yield intrinsic methods for Hamiltonian flows on the sphere, and have potential applications to the simulation of geometrically exact rods, structures and mechanisms. Extensions to Hamiltonian PDEs and uncertainty propagation on Lie groups using noncommutative harmonic analysis techniques will also be discussed.

We will place recent work in the context of progress towards a coherent theory of computational geometric mechanics and computational geometric control theory, which is concerned with developing a self-consistent discrete theory of differential geometry, mechanics, and control.

This research is partially supported by NSF CAREER Award DMS-1010687 and NSF grants CMMI-1029445, DMS-1065972, and CMMI-1334759.

Friday, May 2, 2014

Posted March 11, 2014

3:30 pm Keisler lounge

Spring Awards Ceremony

Wednesday, May 7, 2014

Posted May 1, 2014

1:00 pm Lockett 6

Meeting of Full Professors

Wednesday, May 28, 2014

Posted May 13, 2014
Last modified May 23, 2014

3:00 pm Lockett 285

Meeting of full professors

Monday, August 18, 2014

Posted May 5, 2014
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/ PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, August 20, 2014

Posted May 5, 2014
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive / PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Thursday, August 21, 2014

Posted August 19, 2014

1:30 pm – 3:00 pm B155 Pleasant - basement computer lab

Calculus/WebAssign workshop

For instructors of calculus who wish to know how to use WebAssign online homework assignments.

Friday, August 22, 2014

Posted May 5, 2014
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive / PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Tuesday, August 26, 2014

Posted August 25, 2014

3:30 pm – 4:30 pm 1008B Digital Media Center

Kamana Porwal, Louisiana State University
A Posteriori Error Estimates of Discontinuous Galerkin Methods for Elliptic Obstacle Problems

Thursday, August 28, 2014

Posted August 26, 2014

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:00 pm – 4:00 pm Lockett 232

Jacob Matherne, Department of Mathematics, LSU
Representation Theory of the Symmetric Group

Thursday, September 4, 2014

Posted August 26, 2014
Last modified September 2, 2014

3:30 pm Lockett 241 (refreshments in the lounge at 3:00)

Ling Long, LSU
Hypergeometric functions and some recent applications in number theory

Abstract: Hypergeometric functions, which are solutions of ordinary differential equations with only 3 regular singularities, are an important class of special functions. Hypergeometric functions are very useful for several subjects such as combinatorial identities, triangle groups, modular forms, and algebraic varieties. In this talk, we will give a general introduction to hypergeometric functions and discuss some recent applications in number theory.

Posted August 22, 2014

5:00 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial club meeting

Introducing the new president: Winnie Sloan

Answering questions about the actuarial profession and actuarial concentration

Guest: Recent graduate Nick Crifasi

Discussion of semester activities

Pizza will be served.

Monday, September 8, 2014

Posted August 21, 2014
Last modified February 2, 2022

3:30 pm – 4:20 pm Lockett 233

Phuc Nguyen, Department of Mathematics, Louisiana State University
The Navier-Stokes equations in nonendpoint borderline Lorentz spaces

It is shown both locally and globally that $L_t^∞(L_x^{3,q})$ solutions to the three-dimensional Navier-Stokes equations are regular provided $q\ne ∞$. Here $L_x^{3,q}$, $0 < q \le ∞$, is an increasing scale of Lorentz spaces containing $L_x^3$. Thus the result provides an improvement of a result by Escauriaza, Seregin and Šverák ((Russian) Uspekhi Mat. Nauk 58 (2003), 3–44; translation in Russian Math. Surveys 58 (2003), 211–250), which treated the case $q = 3$. A new local energy bound and a new $\epsilon$-regularity criterion are combined with the backward uniqueness theory of parabolic equations to obtain the result. A weak-strong uniqueness of Leray-Hopf weak solutions in $L_t^∞(L_x^{3,q})$, $q\ne ∞$, is also obtained as a consequence.

Wednesday, September 10, 2014

Posted August 26, 2014
Last modified September 8, 2014

3:30 pm – 4:20 pm 235 Lockett

Xiaoliang Wan, Louisiana State University
Some numerical issues about quantifying the effects of uncertainty

Abstract: The role of uncertainty in mathematical models has received more attention in the last two decades due to the quick development of algorithms and computation capability. In this talk I will discuss numerical computation for three cases to quantify the effects of uncertainty, including parametric uncertainty, stochastic modeling based on Wick product and minimum action method for large deviation principle, where I will focus on the last case. I will describe some recent progress of minimum action method and its application to model the nonlinear instability of wall-bounded shear flows as a rare event.

Posted September 6, 2014

4:30 pm – 5:30 pm Lockett 237

Dillon Mayhew, Victoria University of Wellington, NZ
Inequivalent representations of matroids

A representation of a matroid can be thought of as a one-to-one independence-preserving function from the groundset of the matroid into the points of a projective geometry. Naturally enough, there may be many such functions. Sometimes these functions are equivalent, in the sense that we can apply an automorphism of the projective geometry in such a way that they become identical, but it is also possible for the representations to be genuinely different. The existence of inequivalent representations makes matroid theory significantly more complicated, and quite a lot of effort has been dedicated to understanding, and gaining control over inequivalent representations. This talk will be a survey of some of those efforts.

Posted September 6, 2014

4:30 pm – 5:30 pm Lockett 237

Inequivalent representations of matroids

Thursday, September 11, 2014

Posted September 8, 2014
Last modified March 2, 2021

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:00 pm – 4:00 pm Lockett 113

Richard Frnka, Department of Mathematics, LSU Graduate Student
Farey Sequences, Ford Circles, and Their Application in Rademacher's Theorem for the Partition Function

The Farey Sequence of order n on an interval is the complete ordered sequence of reduced fractions whose denominator does not exceed n in the interval. These fractions can be used to generate Ford Circles, which have some very nice properties including a relation to modular forms. For two consecutive fractions in the sequence of order n (called Farey neighbors), the Ford Circles generated by them are tangent at only one point. By taking the arc on a circle between the two tangent points from both of its Farey neighbors for every fraction in the sequence, we can form a periodic, continous path. Rademacher used this path to integrate the generating function for partitions to come up with an exact formula for the partition number, which had only been approximated before. This talk does not require any background, and will be accessible to any graduate/undergraduate students with a basic knowledge of Euclidean geometry.

Wednesday, September 17, 2014

Posted August 12, 2014
Last modified March 2, 2021

3:30 pm – 4:20 pm Lockett 233

Kristen Hendriks, UCLA
Virtual Seminar: "Localization and the link Floer homology of doubly-periodic knots"

A knot K in S^3 is said to be q-periodic if there is an orientation-preserving action of Z_q on S^3 which preserves K and has fixed set an unknot disjoint from K. There are many classical obstructions to the possible periods of a knot, including Edmonds's condition on the genus and Murasugi's conditions on the Alexander polynomial. We construct localization spectral sequences on the link Floer homology of 2-periodic knots, and show that they give a simultaneous generalization of Edmonds's condition and one of Murasugi's conditions. We conclude with an example in which our spectral sequences give a stronger obstruction than these (although not all) classical conditions.

Thursday, September 18, 2014

Posted September 13, 2014

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:30 pm – 4:30 pm Lockett 113

Lucius Schoenbaum, LSU
Tropical Geometry I

Tropical geometry is a relatively new subject in mathematics which draws connections between algebraic geometry and discrete mathematics and applies them, for example, to enumerative geometry and areas of theoretical physics. In this talk I will introduce the subject and present the graph-theoretic proof of the Riemann-Roch theorem for tropical curves due to Gathmann (2006), based on work of Baker and Norine. This talk should be accessible to any graduate student, or motivated undergraduate familiar with basic abstract algebra and discrete math.

Posted August 26, 2014
Last modified September 15, 2014

3:30 pm – 4:30 pm Lockett 241

Scott Baldridge, Louisiana State University
Using a discrete set of transformations to prove smooth invariants of embedded tori in R^n

Abstract: It has been well known for over 80 years that knots in R^3 can be represented by 2-dimensional knot diagrams, and that three Reidemeister moves on those diagrams could be used to understand and prove invariants of knots. The problem with 2-dimensional diagrams is that smooth invariants that rely on metrics, differential forms, curvature forms, differential equations, etc. cannot be defined nor checked using the 2-dimensional moves. Motivated by search for a "Reidemeister-like" set of moves for embedded surfaces in R^4 (using actual embeddings, not projections), I recently developed the notion of a cube diagram to represent embedded n-tori in R^(n+2). In the case of knots in R^3, we proved that any cube diagram of a knot can be obtained from any other cube diagram of the knot using 2 types of cube diagram moves; this theorem allows us to prove differential topology invariants of knots in R^3 using a discrete set of transformations of the knot. In this talk, I will describe some differential topology applications of cube diagrams to Chern-Simons theory, and (if time) to higher dimensional embeddings.

Monday, September 22, 2014

Posted August 27, 2014
Last modified March 3, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 241

Yaniv Almog, Department of Mathematics, LSU
A Rigorous Proof of the Maxwell-Clausius-Mossotti Formula

We consider a large number of identical inclusions (say spherical), in a bounded domain, with conductivity different than that of the matrix. In the dilute limit, with some mild assumption on the first few marginal probability distribution (no periodicity or stationarity are assumed), we prove convergence in H1 norm of the expectation of the solution of the steady state heat equation, to the solution of an effective medium problem, which for spherical inclusions is obtained through the Maxwell-Clausius-Mossotti formula. Error estimates are provided as well.

Tuesday, September 23, 2014

Posted September 17, 2014

3:30 pm – 4:30 pm 235 Lockett Hall

Emil Horozov (Sofia University), Calogero-Moser Spaces and Representation Theory

We characterize the phase spaces of both rational and trigonometric Calogero-Moser systems in terms of representations of certain infinite-dimensional Lie algebras. The construction makes use of the theory of bispectral operators. The main result is that the Calogero-Moser spaces (in both cases) coincide with the orbit of the vacuum in this representations of reasonably defined group GL_infinity.

Posted September 13, 2014

5:00 pm Keisler Lounge (321 Lockett)

Actuarial club guest

The actuarial club will host:

Brian Small
Senior Vice President and Chief Actuary
Blue Cross Blue Shield of Louisiana

Wednesday, September 24, 2014

Posted September 22, 2014
Last modified March 2, 2021

3:30 pm – 4:20 pm 233 Lockett Hall

Robert Lipshitz, Columbia University
Virtual Seminar: "A Khovanov stable homotopy type"

Khovanov homology is a knot invariant which refines (categorifies) the Jones polynomial. After recalling the definition of Khovanov homology we will introduce a space-level version, and sketch some computations and (modest) applications. This is joint work with Sucharit Sarkar and Tyler Lawson.

Posted July 11, 2014
Last modified July 28, 2014

3:30 pm Lockett 15

Meeting of tenured faculty (P&T)

Thursday, September 25, 2014

Posted September 19, 2014
Last modified May 28, 2015

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:30 pm – 4:30 pm Lockett 113

Bach Nguyen, LSU
Derived Categories

Friday, September 26, 2014

Posted September 23, 2014

1:30 pm Lockett 232

Meeting of professorial faculty to discuss NSF EDT proposal

Monday, September 29, 2014

Posted September 8, 2014
Last modified September 25, 2014

3:30 pm – 4:30 pm Lockett 233

Cristi Guevara, LSU Department of Mathematics
Characterization of finite-energy solutions to the focusing 2-dimensional quintic NLS equation

Abstract. In this lecture we will focus on the mass-supercritical and energy-subcritical nonlinear Schroedinger equation or 2 dimensional quintic NLS. Using the concentration-compactness and rigidity method developed by Kenig-Merle, we characterize global behavior of solutions with H1 (finite energy) initial data. In particular, we will discuss an application of the concentration-compactness to the existence of weak blowup solutions for infinite-variance initial data. In addition, we will describe extensions on the conditions for scattering of globally existing solutions for the d-dimensional case.

Tuesday, September 30, 2014

Posted September 2, 2014
Last modified November 29, 2022

3:30 pm – 4:20 pm DMC, Room 1034

Discrete ABP estimate and rates of convergence of linear elliptic PDEs in non-divergence form

We design a finite element method (FEM) for linear elliptic equations in non-divergence form, which hinges on an integro-differential approximation of the PDE. We show the FEM satisfies the discrete maximum principle (DMP) provided that the mesh is weakly acute. Thanks to the DMP and consistency property of the FEM, we establish convergence of the numerical solution to the viscosity solution.

We derive a discrete Alexandroff-Bakelman-Pucci (ABP) estimate for finite element methods. Its proof relies on a geometric interpretation of Alexandroff estimate and control of the measure of the sub-differential of piecewise linear functions in terms of jumps, and thus of the discrete PDE. The discrete ABP estimate leads to optimal rates of convergence for the finite element method under suitable regularity assumptions on the solution and coefficient matrix.

Tuesday, October 7, 2014

Posted October 2, 2014

Algebra and Number Theory Seminar Questions or comments?

3:00 pm Computer Lab, Room 369, 3rd floor, Lockett Hall

Ben Warren, Department of Mathematics, LSU Graduate Student
You should have a homepage!

Setting up your LSU Math homepage is quick and easy, and this workshop will show you how to do it. Step-by-step instructions will be given, and everyone will leave with a homepage.

Wednesday, October 8, 2014

Posted October 2, 2014
Last modified September 17, 2021

3:30 pm – 4:30 pm 235 Lockett

Susan Montgomery, University of Southern California
On the values of Frobenius-Schur indicators for Hopf algebras

See abstract for Montgomery talk.

Thursday, October 9, 2014

Posted September 15, 2014
Last modified October 4, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 241

Susan Montgomery, University of Southern California
Orthogonal Representations: From Groups to Hopf Algebras

Tuesday, October 14, 2014

Posted October 7, 2014
Last modified May 8, 2021

3:30 pm – 4:30 pm 235 Lockett Hall

Joseph Timmer, Louisiana State University
Bismash Products and Exact Factorizations of $S_n$

With an exact factorization of a finite group $L = FG$, one may construct the bismash product Hopf algebra $H = kG\#kF$. If one were to factor the symmetric group $S_n = FG$, the resulting Hopf algebras have some interesting properties; mostly concerning the indicator values of irreducible modules. In this talk, we present the background of exact factorizations, and present some new results concerning bismash products in general and for those that arise from exact factorizations of $S_n$.

Posted September 15, 2014

5:00 pm Keisler Lounge (321 Lockett)

Actuarial club meeting

Guest: Dr. Joni Shreve, LSU MS in Analytics program + discussion of internships with past summer interns.

Thursday, October 16, 2014

Posted October 9, 2014

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:30 pm – 4:30 pm Lockett 113

Lucius Schoenbaum, LSU
Tropical Geometry II

Posted September 8, 2014
Last modified September 17, 2014

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Howard Elman, University of Maryland
Efficient Solution Algorithms for Stochastic Partial Differential Equations

Abstract: We consider new computational methods for solving partial differential equations (PDEs) when components of the problem such as diffusion coefficients or boundary conditions are not known with certainty but instead are represented as random fields. In recent years, several computational techniques have been developed for such models that offer potential for improved efficiencies compared with traditional Monte-Carlo methods. These include stochastic Galerkin methods, which use an augmented weak formulation of the PDE derived from averaging with respect to expected value, and stochastic collocation methods, which use a set of samples relatively small in cardinality that captures the character of the solution space. We give an overview of the relative advantages of these two methods and present efficient computational algorithms for solving the algebraic systems that arise from them. In addition, we show that these algorithms can be combined with techniques of reduced-order modeling to significantly enhance efficiency with essentially no loss of accuracy.

Tuesday, October 21, 2014

Posted October 7, 2014

3:30 pm – 4:30 pm 235 Lockett Hall

Luca Candelori, Louisiana State University
An algebro-geometric theory of vector-valued modular forms, Part 1

In this talk we describe a geometric theory of vector-valued modular forms attached to Weil representations of rank 1 lattices. More specifically, we construct vector bundles over the moduli stack of elliptic curves, whose sections over the complex numbers correspond to vector-valued modular forms attached to rank 1 lattices. The key idea is to construct vector bundles of Schrodinger representations and line bundles of half-forms over appropriate `metaplectic stacks\' and then show that their tensor products descend to the moduli stack of elliptic curves. We prove an algebraic version of the Eichler-Zagier Theorem comparing vector-valued modular forms to Jacobi forms. We also give an algebraic notion of q-expansions of vector-valued modular forms, and discuss growth conditions at the cusp at infinity.

Wednesday, October 22, 2014

Posted October 7, 2014
Last modified October 23, 2014

3:30 pm – 4:20 pm Lockett 233

James Conway, Georgia Tech
Virtual Seminar: "Transverse Surgery in Contact 3-Manifolds"

Abstract: Much ink has been spilled on surgery on Legendrian knots; much less well studied is surgery on transverse knots. We will investigate transverse surgery, and study its effect on open books, the Heegaard Floer contact invariant, and tightness. We show that surgery on the connected binding of a genus g open book that supports a tight contact structure preserves tightness if the surgery coefficient is greater than 2g-1. In a complementary direction, we give criteria for when positive contact surgery on Legendrian knots will result in an overtwisted manifold.

Posted October 20, 2014

4:30 pm – 5:30 pm Lockett 237

Emily Marshall, LSU
Hamiltonicity and Structure of Classes of Minor-free Graphs

In this talk, we examine the structure of K_{2,5} and K_{2,4} minor-free graphs. Tutte proved that every 4-connected planar graph is Hamiltonian. Not all 3-connected planar graphs are Hamiltonian, however: the Herschel graph is one example. We show that restricting to 3-connected, planar, K_{2,5}-minor-free graphs is enough to ensure Hamiltonicity. We give examples to show that the K_{2,5}-minor-free condition cannot be weakened to K_{2,6}-minor-free. Next we provide a complete characterization of all K_{2,4}-minor-free graphs. To prove both of these results we first provide a characterization of rooted-K_{2,2}-minor-free graphs. We also prove several useful results concerning Hamilton paths in rooted K_{2,2}-minor-free graphs.

Thursday, October 23, 2014

Posted September 4, 2014
Last modified October 8, 2014

3:30 pm – 4:20 pm Lockett 241

Victor Moll, Department of Mathematics, Tulane University
The evaluation of definite integrals

Abstract: The question of finding out a closed-form of a definite integral has its origin with Calculus itself. In spite of many advances, the algorithmic question is still not completely resolved. This talk will present a variety of such evaluations that lead to interesting connections to Number Theory, Combinatorics and (naturally) Special Functions.

Posted October 22, 2014
Last modified March 2, 2021

4:30 pm Lockett 223

Martin Adler, University of Tübingen
Perturbations of generators of C_0-semigroups

The theory of strongly continuous semigroups is an elegant method to investigate the well-posedness of abstract Cauchy problems. After introducing the basic theory of C_0-semigroups needed for this approach, I provide an overview of bounded and unbounded perturbation results. Finally, we will apply this theory to a delay equation.

Friday, October 24, 2014

Posted October 21, 2014

Algebra and Number Theory Seminar Questions or comments?

2:30 pm Keisler Lounge, 3rd Floor, Lockett Hall

Zachary Gershkoff, Mathematics Department, LSU
Formulas and Conditional Formatting in Spreadsheets

If you use LibreOffice Calc or another spreadsheet program to manage grades or finances or other numbers, this talk will show you how to use formulas to make your spreadsheets prettier and your life easier.

Tuesday, October 28, 2014

Posted October 7, 2014

3:30 pm – 4:30 pm 235 Lockett Hall

Luca Candelori, Louisiana State University
An algebro-geometric theory of vector-valued modular forms, Part 2

We follow up on our previous talk by describing applications of our geometric theory of vector-valued modular forms. First, we compute algebraic dimension formulas for the spaces of holomorphic vector-valued modular forms over any algebraically closed field (with mild restrictions on the characteristic) by using the Riemann-Roch theorem for Deligne-Mumford stacks. Second, we describe an algebro-geometric theory of modular forms of half-integral weight, as defined in the complex-analytic case by Shimura. Finally, as time allows, we explain how to extend our algebro-geometric theory to vector-valued modular forms attached to Weil representations of positive-definite lattices of higher rank, not just rank 1.

Posted October 21, 2014

4:30 pm – 5:20 pm Keisler Lounge

Jerome W. Hoffman, Mathematics Department, LSU
The projective plane and elliptic curves

Wednesday, October 29, 2014

Posted July 24, 2014
Last modified July 28, 2014

3:30 pm Lockett 15

Faculty meeting

Posted October 24, 2014

4:30 pm – 5:30 pm Lockett 237

Elyse Yeager, University of Illinois
Disjoint Cycles and a Question of Dirac

In this talk, we explore a refinement of the Corr\\\'adi-Hajnal Theorem. The Corr\\\'adi-Hajnal Theorem states that any graph on at least $3k$ vertices with minimum degree at least $2k$ contains a set of $k$ vertex-disjoint cycles. Our refinement answers a 1963 question posed by G. Dirac about ($2k-1$)-connected graphs that do not possess $k$ disjoint cycles. For a portion of our result, we use techniques from equitable coloring.

Thursday, October 30, 2014

Posted October 18, 2014
Last modified October 27, 2014

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:30 pm – 4:30 pm Lockett 113

Sean Taylor, LSU
Introduction to Theory of Sheaf, Part I

Sheaves are an important tool in modern mathematics that were introduced by Jean Leray during the 1940's. They have since become an integral part of algebraic geometry due to the work of many, not the least of which are Jean-Pierre Serre and Alexander Grothendieck. However, they are fruitful not only to algebraic geometry, but also to such areas as algebraic topology and representation theory. In this talk I will present the basic definition of sheaves, the category of sheaves on a topological space, and the functors that can be associated with these categories. I will also present a theorem relating certain types of sheaves on a topological space and the fundamental group of that space.

Tuesday, November 4, 2014

Posted September 13, 2014

5:00 pm Keisler Lounge (321 Lockett)

Actuarial club guest

The actuarial club will host:
Greg Curran
Consulting Actuary
G. S. Curran & Company, Ltd.

Wednesday, November 5, 2014

Posted October 22, 2014
Last modified October 23, 2014

3:30 pm – 4:20 pm Lockett 277
(Originally scheduled for Wednesday, October 29, 2014, 3:30 pm)

Boris Rubin, Louisiana State University
Gegenbauer-Chebyshev Integrals and Radon Transforms

We suggest new modifications of Helgason\'s support theorems and related characterizations of the kernel (the null space) for the classical hyperplane Radon transform and its dual, the totally geodesic transforms on the sphere and the hyperbolic space, the spherical slice transform, and the spherical mean transform for spheres through the origin. The assumptions for functions are close to minimal and formulated in integral terms. The proofs rely on projective equivalence of these transforms and new facts for the Gegenbauer-Chebyshev fractional integrals.

Posted October 31, 2014

4:30 pm – 5:30 pm Lockett 237

Peter Nelson, University of Waterloo
Exponentially Dense Matroids

The growth rate function for a minor-closed class of matroids is the function $h(n)$ whose value at an integer n is the maximum number of elements in a simple matroid in the class of rank at most n; this can be seen as a measure of the density of the matroids in the class. A theorem of Geelen, Kabell, Kung and Whittle implies that $h(n)$, where finite, grows either linearly, quadratically, or exponentially with base equal to some prime power $q$, in $n$. I will discuss growth rate functions for classes of the exponential sort, determining the growth rate function almost exactly for various interesting classes and giving a theorem that essentially characterises all such functions.

Thursday, November 6, 2014

Posted October 30, 2014

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:30 pm – 4:30 pm Lockett 113

Sean Taylor, LSU
Introduction to Theory of Sheaf, Part II

Monday, November 10, 2014

Posted November 1, 2014

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Room 233 Lockett

Jacob Grey, Department of Mathematics LSU
A qualitative analysis of some Nonlinear Dispersive Evolution Equations

Tuesday, November 11, 2014

Posted October 8, 2014
Last modified October 16, 2014

3:30 pm – 4:30 pm 235 Lockett Hall

Siu-hung (Richard) Ng, LSU
On Weil Representations of Modular Tensor Categories

Associated to a nondegenerate quadratic function on a finite abelian group is a projective representation of the modular group SL(2,Z) that is known as the Weil representation. This projective representation can be renormalized by the Gauss sum of the quadratic function to an ordinary representation of the metaplectic group Mp(2,Z). In this talk, we will discuss the corresponding analog of the Weil representation of a modular tensor category. This talk is intended to be accessible to graduate students with the knowledge of graduate algebra.

Posted October 21, 2014
Last modified February 20, 2022

4:30 pm – 5:20 pm Keisler Lounge

Richard Frnka, Department of Mathematics, LSU Graduate Student
Farey Sequences and Ford Circles

The Farey Sequence of order $n$ on an interval is the complete ordered sequence of reduced fractions whose denominator does not exceed $n$. These fractions can be used to generate Ford Circles, which have some very nice properties including a relation to modular forms. For two consecutive fractions in the sequence of order $n$ (called Farey neighbors), the Ford Circles generated by them are tangent at only one point. By taking the arc on a circle between the two tangent points from both of its Farey neighbors for every fraction in the sequence, we can form a periodic, infinitely continuous path. Rademacher used this path to integrate the generating function for partitions to come up with an exact formula for the partition number, which had only been approximated before. This talk does not require any background, and will be accessible to any students with a basic knowledge of Euclidean geometry.

Thursday, November 13, 2014

Posted November 9, 2014

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:30 pm – 4:30 pm Lockett 113

Dun Liang, LSU
Hodge Theory

Monday, November 17, 2014

Posted November 12, 2014
Last modified March 2, 2022

3:30 pm – 4:20 pm Room 233 Lockett

Michael Malisoff, LSU Roy P. Daniels Professor
Designs and Theory for State-Constrained Nonlinear Feedback Controls for Delay Systems: An Infomercial

This talk will discuss some of my research that is being supported by my two new research grants from the US National Science Foundation Directorate for Engineering. The first grant project is entitled “Robustness of Networked Model Predictive Control Satisfying Critical Timing Constraints” and focuses on resolving contentions in a class of communication networks that are common in automobiles and other real-time control applications, and is joint with the Georgia Institute of Technology School of Electrical and Computer Engineering. The second project, “Designs and Theory of State-Constrained Nonlinear Feedback Controls for Delay and Partial Differential Equation Systems,” covers control designs for classes of ordinary and hyperbolic partial differential equations that arise in oil production and rehabilitation engineering, and is joint with the University of California, San Diego Department of Mechanical and Aerospace Engineering. In the first 10 minutes, I will provide a brief description of the basic ideas of control theory. Then, I will present a 25 minute summary of my research on neuromuscular electrical stimulation (or NMES), which is a biomedical approach for helping to restore movement in patients with mobility disorders. My NMES research designed controls for NMES of the human knee under delays and subject to a constraint on the allowable knee position, and is joint with my PhD student Ruzhou Yang and with Prof. Marcio de Queiroz, who are with the LSU Department of Mechanical and Industrial Engineering. In the last 10 minutes, I will advertise for my open PhD student positions on my grants, by providing a brief nontechnical summary of the problems to be addressed and discussing the role PhD students would play in the research. This talk will be accessible to students and others who are familiar with basic differential equations. No background in controls is needed.

Tuesday, November 18, 2014

Posted November 13, 2014

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Li-yeng Sung, Louisiana State University
Multigrid Methods for Saddle Point Problems

In this talk we will present a general framework for the design and analysis of multigrid methods for saddle point problems arising from mixed finite element discretizations of elliptic boundary value problems. These multigrid methods are uniformly convergent in the energy norm on general polyhedral domains where the elliptic boundary value problems in general do not have full elliptic regularity. Applications to Stokes, Lam\\\'e, Darcy and related nonsymmetric systems will be discussed. This is joint work with Susanne Brenner, Hengguang Li and Duk-Soon Oh.

Posted October 8, 2014
Last modified October 30, 2014

3:30 pm – 4:30 pm 235 Lockett Hall

James Zhang, University of Washington
Homological identities concerning Hopf algebra actions on Artin-Schelter regular algebras

The Nakayama automorphism of an Artin-Schelter regular algebra controls the class of Hopf algebras that act on the algebra. This can be interpreted as a homological identity. Several applications of homological identities will be given. The talk is based on recent work of K. Chan, J.-F. Lu, X.-F. Mao, M. Reyes, D. Rogalski and C. Walton.

Wednesday, November 19, 2014

Posted July 11, 2014
Last modified July 28, 2014

3:30 pm Lockett 15

Faculty meeting with Provost Bell

Posted November 17, 2014

4:30 pm – 5:30 pm Lockett 237

Stefan van Zwam, LSU
Connectivity in Graphs and Matroids

A recurring theme in graph theory and its generalizations is connectivity. Time and again it is found that the presence (or absence!) of connectivity reveals useful structural information about the problem at hand. In this talk I will touch on a variety of examples from graph theory and matroid theory.

Thursday, November 20, 2014

Posted October 30, 2014

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 241

James Zhang, University of Washington
Zariski cancellation problem for noncommutative algebras

Abstract: The famous Zariski cancellation problem asks if the polynomial algebra of more than two variables is cancellative. We consider a noncommutative version of the cancellation problem and obtain an affirmative answer for many classes of noncommutative algebras. Joint work with Jason Bell.

Tuesday, November 25, 2014

Posted November 19, 2014

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:30 pm – 4:30 pm Lockett 113

Dun Liang, LSU
Curves, Jacobian, and Their Moduli

Tuesday, December 2, 2014

Posted October 8, 2014
Last modified November 26, 2014

3:30 pm – 4:30 pm 235 Lockett Hall

Mahir Can, Tulane University
Maximal chains of weak order posets of symmetric varieties

The W-set of an element of a weak order poset is useful in the cohomological study of the closures of spherical subgroups in generalized flag varieties. In this talk, after explaining various applications of this notion, we describe in a purely combinatorial manner the W-sets of the weak order posets of three classical symmetric spaces associated to the general linear group. In particular, we give a complete characterization of the maximal chains of an arbitrary lower order ideal in any of these three posets. This is a joint work with Michael Joyce and Ben Wyser.

Thursday, December 4, 2014

Posted October 2, 2014

3:30 pm – 4:40 pm

F. Alberto Grünbaum, University of California, Berkeley
Time and band limiting and the bispectral problem: motivation, applications and open problems.

Abstract: The problem of how to best use (noisy) partial spectral information to determine a signal of finite duration starts with the work of C. Shannon, D. Slepian, H. Landau and H. Pollak at Bell Labs back around 1960. I will tell parts of this story as well as the way in which it led to the bispectral problem. The mathematics behind the bispectral problem is much richer than one may suspect: integrable systems like KdV, isomonodromic deformations, characters of representations of certain groups, certain non-commutative algebras of matrix valued differential operators, contacts with random matrix theory and other gems are all pieces of this puzzle. I am very interested in making this a two-way street in terms of finding bispectral situations that lead to the \"time-band limiting\" miracle of Slepian, Landau and Pollak in terms of finding a commuting differential operator for a naturally appearing integral one. This ongoing effort involves the work of several people, including Milen Yakimov.

Thursday, December 11, 2014

Posted November 28, 2014

Cain Center Seminar

4:30 pm – 5:30 pm Prescott 205

Peter Wolenski, LSU Department of Mathematics Russell B. Long Professor
Elvis and structured discontinuous systems

Elvis is a calculus dog with an honorary degree from Hope College, Michigan, who has been featured in a plethora of articles and undergraduate mathematical research projects. We first review the underlying mathematical problem in all these articles and projects and demonstrate that it is a particular instance of a generalized framework of optimal control systems with discontinuous dynamic data. The state space is structured with a Whitney-type stratification, which means the state space is partitioned into submanifolds of various dimensions. Each submanifold is endowed with nice dynamics satisfying a structural condition. The latter is imposed to regulate the jumping off of a continuous trajectory from one manifold into another. A key assumption on the submanifolds is that their closures are proximally smooth and relatively wedged, concepts from nonsmooth analysis that ensure well-behaved tangent and normal cones. The main issue is to develop optimal control theory in the whole space with discontinuous dynamics, but of which a well-developed theory is available on each of the submanifolds. We offer some examples and results on weak and strong invariance, and suggest possible future research directions.

Tuesday, January 6, 2015

Posted October 13, 2014
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/ PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, January 7, 2015

Posted October 13, 2014
Last modified December 13, 2022

Algebra and Number Theory Seminar Questions or comments?

1:00 pm – 4:00 pm Lockett 232

Comprehensive/ PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Thursday, January 8, 2015

Posted December 28, 2014

2:30 pm – 3:20 pm 235 Lockett Hall

Taiki Shibata, University of Tsukuba
Modular representations of Chevalley supergroups

An affine group scheme over a field k is a representable functor from the category of commutative k-algebras to the category of groups. Replacing ``algebras\'\' with ``superalgebras\'\' (=Z_2-graded algebras), we obtain the notion of an affine supergroup scheme (or, simply, a supergroup). An important example is a Chevalley supergroup introduced by R. Fioresi and F. Gavarini. I will talk about Hopf algebraic techniques applied to the modular representation theory of Chevalley supergroups. In joint work with A. Masuoka, we showed that, for a Chevalley supergroup G, there is a one-to-one correspondence between the G-modules and the integrable hy(G)-modules. Here, hy(G) is a generalization of the Lie superalgebra of G, called the hyper-superalgebra, due to M. Takeuchi. In my recent work, I obtained a super-analogue of the Steinberg tensor product theorem for Chevalley supergroups, which is a fundamental result in the modular representation theory of algebraic groups. In this talk, I would like to explain these results.

Posted December 28, 2014

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm 235 Lockett Hall

Kenichi Shimizu, Nagoya University
The distinguished invertible object of a finite tensor category and related topics

Fusion categories are an important class of tensor categories, and their non-semisimple generalizations -- finite tensor categories -- are also an interesting subject. I will talk about some properties of ``the distinguished invertible object\'\' of a finite tensor category introduced by Etingof, Nikshych and Ostrik. This is a categorical analogue of the modular function of a Hopf algebra (or, going back further, a locally compact group). As the modular function does in the theory of Hopf algebras, the distinguished invertible object plays an important role in the theory of finite tensor categories. In my talk, I will introduce recent my results on the distinguished invertible object, especially its relation with the monoidal center construction and applications to topological invariants.

Friday, January 9, 2015

Posted October 13, 2014
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/ PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Thursday, January 22, 2015

Posted January 9, 2015
Last modified January 22, 2015

3:30 pm – 4:20 pm Lockett 285

Arnab Ganguly, University of Louisville
Limit theorems in stochastic analysis

Limit theorems for stochastic processes have a variety of applications in diverse fields ranging from statistics to biology. While the weak convergence results often help to identify approximate continuous models from discrete-time ones, the results in the form of moderate and large deviations help to assess the quality of the approximations by studying various 'rare events'. The talk will focus on some systematic approaches to limit theorems for stochastic differential equations, which are particularly beneficial in infinite-dimensional settings. Several specific examples will be discussed illustrating the usefulness of these approaches.

Wednesday, January 28, 2015

Posted January 23, 2015

3:00 pm Keisler Lounge (321 Lockett)

Actuary Club meeting

Jesse Lu will be presenting on his internship experience. Discussion of semester activities.

Thursday, January 29, 2015

Posted January 9, 2015
Last modified January 22, 2015

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:20 pm Lockett 285

Lingjiong Zhu, University of Minnesota
Self-Exciting Point Processes

Self-exciting point processes are simple point processes that have been widely used in neuroscience, sociology, finance and many other fields. In many contexts, self-exciting point processes can model the complex systems in the real world better than the standard Poisson processes. We will discuss the Hawkes process, the most studied self-exciting point process in the literature. We will talk about the limit theorems and asymptotics in different regimes. Extensions to Hawkes processes and other self-exciting point processes will also be discussed.

Monday, February 2, 2015

Posted January 27, 2015

1:30 pm – 2:20 pm Lockett 136

Thomas Lam, University of Michigan
Enumeration of Young tableaux

This talk is primarily aimed at undergraduates. Young tableaux are natural combinatorial objects that appear in combinatorics, representation theory, and algebraic geometry. I will talk about some old and some newer questions related to counting Young tableaux. These questions are closely related to some natural problems such as: how long is the longest increasing subsequence in a sequence of n random numbers? Refreshments will be served in the Keisler lounge at 1:00 pm.

Tuesday, February 3, 2015

Posted January 27, 2015

VIGRE@LSU: Student Colloquium Questions or comments?

2:30 pm – 3:20 pm Lockett 136

Thomas Lam, University of Michigan
Electrical networks and group theory

This talk is primarily for advanced undergraduates and graduate students. I will talk about electrical networks consisting only of resistors. These electrical networks satisfy certain \"relations\"; for example, two resistors in series (or two in parallel) can be replaced by a single resistor with a particular resistance. I will discuss an approach to studying electrical networks using generators and relations, where methods from (Lie) group theory might be applied. There will be refreshments in the Keisler Lounge at 2:00 pm

Posted January 19, 2015
Last modified March 2, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm DMC 1034

Natasha Sharma, University of Texas El Paso
An Adaptive DG-θ Method with Residual-type Error Estimates for Nonlinear Parabolic Problems

In this talk, we propose and analyze a fully discretized adaptive Discontinuous Galerkin-θ (DG-θ) method for nonlinear parabolic problems with the space discretized by the DG finite elements and the time discretization realized by the popular θ-time stepping scheme. The a posteriori error analysis is based on the residual-type estimator derived by Verfurth for conforming approximations in space and θ-scheme in time. This DG-θ estimator will enable us to then realize the adaptive algorithm for local mesh refinement. The desirable properties of reliability and efficiency of the estimator will be then be discussed and finally, we will present numerical results to illustrate the performance of this method.

Posted January 28, 2015
Last modified May 8, 2021

4:00 pm – 5:00 pm 235 Lockett Hall

Thomas Lam, University of Michigan
Whittaker functions and geometric crystals

I will talk about a formula for Archimedean Whittaker functions as integrals over Berenstein and Kazhdan's geometric crystals. This formula is a geometric analogue of the expression for an irreducible character of a complex semisimple Lie algebra as a sum over Kashiwara's crystals. The formula is closely related to mirror symmetry phenomena for flag varieties, and to the study of directed polymers in probability.

Wednesday, February 4, 2015

Posted February 2, 2015

3:30 pm – 4:20 pm 233 Lockett Hall

Emily Stark, Tufts University
Abstract commensurability and quasi-isometric classification in dimension two

Two foundational questions in geometric group theory are to characterize the abstract commensurability and quasi-isometry classes within a class of groups, and to understand for which classes of groups the classifications coincide. In this talk, I will present a solution within the class of groups isomorphic to the fundamental group of two closed hyperbolic surfaces identified along an essential simple closed curve in each. I will discuss current work, joint with Pallavi Dani and Anne Thomas, for right-angled Coxeter groups.

Posted January 30, 2015

5:30 pm Keisler Lounge (321 Lockett)

Actuarial club meeting

Kyla Kucharchuk from LSU career services will be the speaker. This meeting will benefit all students in the actuarial science concentration regardless of whether they are pursuing actuarial science as a profession.

Thursday, February 5, 2015

Posted January 9, 2015
Last modified January 22, 2015

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:20 pm Lockett 285

Eunghyun Lee, Centre de recherches mathématiques, Montréal
The Coordinate Bethe Ansatz Solvable Interacting Particle Systems

Interacting particle systems on the integer lattice that the coordinate Bethe Ansatz method can be applied to have connections to the random matrix theory and the symmetric function theory. Based on the coordinate Bethe Ansatz method, the exact formulas of the transition probabilities of the finite systems are given by the multi-dimensional contour integrals. In particular, we consider two initial configurations of the systems that are related to the GUE Tracy-Widom distribution and the GOE Tracy-Widom distribution. The combinatorial properties arising from our models are also discussed.

Monday, February 9, 2015

Posted February 4, 2015

1:30 pm – 2:20 pm Lockett 136

Lihe Wang, University of Iowa
Mathematics, its origin, meaning, and applications

What is behind the common features of modern sciences? What is the driving force behind the modern productivity? What are the methods to discover information within random numbers? In this talk, we will try to present the miracle power of calculus with algebra and geometry and make clear the ubiquitous presence of mathematics throughout the discovery of calculus, linear algebra, and differential equations. A light lunch will be served in the Keisler lounge at 1:00 pm.

Tuesday, February 10, 2015

Posted February 4, 2015

VIGRE@LSU: Student Colloquium Questions or comments?

2:30 pm – 3:20 pm Lockett 136

Lihe Wang, University of Iowa
Regularity theory for elliptic equations

We will talk about a unified approach to the regularity theory of elliptic and parabolic equations. The introduction of Sobolev spaces, the meaning of embedding theorems, and the geometric and probabilistic meaning of some of the regularity and singularity theory will be discussed. Refreshments will be served in the Keisler lounge at 2:00 pm.

Posted January 26, 2015

3:30 pm – 4:30 pm Lockett 233

Ata Mesgarnejad, Louisiana State University
A variational approach to fracture of thin films under out-of-plane loading

Wednesday, February 11, 2015

Posted January 28, 2015

4:30 pm – 5:30 pm Lockett 276

Jorn van der Pol, TUE
On the number of Matroids

In this talk I will discuss joint work with Nikhil Bansal and Rudi Pendavingh, in which we consider the number of matroids on a ground set of size n. The talk will roughly consist of two parts. In the first part, I will present a technique for bounding the number of stable sets in a graph. The technique uses the spectral properties op the graph to obtain a concise description of any stable set in the graph. This result does not use any matroid theory, and works in a broader setting than matroid enumeration. In the second part, we will see how this spectral technique can be combined with some elementary properties of matroids in order to obtain an upper bound on the number of matroids. This upper bound substantially improves previous upper bounds, and comes quite close to the best known lower bound.

Thursday, February 12, 2015

Posted January 9, 2015
Last modified January 22, 2015

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 285

Grace Wang, Duke University
Data Analysis with Low-dimensional Structures

Analyzing data collected from different fields is a challenge facing scientists and engineers. The property of being high-dimensional makes these data sets hard to investigate. Fortunately, in many cases, data locally concentrate along a low-dimensional subspace, which makes it possible to analyze. This talk will demonstrate different objectives where low-dimensional structures can be utilized for various data analysis purposes.

A major part of the talk will introduce a solution to the high-dimensional regression problem. More precisely, given a set of high-dimensional predictors {xi} and the corresponding high-dimensional responses {yi}, the high-dimensional regression problem seeks a function f such that f(xi) is sufficiently close to yi for all i. An algorithm with piecewise linear mappings built on a tree structure is proposed. It is designed to handle high-dimensional predictors and responses, and in particular, cases where closeness of predictors is inconsistent with closeness of responses. Experimental results demonstrate the excellent performance of our method.

Additional problems in the area will be discussed briefly, including the consistency analysis of a subspace-based classification algorithm and an automated J wave (anomaly) detection in heart (electrocardiography) signals.

Thursday, February 19, 2015

Posted February 13, 2015

3:30 pm – 4:20 pm Lockett 235

Henry Tucker, University of Southern California
Frobenius-Schur indicators for near group fusion categories

Fusion categories are C-linear, rigid, semisimple tensor categories. They appear in a diverse range of mathematics, including representation theory of quantum groups, subfactor theory, and conformal field theory. The classical Frobenius-Schur indicator was first defined for representations of a finite group -- the most well-known example of a fusion category. The definition of the indicator has been extended to objects in a general fusion category by work of Ng-Schauenburg. This talk will report on progress toward computation of these indicators for near group fusion categories, which are fusion categories with one non-invertible object.

Posted February 6, 2015
Last modified February 18, 2015

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

4:30 pm – 5:30 pm Lockett 233

Eric Bucher, LSU
Maximal Green Sequences

Tuesday, February 24, 2015

Posted January 30, 2015

3:30 pm – 4:30 pm Lockett 233

Mark Wilde, LSU Department of Physics/CCT
Attempting to Reverse the Irreversible in Quantum Physics

Wednesday, February 25, 2015

Posted February 18, 2015

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett 16

Meeting of the tenured and tenure-track faculty

Thursday, February 26, 2015

Posted February 25, 2015

3:30 pm – 4:30 pm 235 Lockett Hall

Daqing Wan, UC Irvine
Slopes of Modular Forms

The p-adic valuation of the p-th coefficient of a normalized modular eigenform is called the slope of the modular form. Understanding the slope distribution and variation is a major intriguing arithmetic problem in modern number theory and arithmetic geometry. In this talk, I will present a simple introduction to this fascinating subject, ending with our recent joint work with Liang Xiao, Jun Zhang and Ruochuan Liu.

Friday, February 27, 2015

Posted February 23, 2015
Last modified March 2, 2021

3:30 pm

Itai Shafrir, Department of Mathematics, Technion - Israel Institute of Technology
Asymptotic behavior of critical points of an energy involving a "circular-well" potential

We study the singular limit of critical points of an energy with a penalization term depending on a small parameter. The energy involves a potential which is a nonnegative function on the plane, vanishing on a closed curve. We generalize to this setting results obtained by Bethuel, Brezis and Helein for the Ginzburg-Landau energy. This is a joint work with Petru Mironescu (Lyon I).

Monday, March 2, 2015

Posted February 15, 2015

3:30 pm – 4:20 pm Lockett Hall Room 233

Robert P. Viator, Jr., LSU
Perturbation Theory of High-Contrast Photonic Crystals

Wednesday, March 4, 2015

Posted February 27, 2015
Last modified March 3, 2021

3:30 pm – 4:20 pm Lockett 277

Eli V Roblero-Mendez, LSU
Rigidity of actions of simple Lie groups, I

In this talk we'll give an introduction to Rigidity Theory and the study of actions of simple Lie groups on manifolds which preserve some geometric structure. We'll also give an overview on some recent results obtained in Zimmer's Program and some techniques of how these results have been obtained.

Posted February 20, 2015

5:30 pm Keisler Lounge (321 Lockett)

Meeting of the student actuarial club

Rodney Friedy from the Louisiana Department of Insurance (where he is the director of life actuarial services) will be visiting.

Thursday, March 5, 2015

Posted February 10, 2015
Last modified October 4, 2021

3:30 pm – 4:20 pm 285 Lockett

Tadele Mengesha, The University of Tennessee, Knoxville
The variational convergence of some nonlocal convex functionals

In this talk, I will discuss a class of variational problems associated with nonlocal elastic energy of peridynamic-type which result in nonlinear nonlocal systems of equations with various volumetric constraints. The well-posedness of variational problems is established via careful studies of the related energy spaces which are made up of vector-valued functions. In the event of vanishing nonlocality we establish the convergence of the nonlocal energy to a corresponding local energy via Gamma convergence. For some convex energy functionals we will explicitly find the corresponding limit energy. As a special case the classical Navier–Lamé potential energy will be realized as a limit of linearized peridynamic energy offering a rigorous connection between the nonlocal peridynamic model to classical mechanics for small uniform strain.

Monday, March 9, 2015

Posted February 15, 2015
Last modified March 8, 2015

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:20 pm Room 233 Lockett Hall

Anthony Polizzi, LSU
An asymptotic formula for solutions to a heterogeneous logistic equation with small diffusion rate

Of concern is a semilinear elliptic boundary value problem on a bounded domain with a smooth boundary. Its solution u(x) represents the steady state population density of a species in an insulated habitat with a given resource profile a(x) and a given nonnegative coefficient representing the species' rate of random diffusion. We study asymptotic expansions for solutions in the form of Taylor series in the diffusion coefficient. It turns out that, in the presence of diffusion, u(x) depends analytically on the diffusion coefficient, which trivializes the convergence of such a series. We therefore focus our attention primarily on the more delicate case of zero diffusion, in which u(x) is not analytic in the coefficient. It is known that u(x) tends to a(x) as the coefficient tends to zero. We generalize this result by rigorously establishing the desired expansions under suitable assumptions on a(x). Our main result is their convergence on the closure of the domain in this case. We also give an explicit formula for each coefficient of the expansions.

Tuesday, March 10, 2015

Posted March 3, 2015
Last modified March 4, 2015

1:30 pm – 2:20 pm Lockett 138

Ben Webster, University of Virginia
Untying knots: topology, DNA, and coloring

I\'m sure you\'ve all seen a very tangled rubber band in your life. You know logically that it must be possible to untangle the band without breaking it but this can be hard to put this knowledge into practice. In fact, if your obnoxious roommate had cut the rubber band, tangled its ends together, and then carefully glued the ends together (isn\'t he always doing stuff like that?), how would you know? Of course, you\'d know you hadn\'t untangled it yet, but you can try every possible way.

Luckily, mathematicians have your back. They\'ve worried precisely this for a century (they can\'t trust their roommates either, apparently). Bacteria have worried about it a lot longer (with isomerase playing the role of the prankster roommate). I\'ll give a basic introduction to the theory of knots and their use in mathematics and biology. In particular, I\'ll show you how to wise up to your roommate\'s tricks (though it may take a while) .

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There will be a light lunch in the Keisler lounge at 1:00 pm.

Posted March 4, 2015

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 235

Ben Webster, University of Virginia
Quantizations and duality for symplectic singularities

Since they were introduced about 2 decades ago, symplectic singularities have shown themselves to be a remarkable branch of algebraic geometry. They are much nicer in many ways than arbitrary singularities, but still have a lot of interesting nooks and crannies.

I\'ll talk about these varieties from a representation theorist\'s perspective. This might sound like a strange direction, but remember, any interesting symplectic structure is likely to be the classical limit of an equally interesting non-commutative structure, whose representation theory we can study. While this field is still in its infancy, it includes a lot of well-known examples like universal enveloping algebras and Cherednik algebras, and has led a lot of interesting places, including to categorified knot invariants and a conjectured duality between pairs of symplectic singularities. I\'ll give a taste of these results, in particular on very recent progress in constructing this duality.

Posted March 2, 2015
Last modified November 29, 2022

3:30 pm – 4:30 pm 1034 Digital Media Center

Hongchao Zhang, Louisiana State University
A Fast Algorithm for Polyhedral Projection

In this talk, we discuss a very efficient algorithm for projecting a point onto a polyhedron. This algorithm solves the projection problem through its dual and fully exploits the sparsity. The SpaRSA (Sparse Reconstruction by Separable Approximation) is used to approximately identify active constraints in the polyhedron, and the Dual Active Set Algorithm (DASA) is used to compute a high precision solution. Some interesting convergence properties and very promising numerical results compared with the state-of-the-art software IPOPT and CPLEX will be discussed in this talk.

Wednesday, March 11, 2015

Posted February 27, 2015
Last modified March 3, 2021

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:30 pm Lockett 277

Eli V Roblero-Mendez, LSU
Rigidity of actions of simple Lie group, II

Thursday, March 12, 2015

Posted March 3, 2015
Last modified March 4, 2015

2:30 pm – 3:40 pm Lockett 138

Ben Webster, University of Virginia
Symmetric Groups and Lie Algebras

I\'ll give an expository talk about the representation theory of symmetric groups over the rational numbers or finite field. While this is a very classical subject, it\'s one which is very rich, and where there is still a lot to say. I\'ll emphasize the connection to the emerging field of categorification, and explain in what sense a Lie algebra acts on the category of representations of S_n (for all n).

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There will be refreshments in the Keisler lounge at 2pm.

Posted March 5, 2015

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:40 pm – 4:30 pm Lockett 233

Joseph Timmer, Louisiana State University
An Introduction to Hopf Algebras

Hopf algebras have grown in usefulness since their introduction and seem to be a pervasive element in many areas of mathematics. They appear in Topology, Representations of Groups, Lie Theory, Category Theory and even Applied Mathematics. In this talk, we introduce the definitions, structures and \"well known\" theory. We will focus on examples and ideas of the field. The talk will be accessible to first year graduate students. The only assumed knowledge will be very basic ring theory and some linear algebra.

Friday, March 13, 2015

Posted March 2, 2015
Last modified March 13, 2015

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm Keisler Lounge, 3rd Floor, Lockett Hall
(Originally scheduled for Tuesday, March 3, 2015)

Simon Pfeil, Louisiana State University
Graphics in LaTeX: An Introduction to TikZ

Bring your laptop to this crash course in TikZ graphics programming. This talk will cover the basics of using TikZ in LateX to make graphs and diagrams.

Monday, March 16, 2015

Posted March 9, 2015

1:30 pm – 2:20 pm Lockett 138

Aaron Lauda, University of Southern California
Diagrammatic Algebra

In this talk we will introduce a calculus of planar diagrams that can be used to represent algebraic structures in a wide variety of contexts. We will start by introducing a diagrammatic framework for studying linear algebra. In this framework, familiar notions such as trace and dimension take on a diagrammatic meaning. We will see how the notion of duality transforms algebraic notions into intuitive manipulations of diagrams. Finally, we will see how this diagrammatic reformulation of linear algebra can be used to study invariants of tangled pieces of string (knot theory).

Refreshments will be served in the Keisler lounge at 1:00pm.

Tuesday, March 17, 2015

Posted March 9, 2015

VIGRE@LSU: Student Colloquium Questions or comments?

1:30 pm – 2:20 pm Lockett 138

Aaron Lauda, University of Southern California
From Ladder Diagrams to Knot Theory

The star of this talk will be an algebraic object called a quantum group. This is an algebraic object closely connected to Lie theory. We will review some basic facts about the representation theory of quantum groups before turning our attention to representations one can construct on certain planar diagrams called \'ladder diagrams\'. Our aim is to provide a hands-on introduction to representation theory by exploring how quantum groups impose structure on these ladder diagrams. Though this example may seem somewhat trivial, we will show that viewing ladder diagrams as representations of quantum groups allows us to construct diagrammatically defined knot invariants in an elementary way. Our aim is to demonstrate that using only the definition of the quantum group and one additional ingredient, one can produce a wealth of diagrammatically defined knot invariants including the Jones polynomial. We do not assume any previous background in topology or Lie theory. Refreshments will be served in the Keisler Lounge at 1pm.

Posted March 6, 2015

3:30 pm – 4:20 pm Lockett 285

Aaron Lauda, University of Southern California
Traces and diagrams on the annulus

In this talk we will explore the notion of \"trace\" and how it can be generalized and given a graphical description in terms of diagrams on an annulus. Extending these notions beyond vector spaces and linear maps, we will show how the notion of trace can be generalized to any situation in which an algebraic object admits a graphical description in terms of planar diagrammatics. We will explain how these ideas provide a simple and intuitive way to understand sophisticated constructions arising in \"categorification\" and geometric representation theory.

Posted January 26, 2015

3:30 pm – 4:30 pm 1034 Digital Media Center

Yi Zhang, University of Tennessee
Finite Element Methods for the Stochastic Allen-Cahn Equation with Gradient-type Multiplicative Noises

Abstract: In this talk, we study two fully discrete finite element methods for the stochastic Allen-Cahn equation with a gradient-type multiplicative noise that is white in time and correlated in space. The sharp interface limit of this stochastic equation formally approximates a stochastic mean curvature flow. Strong convergence with rates are established for both fully discrete methods. The key ingredients are bounds for arbitrary moments and Holder estimates in the L2 and H1 norms for the strong solution of the stochastic equation. Numerical results are presented to gauge the performance of the proposed fully discrete methods and to study the interplay of the geometric evolution and gradient type noises. This is the joint work with Xiaobing Feng and Yukun Li.

Wednesday, March 18, 2015

Posted March 3, 2015
Last modified March 16, 2015

3:30 pm – 4:20 pm

Jeremy Van Horn-Morris, University of Arkansas
Virtual Seminar: On the coarse classification of Stein fillings

Abstract: In the '90s, Donaldson showed that every symplectic 4-manifold can be equipped with the structure of a Lefschetz pencil, a kind of singular surface bundle over CP^1. This pencil can be (non-uniquely) encoded as a relation in the mapping class group of a punctured surface, and while this factorization completely determines the manifold, it is in general very complicated. One might hope that some simpler shadow of the pencil might give useful information about the topology of the symplectic manifold. For example, what information does the genus of the pencil tell you about the symplectic manifold? Many of the initial conjectures about this relationship, as well as its generalization to open book decompositions, have been shown to be false. But, it turns out that in certain cases, there is very useful information available. We'll discuss the examples and the constraints. This is joint work with Inanc Baykur and Naoyuki Monden.

Posted March 13, 2015

4:30 pm – 5:30 pm Friday, March 18, 2016 Lockett 285

Carolyn Chun, Brunel University, London Former LSU graduate student
Delta-matroids and ribbon graphs

Tutte famously observed that, ``If a theorem about graphs can be expressed in terms of edges and circuits alone it probably exemplifies a more general theorem about matroids.\" It is well known that graphs and matroids have a mutually enriching relationship. In this talk, we discuss the mutually enriching relationship between ribbon graphs and delta-matroids and give some results based on this relationship, in order to support our claim that, ``If a theorem about embedded graphs can be expressed in terms of quasi trees alone it probably exemplifies a more general theorem about delta-matroids.\"

Thursday, March 19, 2015

Posted March 15, 2015
Last modified March 2, 2021

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:30 pm – 4:30 pm Lockett 233

Ian Runnels, LSU
Higher Polytopal Relations for Wigner's 6j-symbol

In the quantum theory of angular momentum, Eugene Wigner introduced a gadget called the 6j-symbol to calculate recoupling coefficients for interactions between several particles. Mathematically, these gadgets found uses in the representation theory of what Wigner called "Simply Reducible Groups", classical groups with the property that each irreducible representation is self-dual and multiplicity free; one such example is the Lie group SU(2,C). Over the next few decades, both physicists and mathematicians worked out many symmetries and relations for 6j-symbols, the most famous of which is called the Elliot-Biedenharn identity (secretly this is just the pentagon identity for tensor categories). In this talk, I will develop the definition of the 6j-symbol through the representation theory of SU(2) and introduce some new identities stemming from the combinatorics of these gadgets.

Posted March 12, 2015
Last modified March 18, 2015

3:30 pm – 4:30 pm 112 Lockett Hall

Robert P. Viator, Jr., LSU
Perturbation Theory for High-Contrast Photonic Crystals

Abstract: Transverse-electric Bloch-wave modes propagating through a high-contrast photonic crystal are analyzed. A power series for the frequency ω^2 terms of the high-contrast parameter z is established, along with a radius of convergence. The radius of convergence is controlled by eigenvalues (called quasi-static resonances) from a related spectral problem in the quasi-periodic Sobolev space, which are obtained via Layer Potentials.

Friday, March 20, 2015

Posted September 17, 2014
Last modified November 13, 2014

12:00 pm – 5:00 pm Saturday, March 21, 2015 Tulane University

Scientific Computing Around Louisiana 2015 (SCALA 2015)

http://tulane.edu/sse/ccs/news/scala-2015.cfm

Monday, March 23, 2015

Posted February 13, 2015

3:30 pm – 4:30 pm 233 Lockett Hall

Aleksandr Smirnov, Department of Mathematics, LSU
A discrete model of a fracture in an inhomogeneous strip

Posted March 20, 2015

4:30 pm – 5:30 pm Lockett 284

Alexander Garver, University of Minnesota
Maximal Green Sequences and Type A Quivers

A quiver Q is simply a directed graph. Quiver mutation is a combinatorial operation one performs on a quiver Q by selecting one of its vertices k and changing some of the edges of Q that are close to k. Certain sequences of quiver mutations called maximal green sequences are currently the subject of intense study by combinatorialists, representation theorists, and string theorists. I will explain some of the connections between maximal green sequences and combinatorics and I will discuss how to explicitly construct maximal green sequences for a class of quivers called type A quivers. This is joint work with Gregg Musiker.

Tuesday, March 24, 2015

Posted March 22, 2015
Last modified March 24, 2015

Algebra and Number Theory Seminar Questions or comments?

2:30 pm Keisler Lounge, 3rd Floor, Lockett Hall

Lucius Schoenbaum, LSU
Introduction to SINGULAR

SINGULAR is a computer algebra system for computations in commutative algebra, algebraic geometry, and singularity theory. I will introduce the system and present some examples to help first-time users get started. Prerequisite: an undergraduate or graduate course in abstract algebra should be sufficient.

Posted March 23, 2015

3:30 pm – 4:30 pm 235 Lockett Hall

Alexander Garver, University of Minnesota
Combinatorics of Exceptional Sequences in Type A

Exceptional sequences are certain ordered sequences of quiver representations with applications to noncrossing partitions, factorizations of Coxeter elements, cluster algebras, and the representation theory of algebras. We introduce a class of combinatorial objects called strand diagrams that we use to classify exceptional sequences of representations of type A Dynkin quivers. We also use variations of the model to classify c-matrices of type A Dynkin quivers, to interpret exceptional sequences as linear extensions of certain posets, and to give an elementary bijection between exceptional sequences and certain chains in the lattice of noncrossing partitions. This is part of ongoing work with Kiyoshi Igusa, Jacob Matherne, and Jonah Ostroff.

Posted March 2, 2015
Last modified March 18, 2015

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Clint Whaley, Louisiana State University
Automated Empirical Computational Optimization in ATLAS and iFKO

Abstract: This talk will overview empirical tuning, and highlight its importance for computational scientists / applied mathematicians of all types. Clint Whaley will present the two main empirical tuning projects that he maintains as part of his empirical tuning research, ATLAS and iFKO. Both of these research projects involve large software frameworks designed to be used by computational scientists. ATLAS provides dense linear algebra routines designed for direct for use by mathematicians, engineers, and industry, and is already used by hundreds-of-thousands worldwide. iFKO is a computational-oriented compiler framework, which is currently targeted for computational groups with significant tuning expertise. div

Wednesday, March 25, 2015

Posted March 13, 2015
Last modified March 19, 2015

1:30 pm – 2:20 pm Lockett 138

Peter Kuchment, Texas A&M
Tomography, mathematics of seeing invisible

Everyone has heard of CT, MRI, and Ultrasound medical scanners. Not many, though, know that mathematics plays a major role in obtaining the corresponding images. I will introduce basics of the mathematics of tomographic imaging. No prior knowledge of the subject is assumed. Refreshments will be served in the Keisler lounge at 1:00 pm.

Posted March 18, 2015

5:30 pm the Keisler Lounge (321 Lockett)

Actuarial Club Meeting

Paul Richmond from the Louisiana Legislative Auditor Office will be the speaker.

Thursday, March 26, 2015

Posted March 22, 2015

9:00 am – 10:00 am Keisler Lounge, 321 Lockett

A Conversation with Professor Peter Kuchment

Posted September 9, 2014
Last modified March 20, 2015

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:40 pm TBA

Peter Kuchment, Texas A&M
Can one hear the heat of a body? Mathematics of hybrid imaging

Medical/industrial/geophysical imaging has been for decades an amazing area of applications of mathematics, providing a bonanza of beautiful and hard problems with real world applications. One can find almost any area of math being involved there. In this talk, I will survey a recent trend of designing the so called coupled physics (or hybrid) imaging methods and mathematical problems arising there. No prior knowledge of mathematics of imaging is assumed.

Friday, March 27, 2015

Posted March 13, 2015
Last modified March 19, 2015

2:30 pm – 3:20 pm Lockett 138

Peter Kuchment, Texas A&M
The Nodal Count Mystery

The beautiful nodal patterns of oscillating membranes, usually called by the (incorrect) name Chladny patterns, have been known for several centuries (Galileo, Leonardo, Hooke) and studied in the last hundred years by many leading mathematicians. In spite of that, many properties of these patterns remain a mystery. We will present the history and a recent advance in the area of counting the nodal domains. No prior knowledge of the subject is assumed. Refreshment will be served in the Keisler lounge at 2:00 pm.

Monday, March 30, 2015

Posted February 3, 2015

3:30 pm – 4:30 pm 233 Lockett Hall

Yuri Antipov, Mathematics Department, LSU
Singular integral equations in a segment with two fixed singularities and applications

Tuesday, March 31, 2015

Posted March 22, 2015

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Bin Zheng, Pacific Northwest National Laboratory
Fast Multilevel Solvers for Discrete Fourth Order Parabolic Problems

Abstract: In this work, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element method. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to construct efficient preconditioners. We provide eigenvalue analysis for the preconditioned system and estimate the convergence rate of the preconditioned GMRes method. Furthermore, we show these preconditioners only need to be solved inexactly by optimal multigrid algorithms. We also investigate the performance of multigrid algorithms with either collective smoothers or distributive smoothers when solving the preconditioner systems. Our numerical examples indicate the proposed preconditioners are very efficient and robust with respect to both discretization parameters and diffusion coefficients.

Wednesday, April 1, 2015

Posted March 30, 2015

1:30 pm – 2:20 am Lockett 235

Congming Li, Colorado State University
The maximum principle-from simple calculus to frontier research

In this talk, we present the following topics:

the calculus of the local maxima,

the maximum principle for partial differential equations, and

the method of moving planes.

We hope to help our students learn the frontier research on the method of moving planes from the very simple characteristics of local maxima:
f\'(x_0) = 0 and f\'\'(x_0) <= 0.

Refreshments will be served in the Keisler lounge at 1:00 pm.

Posted December 11, 2014
Last modified January 27, 2015

3:30 pm Lockett 16

Math faculty meeting with Dean Peterson

Thursday, April 2, 2015

Posted March 30, 2015

2:30 pm – 3:20 pm Lockett 235

Congming Li, Colorado State University
The method of moving planes and it applications

In this talk, I will give a brief introduction on the method of moving planes, show some interesting applications of this method, and present some key points in making new advancements.

Refreshments will be served in the Keisler lounge at 2:00 pm.

Tuesday, April 14, 2015

Posted April 13, 2015

9:00 am – 10:00 am Keisler Lounge, 321 Lockett

A Conversation with Professor Clint Dawson

Posted March 2, 2015
Last modified March 18, 2015

Algebra and Number Theory Seminar Questions or comments?

2:00 pm – 3:00 pm 1034 Digital Media Center

Clint Dawson, University of Texas at Austin
Can the Gulf Coast Protect Itself from Hurricane Storm Surge?

Abstract: The active hurricane seasons of the past decade have resulted in significant efforts to understand risk and attempt to mitigate storm surge from hurricanes and tropical storms. Mitigation systems may consist of shoring up existing levees and seawalls, building new structural protection systems, or maintaining or creating natural systems such as barrier islands and wetlands. Modeling and computer simulation are central to investigating the efficacy of these systems. Mathematical models and algorithms which are multi-scale, multi-physics, and high fidelity are required for these efforts. In this talk, we will describe two modeling systems for studying the impacts of surge and waves, and the application of these models to studying built and natural storm surge protection systems. The first model is the well-known Advanced Circulation Model (ADCIRC), which has been widely used to study Gulf storms. We will describe recent studies where this model has been applied to proposed mitigation systems in the Houston-Galveston region, and the complexities associated with these types of studies. The second model we will discuss is a novel fluid-structure model, based on large eddy simulation coupled with a beam equation, for modeling flow through dense and flexible vegetation. Applications to flow through wetlands will be described.

Posted April 2, 2015

3:30 pm – 4:20 pm Lockett 235

Liang Chang, Texas A&M University
Generalized Frobenius-Schur Indicators and Kuperberg 3-manifold Invariants

Frobenius-Schur indicators were defined originally for finite groups and generalized for Hopf algebras. They are examples of gauge invariants for Hopf algebras, which are useful for the category of representations. Recently, the generalized indicators turned out to coincide with Kuperberg 3-manifold invariants for Lens spaces, which provides topology interpretation for Hopf algebra invariants. In this talk, I will explain these algebraic and topological invariants and recent work on their relation.

Wednesday, April 15, 2015

Posted March 27, 2015

4:30 pm L 16

Tenured faculty meeting followed by meeting of full professors

Thursday, April 16, 2015

Posted April 15, 2015

2:30 pm – 3:30 pm Keisler Lounge, 3rd Floor, Lockett Hall

Gerhardt Funk, Department of Mathematics, Louisiana State University Graduate Student
Prime Number Generation in Python

The prime numbers are of fundamental importance to number theory and have generally interested mathematicians since antiquity. But how do we find them? In this interactive talk, we\'ll create a program in Python which generates the primes and try to maximize its efficiency. This talk will be particularly informative for those who want to know more about the basics of coding and computer science.

Posted October 20, 2014
Last modified March 31, 2015

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett 285

Henri Cohen, University of Bordeaux I
Number Fields, Class Groups, and Regulators.

Abstract: In this talk, I will present the main results and conjectures related to the enumeration of number fields, and to their class groups and regulators. I will in particular give the known results on the enumeration of number fields of small degree, general conjectures on the subject, known theorems on the size of the class number, and the main heuristic predictions concerning class groups. I will also mention the computational tools used to obtain data concerning these objects.

Tuesday, April 21, 2015

Posted April 15, 2015
Last modified March 3, 2021

3:30 pm – 4:30 pm Lockett 235

Tom Lenagan, University of Edinburgh
The totally nonnegative grassmannian

This will be a survey talk about the cell decomposition of the totally nonnegative grassmannian. Points in the classical kxn grassmannian are k-dimensional subspaces in an n-dimensional vector space. Such points are described by their Plucker coordinates. The totally nonnegative grassmannian consists of those points for which all Plucker coordinates are nonnegative. There is a cell decomposition of the totally nonnegative grassmannian given by specifying the vanishing pattern of the Plucker coordinates. In order to describe this cell decomposition, Postnikov introduced several interesting combinatorial devices and we will mention some of these. If time permits, connections between the cell structure of the totally nonnegative grassmannian and the invariant prime spectrum of the quantum grassmannian algebra will be discussed.

Posted March 2, 2015
Last modified March 18, 2015

3:30 pm – 4:30 pm 1034 Digital Media Center

Xin (Shane) Li, Louisiana State University
Partial Geometric Mapping for Data Reassembly and Reconstruction

To compute geometric mapping is to establish a bijective correspondence between two 3D objects/regions or images. Effective mapping computation could facilitate pattern discovery, similarity detection, and deformation tracking/prediction in geometric data analysis. I will discuss the partial geometric mapping problem between two objects and among multiple objects, which has many practical applications in data reassembly and reconstruction. A few algorithms recently developed in our group will be explained and their applications in computational forensics and medical imaging will be demonstrated.

Wednesday, April 22, 2015

Posted October 7, 2014
Last modified January 10, 2022

3:30 pm – 4:20 pm tba

Tullia Dymarz, University of Wisconsin, Madison
Virtual Seminar: Non-rectifiable Delone sets in amenable groups

In 1998 Burago-Kleiner and McMullen constructed the first examples of coarsely dense and uniformly discrete subsets of R^n that are not bi-Lipschitz equivalent to the standard lattice Z^n. Similarly we find subsets inside the three dimensional solvable Lie group SOL that are not bi-Lipschitz equivalent to any lattice in SOL. The techniques involve combining ideas from Burago-Kleiner with quasi-isometric rigidity results from geometric group theory.

Friday, April 24, 2015

Posted April 23, 2015

3:30 pm Keisler Lounge, 3rd Floor, Lockett Hall

Jennifer Li, Louisiana State University
An Introduction to Sage

Sage is an important tool for mathematicians from many different areas. The purpose of this talk is to introduce some basic Sage functions, with an emphasis on its algebraic capabilities. I will show examples of Sage computations related to topics seen in a first year abstract algebra course, such as modular arithmetic and group theory, as well as from more specialized areas, such as number theory and elliptic curves.

Thursday, April 30, 2015

Posted April 18, 2015

3:30 pm – 4:20 pm Lockett 285

Ruth Charney, Brandeis University
Hyperbolic-like Boundaries

Boundaries of hyperbolic spaces play an important role in the study of hyperbolic groups and hyperbolic manifolds. Analogous boundaries exist for simply connected spaces of non-positive curvature (CAT(0) spaces) but they are not as well behaved and hence less effective. I will discuss the differences between these two settings and then introduce a new boundary for a very general class of metric spaces, designed to capture hyperbolic-like behavior in non-hyperbolic spaces. (Joint work with Harold Sultan and Matt Cordes)

Friday, May 1, 2015

Posted April 22, 2015

3:00 pm Keisler Lounge (Third floor, Lockett Hall)

Math Deparatment spring awards ceremony

Refreshments at 3 pm; awards ceremony begins at 3:30 pm

Monday, May 4, 2015

Posted April 29, 2015
Last modified March 2, 2022

3:30 pm – 4:20 pm Room 233 Lockett Hall

Kaushik Dayal, Carnegie Mellon University
A Dynamic Phase-field Model for Structural Transformations and Twinning: Regularized Interfaces with Transparent Prescription of Complex Kinetics and Nucleation

Phase-field models enable easy computations of microstructure because they regularize sharp interfaces. In addition, the nucleation of new interfaces and the kinetics of existing interfaces occurs “automatically” using only the energy and a gradient descent dynamics. This automatic nucleation and kinetics is often cited as an advantage of these models, and is not present in sharp interface approaches where nucleation and kinetics must be explicitly prescribed.

However, this is not necessarily an advantage. Rather, it does not allow us to use nucleation and kinetic insights that may be gained from experiment and/or molecular simulations. Hence, this feature is actually a disadvantage because it breaks the multiscale modeling hierarchy of feeding information through the scales. Motivated by this, we have developed a phase-field model (i.e., with regularized interfaces) that allows for easy and transparent prescription of kinetics and nucleation. We present the formulation of the model, and characterization through various examples.

Friday, May 8, 2015

Posted May 3, 2015

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett 233

Rainer Nagel, University of Tübingen
Some Operator Theoretic Aspects of Ergodic Theory

We discuss some techniques and results on linear operators in Banach spaces as, e.g., appearing in the proof of the Green-Tao Theorem on arithmetic progressions in the primes. The main object is the so called Koopman operator yielding a linear model of a nonlinear dynamical system. It is joint work with Tanja Eisner, Balint Farkas and Markus Haase appearing as Springer Graduate Text in Mathematics.

Wednesday, May 13, 2015

Posted May 6, 2015

Special math professional development seminar

2:45 pm 205 Prescott Hall

Fabiana Cardetti, University of Connecticut Associate Professor & Graduate Director for Instructional Development, Department of Mathematics
Constructing and Critiquing Arguments: Supporting Teachers in the Implementation of the Common Core Standard for Mathematical Practice 3

Tuesday, May 26, 2015

Posted May 17, 2015

3:30 pm – 4:20 pm Lockett 235

Cris Negron, University of Washington
Braided structures and the Gerstenhaber bracket on Hochschild cohomology

Given a finite dimensional Hopf algebra H acting on an algebra A, we can form an intermediate cohomology H˙(H, A) which comes equipped with a natural right H-action, and recovers the Hochschild cohomology of the smash product A#H after taking invariants. In fact, the cohomology H˙(H, A) is a Yetter-Drinfeld module over H and is a braided commutative algebra under the natural braiding induced by the Yetter-Drinfeld structure. This multiplicative structure has proved useful in verifying finite generation of Hopf cohomology, and has been studied extensively by Forest-Greenwood, Shepler, and Witherspoon. Supposing H has finite exponent, I will discuss how one can produce a braided antisymmetric bracket on H˙(H, A) which lifts the Gerstenhaber bracket to this braided setting, in the sense that it recovers the Gerstenhaber bracket after taking invariants.

Monday, August 17, 2015

Posted April 30, 2015
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive / PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, August 19, 2015

Posted April 30, 2015
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive / PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, August 21, 2015

Posted April 30, 2015
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive / PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Posted March 25, 2015
Last modified August 19, 2015

2:30 pm – 3:20 pm Lockett 284

Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Brownian Bridge in Quantum Probability

Thursday, August 27, 2015

Posted August 25, 2015

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:15 pm – 4:15 pm Lockett 233

Jacob Matherne, Department of Mathematics, LSU
The Hilbert scheme of points in the plane

Abstract: We will begin with a few brief notions in algebraic geometry needed to introduce the Hilbert scheme of points in the plane. The Hilbert scheme is a compactification of a configuration space of n distinct particles moving around on a plane. Our main tool for studying it will be the combinatorics of Young diagrams. Time permitting, we may discuss torus actions on the Hilbert scheme and the computation of its cohomology. The talk should be accessible to first-year graduate students (even if the words seem scary at first), so come by!

Thursday, September 3, 2015

Posted August 27, 2015

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:15 pm – 4:15 pm Lockett 233

Kyle Istvan, LSU
Quantum Invariant Theory

This informal discussion will focus on motivating the use of quantum groups to creating topological invariants, following the perspective of Manin. We will begin with a brief discussion of SL(2,C), its action on C^2, and why this particular group is of interest in geometry, topology, (and vaguely, number theory.) We will then define a new \"geometric\" object, the quantum complex plane C_q^{2}, and proceed to derive the necessary deformation of SL(2,C) in order to have a useful action on the quantum plane. If time permits, we will see the Kauffman relations (from the study of links and 3-manifolds) appear very naturally in this setting as the quantum analogue of the Cayley-Hamilton Identity, and hopefully motivate the further study of deformations of classical groups. This talk is based on a series of lectures given by Roland van der Veen at Gazi University in August 2015.

Thursday, September 10, 2015

Posted August 31, 2015
Last modified October 4, 2021

3:30 pm – 4:20 pm Lockett 277

Pramod Achar, Mathematics Department, LSU
Intersection cohomology and representation theory

Intersection cohomology (a variant of the usual singular cohomology) has been a powerful tool in representation theory for over 35 years, playing a role in such major developments as the proof of the Kazhdan–Lusztig conjectures. After discussing some classical applications of complex intersection cohomology through examples, I will focus on new developments that have made intersection cohomology with Z/pZ coefficients more accessible, along with applications such as the proof of the Mirković–Vilonen conjecture.

Monday, September 14, 2015

Posted September 11, 2015

3:30 pm – 4:30 pm 285 Lockett

Arnab Ganguly, LSU
Moderate and large deviation principles for stochastic differential equations

Abstract: Moderate and large deviation principles involve estimating the probabilities of rare events. In particular, they often help to assess the quality of approximating models obtained through law of large number-type results. The talk will first give an introduction to large deviation principles and then focus on a weak convergence based approach of proving them for stochastic differential equations.

Posted August 25, 2015
Last modified August 26, 2015

5:00 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial club meeting

Introducing the new officers
President: Andrew Crespo
Vice President: Nicholas Xenaki

Discussion about preparing for a career as an actuary and planning the fall semester's activities
Pizza will be served.

Tuesday, September 15, 2015

Posted September 3, 2015

3:30 pm – 4:30 pm 1034 Digital Media Center

Amanda Diegel, Louisiana State University
Numerical Analysis of Convex Splitting Schemes for Cahn-Hilliard and Coupled Cahn- Hilliard-Fluid-Flow Equations

Abstract: In this talk, we investigate numerical schemes for the Cahn-Hilliard equation and the Cahn-Hilliard equation coupled with a Darcy-Stokes flow. Considered independently, the Cahn-Hilliard equation is a model for spinodal decomposition and domain coarsening. When coupled with a Darcy-Stokes flow, the resulting system describes the flow of a very viscous block copolymer fluid. Challenges in creating numerical schemes for these equations arise due to the nonlinear nature and high derivative order of the Cahn-Hilliard equation. Further challenges arise during the coupling process as the coupling terms tend to be nonlinear as well. The numerical schemes which will be presented preserve the energy dissipative structure of the Cahn-Hilliard equation while maintaining unique solvability and optimal error bounds.

Posted September 11, 2015
Last modified September 15, 2015

Joint Algebra & Number Theory / Harmonic Analysis Seminar

3:30 pm – 4:20 pm Lockett 277

Baiying Liu, University of Utah and IAS
On cuspidality of global Arthur packets of quasi-split classical groups

Based on the theory of endoscopy, Arthur classified the automorphic discrete spectrum of quasi-split classical groups up to global Arthur packets parametrized by Arthur parameters. Towards studying representations in each Arthur packet, a natural question one may ask is that whether a given Arthur packet has cuspidal representations or not. In this talk, I will introduce some recent progress on this aspect, which is based on relations between the structure of Fourier coefficients of automorphic forms in an Arthur packet and the structure of the corresponding Arthur parameter. This work is joint with Dihua Jiang.

Wednesday, September 16, 2015

Posted June 3, 2015
Last modified September 9, 2015

3:30 pm – 4:30 pm Lockett 233

Adam Saltz, Boston College
Virtual Seminar: A transverse invariant from annular Khovanov homology

Abstract: Annular Khovanov homology is a refinement of Khovanov homology for links embedded in an annulus. Braid closures are natural examples of such links, and there is a well-known correspondence between braids and transverse links. Expanding on work of Plamenevskaya, I will present a computable conjugacy class invariant whose minimum we hope to be an effective transverse invariant. The invariant has applications to the word problem, the lengths of certain spectral sequences, and some classical questions about braids. This is joint work with Diana Hubbard.

Thursday, September 17, 2015

Posted August 31, 2015
Last modified September 4, 2015

3:30 pm – 4:20 pm Lockett 277

Shawn Walker, LSU
Numerical Analysis For Multi-Physics Moving Interface Problems

Moving interface and free boundary problems play a critical role in many areas of mathematics, physics, and engineering (examples are surface tension/curvature-driven flows and other geometric flows). Many new computational methods have been developed in recent years to tackle these problems in the presence of other physical effects. In this talk, I will discuss modeling and numerical analysis for three areas: two-phase problems, shape optimization, and liquid crystals. I will highlight theoretical results for modeling and simulating these problems, as well as show numerical results and simulations to illustrate the methods.

Monday, September 21, 2015

Posted September 20, 2015

3:30 pm – 4:30 pm 285 Lockett

Karl Mahlburg, Department of Mathematics, LSU
Loeb Measure and Additive Number Theory

Abstract: Additive Number Theory is concerned with questions regarding the density of various sets of integers, and how these are affected by arithmetic operations. As a notable example, Szemeredi\'s Theorem from 1975 states that any set of natural numbers with positive (upper) density contains arbitrarily long arithmetic progressions. I will discuss applications of continuous (and probabilistic) techniques in Number Theory, particularly the construction of Loeb measure on the hyperfinite integers from nonstandard analysis. Once recent result is a partial proof of a conjecture of Erdos, which states that if A has positive density, then there exist two infinite sets B and C such that B + C is contained in A; the present result shows that this is true up to at most one additional shift.

Tuesday, September 22, 2015

Posted September 4, 2015

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 2

Meeting of department faculty

Discussion about conducting an external search for a new department chair.

Thursday, September 24, 2015

Posted September 21, 2015
Last modified September 22, 2015

12:30 pm – 1:30 pm 381 Lockett Hall

Michael Malisoff, LSU Roy P. Daniels Professor
Control of Neuromuscular Electrical Stimulation: A Case Study of Predictor Control under State Constraints

We present a new tracking controller for neuromuscular electrical stimulation, which is an emerging technology that artificially stimulates skeletal muscles to help restore functionality to human limbs. The novelty of our work is that we prove that the tracking error globally asymptotically and locally exponentially converges to zero for any positive input delay, coupled with our ability to satisfy a state constraint imposed by the physical system. Also, our controller only requires sampled measurements of the states instead of continuous measurements and allows perturbed sampling schedules, which can be important for practical purposes. Our work is based on a new method for constructing predictor maps for a large class of time-varying systems, which is of independent interest. See http://dx.doi.org/10.1002/rnc.3211.

Posted September 17, 2015

2:30 pm – 3:30 pm Keisler Lounge (321 Lockett Hall)

Semester Kick-Off Event: Why We Do Applied Mathematics

Come learn about the SIAM Student Chapter. Some of our members will talk about their research.
Refreshments will be provided.

Posted September 21, 2015

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:15 pm – 4:15 pm Lockett 233

Neal Livesay, LSU
An excursion into the mathematics of Jacques Tits

Abstract: The theory of buildings provides a beautiful combinatorial and geometric viewpoint to the theory of algebraic groups. It can be shown that every group G with an algebraic condition (having a BN-pair) corresponds to a simplicial complex (a building) endowed with a compatible action by G. We will discover this correspondence by working out the details for G=GL_2(k) and GL_3(k).

Monday, September 28, 2015

Posted September 24, 2015

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm 285 Lockett

Xiaoliang Wan, Louisiana State University
Some numerical issues in applying large deviation principle

Abstract: In this talk, we mainly address two numerical issues in applying the large deviation principle to spatially extended systems. The first issue is to deal with the difficulties induced by the separation of slow and fast dynamics, where will introduce a new minimum action method. The second issue is to deal with the inverse of the spatial covariance operator. This issue will be illustrated by an elliptic problem perturbed by small spatial Gaussian noise.

Thursday, October 1, 2015

Posted September 28, 2015

12:30 pm – 1:30 pm Room 284 Lockett Hall

Cristopher Hermosilla, Universidad Técnica Federico Santa María
On the Construction of Continuous Suboptimal Feedback Laws

An important issue in optimal control is that optimal feedback laws (the minimizers) are usually discontinuous functions on the state, which yields to ill-posed closed loop systems and robustness problems. In this talk we show a procedure for the construction of a continuous suboptimal feedback law that allows overcoming the aforesaid problems. The construction we exhibit depends exclusively on the initial data that could be obtained from the optimal feedback. This is a joint work with Fabio Ancona (Universita degli Studi di Padova, Italy)

Monday, October 5, 2015

Posted October 2, 2015

3:30 pm – 4:30 pm 285 Lockett

P. Sundar, Department of Mathematics, LSU
The Boltzmann equation and related processes

Abstract: The Boltzmann equation will be considered in weak form, and viewed as the Kolmogorov equation for a stochastic process after a spatial smoothing is introduced. The process is identified as the solution of a McKean-Vlasov equation with jumps. Its invariant measure will be verified in the Gaussian case.

Wednesday, October 7, 2015

Posted May 27, 2015
Last modified October 6, 2015

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 15

Meeting of the tenured faculty

Thursday, October 8, 2015

Posted October 5, 2015
Last modified October 8, 2015

12:30 pm – 1:30 pm Room 284 Lockett Hall

Hugo Leiva, Visiting Professor, Louisiana State University
Semilinear Control Systems with Impulses, Delays and Nonlocal Conditions.

Mathematical control theory is the area of applied mathematics dealing
with the analysis and synthesis of control systems. To control a system
means to influence its behavior so as to achieve a desired goal such as
stability, tracking, disturbance rejection or optimality with respect to
some performance criterion. For many control systems in real life,
impulses and delays are intrinsic phenomena that do not modify their
controllability. So we conjecture that, under certain conditions,
perturbations of the system caused by abrupt changes and delays do not
affect certain properties such as controllability.
In this investigation we apply Fixed Point Theorems to prove the
controllability of Semilinear Systems of Differential
Equations with Impulses, delays and Nonlocal Conditions.
Specifically, Under additional conditions we prove the following statement:
If the linear $\\acute{z}(t) = A(t)z(t) + B(t)u(t)$ is controllable on $[0, \\tau]$,
then the semilinear system $z^{\\prime}(t) = A(t)z(t) + B(t)u(t)+f(t,z(t),u(t))$
with impulses, delays, and nonlocal conditions is also controllable on $[0, \\tau]$.
Moreover, we could exhibit a control steering the semilinear system from an
initial state $z_0$ to a final state $z_1$ at time $\\tau >0$.
This is a recent research work with many questions and open problems.

Monday, October 12, 2015

Posted October 4, 2015

3:30 pm Lockett 223

Bálint Farkas, University of Wuppertal
The periodic decomposition problem for semigroups

Given commuting power-bounded linear operators T₁,...,T_n on a Banach space the periodic decomposition problems, originally due to I.Z. Ruzsa, asks whether and under which conditions the equality ker (T₁-I) ··· (T_n-I) = ker(T₁-I)+···+ker (T_n-I) holds true. In this talk we focus also on the case when T_j=T(t_j), t_j >0, j=1,..., n for some (strongly continuous) one-parameter semigroup (T(t))_t≥0. Moreover, we look at a generalization of the periodic decomposition problem when instead of the cyclic semigroups {T_jⁿ:n ∈ N} more general semigroups of bounded linear operators are considered.

Posted October 9, 2015

3:30 pm – 4:30 pm 285 Lockett

Ambar Sengupta, Mathematics Department, LSU
Gaussian Random Matrices and the Large-N Limit

Abstract: A Gaussian random matrix A is an NxN matrix whose entries are random variables with jointly Gaussian distribution. In this talk we will explore the behavior of some natural functions of such matrices, such as the traces of powers of A. We will also discuss the limiting behavior of such functions when N goes to infinity. This is an expository talk and we will use little more than basic matrix algebra and knowledge of the standard Gaussian distribution.

Posted September 18, 2015

5:00 pm Keisler Lounge (321 Lockett)

Actuarial Club meeting

David Ellsworth and Gino Pagano from Starmount Life Insurance Company will be visiting. They will host a Q&A on exams and the profession. They will also discuss a possible Summer Internship for 2016.

Tuesday, October 13, 2015

Posted September 3, 2015

3:30 pm – 4:30 pm 1034 Digital Media Center

Christopher Davis, Tennessee Tech University
A Two Level Additive Schwarz Preconditioner for a Partition of Unity Method

Abstract: The partition of unity finite element method is a type of finite element method that enables one to construct smooth approximation functions at low cost. Investigation into the conditioning of partition of unity methods is an active field or research. In this talk, we discuss the use of two level additive Schwarz preconditioners for a partition of unity method. The numerical algorithm will be presented and analyzed. Numerical examples will be given to demonstrate the effectiveness of the method. This is joint work with Susanne C. Brenner and Li-yeng Sung.

Thursday, October 15, 2015

Posted October 12, 2015

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:15 pm – 4:15 pm Lockett 233

Bach Nguyen, LSU
A New Look into the Center of the Quantized Enveloping Algebra of a Complex Semi-simple Lie Algebra

Abstract: In the paper \\textit{``Local Finiteness of the Adjoint Action for Quantized Enveloping Algebras\'\'} by Anthony Joseph and Gail Letzter, they show that the center of $U_{q}(\\mathfrak{g})$ ($\\mathfrak{g}$ is the Kac-Moody algbra) is isomorphic to the $W$-invariants in the ring $k(q)[T^0]$, where $W$, the Weyl group, acting by traslation, and $T^{0}=T_{<}^{-1}T_{<}$, where $T_<=-R^+$, and $R^+$ is the intersection of four times the dominant weight with the extended root lattice. Recently, in \\textit{``Generalized Joseph\'s Decompositions,\'\'} Arkady Berenstein and Jacob Greenstein give a new construction for the basis of $\\mathcal{Z}(U_q)$ which allows us to identify the center with the ring of symmetric functions. In this talk, we\'ll be discussing the construction that lead to this new basis of $\\mathcal{Z}(U_q)$.

Wednesday, October 21, 2015

Posted October 19, 2015

3:30 pm – 4:30 pm 233 Lockett Hall

Nicholas Owad, University of Nebraska, Lincoln
Virtual Seminar: Recent results concerning bridge spectra

Abstract: The bridge spectrum of a knot is a generalization of the classic invariant defined by Schubert, the bridge number of a knot. We will introduce the relevant background and some known results. Then we will give a short sketch of a proof of our main result, and end with open questions.

Posted October 10, 2015
Last modified October 11, 2015

LSU AWM Student Chapter LSU AWM Student Chapter Website

3:30 pm – 4:30 pm 277 Lockett

Chanun Lewchalermvongs, Louisiana State University
Graphs Without W4 and K5-e as Induced Minors

We concern with graphs that contain neither W4 (a wheel graph with 5 vertices) nor K5-e (the complete graph K5 minus one edge) as an induced minor. This class of graphs will be denoted by $\mathscr{W}$. We show that a graph in $\mathscr{W}$ can be constructed by the 0-, 1-, 2-sums of cliques with the specific condition on 2-sum. We also prove that $\mathscr{W}$ is not well-quasi-ordered by the induced minor relation. To prove this statement, we construct an infinite antichain, $\mathscr{D}^{\Gamma}$, in $\mathscr{W}$. Moreover, we prove as the main result that for any closed subclass $\mathscr{Z}$ of $\mathscr{W}$, $\mathscr{Z}$ contains an infinite antichain if and only if $\mathscr{Z} \cap \mathscr{D}^{\Gamma}$ is infinite.

Thursday, October 22, 2015

Posted October 9, 2015

3:00 pm – 4:30 pm Keisler Lounge

How to Apply to Graduate School

Graduate students will be on hand to answer your questions about filling out your graduate school applications.

Posted October 17, 2015
Last modified October 21, 2015

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:15 pm – 4:15 pm Lockett 232

Richard Frnka, Department of Mathematics, LSU Graduate Student
Partitions, Unimodal Sequences, and some Congruence Relations

Abstract: The partition number p(n) is an important mathematical idea that has applications in Combinatorics, Number Theory, and even Representation Theory. In this talk, we will discuss the generating function for p(n), some important relations linking infinite products to theta functions, and will consider different restrictions on the parts that make up the partitions. The only requirement for this talk will be a basic knowledge of geometric series. The plan is to make this talk very accessible and basic, so we will be able to go deeper into the asymptotics of the partition function and unimodal sequences in a later talk.

Friday, October 23, 2015

Posted October 9, 2015
Last modified October 13, 2015

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 232

Ko-Shin Chen, U. Conn.
Ginzburg-Landau and Gross-Pitaevskii Vortices on Surfaces

We consider the Ginzburg-Landau energy on compact and simply-connected surfaces. The first result is the instability of critical points of the Ginzburg-Landau energy. We show on a surface without boundary, any non-constant critical points must be unstable for small epsilon if at least one limiting vortex is located at a point of positive Gauss curvature. The second is the vortex dynamics for the Ginzburg-Landau heat flow, both in the asymptotic regime where the parameter 'epsilon' attends to zero and for a fixed epsilon. We show the vortices of a solution evolve according to the gradient flow of the renormalized energy. Then we establish vortex annihilation results for both ODE and PDE settings. The third is a similar analysis of vortex motion for the Gross-Pitaevskii equation. We show the vortices of a solution follow the Hamiltonian point-vortex flow associated with the renormalized energy. Then on surfaces of revolution, we find rotating periodic solutions to the generalized point-vortex problem and seek a rotating solution to the Gross-Pitaevskii equation having vortices that follow those of the point-vortex flow for small epsilon.

Tuesday, October 27, 2015

Posted October 18, 2015
Last modified October 21, 2015

3:30 pm – 4:20 pm Lockett 277

Ling Long, LSU
Hypergeometric functions and their finite field analogues I

Hypergeometric functions are an important class of special functions and they play important roles in many aspects of number theory. In this talk, we will review definitions and basic properties of classical hypergeometric functions and define their analogues over finite fields. This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher and Fang-Ting Tu.

Wednesday, October 28, 2015

Posted October 11, 2015
Last modified October 14, 2015

4:30 pm – 5:30 pm 277 Lockett

Benjamin Clark, Louisiana State University
Towards an excluded-minor characterization of the Hydra-5 matroids

One of the longstanding goals of matroid theory is to find excluded-minor characterizations of classes of representable matroids. The immediate problem that looms large is that of finding the excluded minors for the class of GF(5)-representable matroids. While this problem is beyond the range of current techniques, there is a road map for an attack that reduces the problem to a finite sequence of excluded-minor problems. This talk will give an overview of excluded-minor characterizations of classes of representable matroids, and outline the progress made towards an excluded-minor characterization of the class of Hydra-5 matroids.

Monday, November 2, 2015

Posted September 13, 2015

VIGRE@LSU: Student Colloquium Questions or comments?

10:30 am – 11:30 am 1034 Digital Media Center

Raymond Chan, Chinese University of Hong Kong
A Two-stage Image Segmentation Method Based on the Mumford-Shah Model with Thresholding

Abstract: The Mumford-Shah model is one of the most important image segmentation models, and has been studied extensively in the last twenty years. In this talk, we will first survey the past development of the method. Then we introduce our two-stage segmentation method based on the Mumford-Shah model. The first stage of our method is to find a smooth solution g to a convex variant of the Mumford-Shah model. Once g is obtained, then in the second stage, the segmentation is done by thresholding g into different phases. The thresholds can be given by the users or can be obtained automatically using any clustering methods. Because of the convexity of the model, g can be solved efficiently by standard techniques. We prove that our method is convergent and the solution g is always unique. Experimental results show that our two-stage method performs better than many standard two-phase or multi-phase segmentation methods for very general images, including anti-mass, tubular, MRI, noisy, and blurry images; and for very general noise models such as Gaussian, Poisson and multiplicative Gamma noise. We will also mention the generalization to color images.

https://www.cct.lsu.edu/lectures/two-stage-image-segmentation-method-based-mumford-shah-model-thresholding

Posted September 25, 2015
Last modified October 26, 2015

2:30 pm – 3:20 pm Lockett 114

Clayton Shonkwiler, Colorado State University
15 Views of the Hyersphere

Abstract: The usual sphere in 3-dimensional space---meaning a hollow sphere, like a basketball--- is such a simple and familiar object that we don't really need to think about how to visualize it. The corresponding shape in 4-dimensional space, called the hypersphere, is a very natural mathematical object which is also important in general relativity and other areas of physics. Of course, it's a bit harder to visualize without 4-dimensional eyes, but I'll present 15 ways of thinking about the hypersphere which will hopefully make it a little more familiar and understandable. There will be lots of pictures and animations.

A light lunch will be served in the Keisler Lounge at 2:00pm.

Posted October 26, 2015

3:30 pm Lockett 223

Boris Baeumer, University of Otago, New Zealand
Anomalous Reaction-Diffusion Equations

Abstract: We show how a simple random walk model can be build up step by step to lead to a Volterra integral equation problem whose kernel depends on its solution. The build-up includes fractional differential equations, continuous time random walk limits, and surprising reaction effects. Variants or special cases of the model have been used to describe phenomena in cell dynamics, ecology, epidemiology, and hydrology.

Posted October 27, 2015

Algebra and Number Theory Seminar Questions or comments?

5:00 pm Keisler Lounge (321 Lockett)

Actuarial Club meeting

Frederick Sakon (Tulane University) will be demonstrating the use of ADAPT, an interactive exam preparation tool. Muffulettas and District Donuts served.

Tuesday, November 3, 2015

Posted October 18, 2015
Last modified November 2, 2015

1:30 pm – 2:20 pm Lockett 285

Ling Long, LSU
Hypergeometric functions and their finite field analogues II

In this talk, we will discuss the Galois perspective of hypergeometric functions over finite fields. In particular we will associate Galois representations to the classical 2F1 hypergeometric functions with rational parameters via the generalized Legendre curves. Then we will use the Galois perspective to translate several types of classical hypergeometric formulas to the finite field settings. This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher and Fang-Ting Tu.

Posted September 25, 2015
Last modified October 26, 2015

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:20 pm Lockett 114

Clayton Shonkwiler, Colorado State University
A Geometric Perspective on Ranom Walks with Topological Constraints

Abstract: A random walk in 3-space is a classical object in geometric probability, given by choosing a direction at random, taking a step, and repeating n times. Random walks with topological constraints are collections of random walks which are required to realize the edges of some predetermined multigraph. The simplest nontrivial example is a random polygon, which is just a random walk which is required to form a closed loop. Since random walks are used to mdoel polymers, random walks with topological constraints give models for polymer conformations with nontrivial topologies. Examples range in complexity from plasmids and viral DNA, which form simple closed loops, to rubbers and gels, which form large networks. Consequently, there is keen interest both in analyzing the geometric probability theory of such walks and in developing fast simulation algorithms. In this talk I will describe some of the most exciting recent developments in the mathematics of random walks with topological constraints, focusing on the case of random polygons. These developments arise from a purely geometric understanding of the space of possible polygon configurations. Despite being based on rather deep theorems from symplectic/algebraic geometry, this geometric perspective is surprisingly elementary and has already yielded both exact theoretical statements and powerful new algorithms. This includes joint work with Jason Cantarella (University of Georgia) and Tetsuo Deguchi and Erica Uehara (Ochanomizu University, Tokyo).

Refreshments with be served in the Keisler Lounge at 3:00pm.

Wednesday, November 4, 2015

Posted October 30, 2015

3:30 pm – 4:30 pm Lockett 277

Kyle Istvan, LSU
Detecting Rotational Symmetry in Knot and Links

In low-dimensional topolgy, a link is an embedding of a disjoint set of
circles into 3-dimensional space. We can represent a link by projecting
its image onto a plane to get a 4-valent planar graph, together with
some extra information on the vertices. Every link has infinitely many
diagrams, but there is a well-defined notion of equivalence between
diagrams of the same link. A link is periodic if it has a diagram with
rotational symmetry. I will define a necessary condition for a link to
be periodic that arises from an evaluation of the 2-variable Kauffman
polynomial, a topological invariant of links. The result is derived
using a diagrammatic state sum formula for the polynomial. The states
are planar trivalent graphs, each of which is paired with a perfect
matching.

Posted June 17, 2015
Last modified November 4, 2015

3:30 pm – 4:30 pm 233 Lockett Hall

Clayton Shonkwiler, Colorado State University
Virtual Seminar: "The Symplectic Geometry of Polygon Space and How to Use It"

Abstract: In statistical physics, the basic (and highly idealized) model of a ring polymer is a closed random walk in 3-space with equal-length steps, often called a random equilateral polygon. In this talk, I will describe the moduli space of random equilateral polygons, giving a sense of how this fits into a larger symplectic and algebraic geometric story. In particular, the space of equilateral n-gons turns out to be a toric symplectic manifold, yielding a (nearly) global coordinate system. These coordinates are powerful tools both for proving theorems and for developing numerical techniques, some of which I will describe, including a very fast algorithm for directly sampling random polygons recently developed with Jason Cantarella (University of Georgia), Bertrand Duplantier (CEA/Saclay), and Erica Uehara (Ochanomizu University).

Thursday, November 5, 2015

Posted September 23, 2015
Last modified October 18, 2015

3:30 pm – 4:20 pm Lockett 277

Geoffrey Mason, UC Santa Cruz
The unbounded denominator conjecture

The unbounded denominator conjecture (UBD) is a very general statement that includes as special cases both the main modular-invariance conjecture in rational conformal field theory and an old conjecture of Atkin-Swinnerton-Dyer about noncongruence modular forms. We will explain the origins of UBD, its connections with the Fuchsian theory of linear differential equations, and how it can be proved in low dimensions. The talk is aimed at a general audience -- no special expertise required.

Saturday, November 7, 2015

Posted November 5, 2015

9:30 am – 5:30 pm Lockett 277 and 285

Lie Theory Workshop

See https://www.math.lsu.edu/~pramod/LieTheory2015 for the schedule and complete information.

Tuesday, November 10, 2015

Posted November 5, 2015

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Hongchao Zhang, Louisiana State University
Inexact Alternating Direction Algorithm for Separable Convex Optimization

Abstract: We introduce inexact alternating direction algorithms with variable stepsize for solving separable convex optimization. These algorithms generate the Bregman Operator Splitting Algorithm with Variable Stepsize (BOSVS) to the multiblock case and allow to solve the convex subproblems to an adaptive accuracy. Global convergence and some preliminary numerical results will be discussed.

Posted October 18, 2015
Last modified October 25, 2015

3:30 pm – 4:20 pm Lockett 277

Cris Negron, Mathematics Department, LSU
A new approach to the Gerstenhaber bracket on Hochschild cohomology and applications

I will discuss a new approach to the Gerstenhaber bracket on Hochschild cohomology, and illustrate this new approach with a particular example related to finite group actions on affine space. The Hochschild cohomology of an algebra, along with the Gerstenhaber bracket, is (the cohomology of) a (dg) Lie algebra controlling the formal deformation theory of that algebra. In the talk I will focus on the aforementioned example in order to explain how our new results relate to, and in this case advance, both classical and current understandings of the Gerstenhaber bracket in geometric contexts. This is joint work with Sarah Witherspoon.

Thursday, November 12, 2015

Posted November 9, 2015

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:15 pm – 4:15 pm Lockett 233

Cris Negron, Mathematics Department, LSU
Cohomology for the Young and Restless

Posted November 5, 2015
Last modified February 6, 2021

3:30 pm – 4:20 pm Lockett 277

Amer Darweesh, LSU
Wavelets, Coorbit Theory, and Projective Representation

Monday, November 16, 2015

Posted November 13, 2015

3:30 pm – 4:30 pm 285 Lockett

Supratik Mukhopadhyay, Division of Computer Science and Engineering, LSU
Synthesis of Geometry Proof Problems

We present an automated methodology for generating geometric proof problems of the kind found in a high school curriculum. We formalize the notion of a geometry proof problem and describe an algorithm for generating such problems over a user-provided figure. Our experimental results indicate that our problem generation algorithm can effectively generate proof problems in elementary geometry. On a corpus of 110 figures taken from popular geometry textbooks, our system generated an average of about 443 problems per figure in an average time of 4.7 seconds per figure. This is a joint work with S. Gulwani (Microsoft Research, Redmond) and R. Majumdar (Max Planck Institute-SWS)

Posted November 10, 2015

VIGRE@LSU: Student Colloquium Questions or comments?

5:00 pm Keisler Lounge (321 Lockett)

Meeting of Actuarial Club

There will be presentations by Andrew Crespo and Radha Kumar on their internships. Pizza will be served.

Wednesday, November 18, 2015

Posted September 25, 2015
Last modified November 13, 2015

2:30 pm – 3:20 pm Lockett 134

Mark Goresky, Institute for Advanced Study
A glamorous Hollywood star, a renegade composer, and the mathematical development of spread spectrum communications

Abstract: During World War II Hedy Lamarr, a striking Hollywood actress, together with George Antheil, a radical composer, invented and patented a secret signaling system for the remote control of torpedoes. The ideas in this patent have since developed into one of the ingredients in modern digital wireless communications. The unlikely biography of these two characters, along with some of the more modern developments in wireless communications will be described. <\p><\p> A light lunch will be served in the Keisler Lounge at 2:00pm.

Posted November 6, 2015

3:40 pm Lockett 15

Faculty meeting

Posted November 16, 2015
Last modified November 17, 2015

VIGRE@LSU: Student Colloquium Questions or comments?

4:30 pm – 5:30 pm Lockett 277

Emily Marshall, LSU
Excluding theta graphs

A theta graph, denoted theta_{a,b,c}, consists of a pair of vertices together with three disjoint paths between the vertices of lengths a, b, and c. In this talk, we characterize graphs which exclude certain theta graphs as a minor. We begin with small theta graphs, in particular those with at most 7 edges. This work is part of a larger project which characterizes H-minor-free graphs for all 2-connected graphs H on at most 7 edges and is joint with Mark Ellingham, Tom McCourt, and Tony Nixon. Next we look at excluding large theta graphs. We allow at least one of the paths to be arbitrarily long. The most complicated case is excluding theta_{t,t,t} where t is any large integer. The work on large theta graphs is joint with Guoli Ding.

Thursday, November 19, 2015

Posted September 25, 2015
Last modified March 2, 2021

3:30 pm – 4:20 pm Lockett 114

Mark Goresky, Institute for Advanced Study
Modular forms and beyond

Several examples of the spectacular coincidences in number theory that can be "explained" using elliptic curves and modular forms will be described. A plan to find (and prove) higher dimensional generalizations of these phenomena was mapped out 40 years ago by Robert Langlands. Since then, Langlands "program" has occupied the attentions of hundreds of talented mathematicians in what surely must be one of the grandest mathematical gestures in history. Today, much of Langlands' plan is nearing completion, but many mysteries still remain. Some of the ingredients in this vast circle of ideas will be described.

Refreshments will be served in Keisler Lounge at 3:00pm.

Monday, November 23, 2015

Posted November 19, 2015

3:30 pm – 4:30 pm Keisler Lounge

Applied Mathematics Student Talks

Posted November 20, 2015

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 285 Lockett

Shuangqing Wei , School of Electrical Engineering and Computer Science, LSU
Transmission of Partitioning Information over Non-Adaptive Noisy Multi-Access Boolean Channel

Abstract: In this talk, we first formulate a problem on the transmission of partitioning information over noisy Boolean multi-access channels. The objective of transmission is not for message restoration purpose, but rather to make active users partitioned into distinct groups so that they can transmit their messages without collision subsequently. Under a novel framework for strong coloring of hypergraphs, we then modify the sequential decoding method used in the case without noise, and present a general decoding method based on strong typical set and joint decision approaches. A large deviation technique is then employed to find the deviation exponent for the induced Markov chain in a simple but nontrivial case with two active users. The derived achievable bound is shown better when the noise is small than the converse bound of group testing, which is intended for identification of all active users, rather than the partition we are seeking for, thereby further demonstrating the uniqueness of our problems.

Tuesday, November 24, 2015

Posted October 18, 2015

3:30 pm – 4:20 pm Lockett 277

Xingting Wang, Temple University
Quantum p-Groups and Their Classification in Low Dimensions

The classification of p-groups is a fundamental but notoriously difficult problem in group theory. In this talk, the speaker will introduce quantum p-groups as a generalization of p-groups.

Discussion during the talk will be focusing on the recent progress in the complete classification of quantum p-groups in low dimensions. Such classification is part of the classification on finite-dimensional quantum groups in positive characteristic, and also contributes to the understanding of unipotent group schemes in positive characteristic.

Relations between isomorphism classes of quantum p-groups and ordinary p-groups will also be illustrated, which opens a door to using geometric methods in the study of classification of p-groups.

Monday, November 30, 2015

Posted November 28, 2015
Last modified February 20, 2022

3:30 pm – 4:30 pm 285 Lockett

Hyun Woo Jeon, Dept. of Mechanical and Industrial Engineering, LSU
Manufacturing Energy Models based on Probabilistic Approaches

Many managerial decisions impact energy consumption of discrete manufacturing firms. Since an energy amount to be consumed in manufacturing systems is closely connected to energy costs and environmental consequences, these managerial decisions can have long-lasting effects. Hence, making informed decisions with the aid of energy estimation tools is important to manufacturing firms. Estimating energy consumption in manufacturing is not, however, straightforward. There are a number of different manufacturing processes, and energy consumption of each process is dependent on many operational parameters. Thus, for better manufacturing energy analysis, power profiles need to be collected and analyzed from real manufacturing machines, and various methods including analytical and simulation approaches should be proposed and tested based on the collected data. Furthermore, since many previous studies are focusing on mean power demands for evaluating energy consumption, variability of manufacturing power demands also need to be investigated to explore how the uncertainty impacts manufacturing energy.

Addressing the issues, this study proposes methods and applications of probabilistic approaches. At the beginning, this study introduces an analytical manufacturing energy model based on queueing network theory. In the model, manufacturing energy consumption is presented in a closed form equation by considering Markovian and non-Markovian assumptions. Then, this analysis develops previous models further for energy efficiency benchmarking. Comparing manufacturing energy in a hypothetical system with that of peers in the U.S., the proposed model shows how to assess energy efficiency in a manufacturing plant based on simulation and stochastic frontier analysis. After energy estimation and energy efficiency assessment are discussed, this study transcends previous studies by considering uncertainty and variability on manufacturing electrical demands. The approach presents benefits of considering uncertainty in manufacturing power demands, and proposes a systemic method to estimate mean and uncertainty by applying probabilistic techniques. At each discussion, a proposed method is validated and verified in a suitable manner, and accuracy of the proposed method is also checked in detail.

Wednesday, December 2, 2015

Posted September 24, 2015
Last modified November 30, 2015

3:30 pm – 4:30 pm

Chris Hruska, UW Milwaukee
Virtual Seminar: Distortion of surfaces in 3-dimensional graph manifolds

Abstract: (Joint with Hoang Thanh Nguyen) In geometric group theory, one often studies a finitely generated group as a geometric object, by equipping the group with a word metric. Using the word metric, Milnor observed that the fundamental group of any compact manifold closely resembles the universal cover of the manifold. If H is a finitely generated subgroup of G, then the inclusion of H into G may distort the geometry of H. In other words, distances between elements of H may be quite different when measured in the metrics of G and of H. We examine the large scale geometry of immersed horizontal surfaces in 3-dimensional graph manifolds. An immersed surface in a 3-manifold is said to be virtually embedded if the immersion lifts to an embedding into a finite sheeted cover of the manifold. We prove that the distortion of a horizontal surface is quadratic if the surface is virtually embedded, and is exponential otherwise. The proof depends on a combinatorial characterization of horizontal surfaces that virtually embed, due to Rubinstein-Wang. I will not assume any familiarity with geometric group theory or 3-dimensional manifolds in this talk.

Thursday, December 3, 2015

Posted November 30, 2015

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:15 pm – 4:15 pm Lockett 233

Jesse Levitt, LSU
Nearly Commutative Rings and Algebras: Properties preserved by controlled non-commutativity

Friday, December 4, 2015

Posted November 19, 2015

3:30 pm Lockett 15

Second faculty meeting to discuss undergraduate curriculum

Wednesday, January 6, 2016

Posted October 26, 2015
Last modified December 13, 2022

1:00 pm – 4:00 pm 232 Lockett

Comprehensive/ PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, January 8, 2016

Posted October 26, 2015
Last modified December 13, 2022

1:00 pm – 4:00 pm 232 Lockett

Comprehensive/ PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Monday, January 11, 2016

Posted October 26, 2015
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/ PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, January 20, 2016

Posted December 17, 2015
Last modified January 12, 2016

3:30 pm 16 Lockett

Presentation by Milen Yakimov

A 30 minute presentation will be followed by faculty questions.

Thursday, January 21, 2016

Posted December 17, 2015
Last modified January 12, 2016

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm 16 Lockett

Presentation by Oliver Dasbach

A 30 minute presentation will be followed by faculty questions.

Tuesday, January 26, 2016

Posted January 22, 2016

2:30 pm – 3:30 pm Lockett 136

Tom Braden, University of Massachusetts, Amherst
Geometry of machines

Abstract:

One interesting kind of space whose geometry we can study is a configuration space: a space whose points represent possible states in a mechanism or other physical system. Navigating along a path inside the space is then represented by motions of the machine. Some quite complicated and high dimensional sdpaces which cannot be visualized directly can be explored very concretely in this way.

I will focus mainly on configuration spaces of planar bar-and-joint machines, which are two-dimensional machines made from rigid bars, hinges, and anchors. Amazingly, a theorem of Kapovich and Milson says roughly that any manifold can appear as (part of) the configuration space of such a machine.

A light lunch will be served in the Keisler Lounge at 2:00pm.

Posted January 15, 2016
Last modified January 25, 2016

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 277

Jesse Levitt, LSU
Classifying connected Hopf algebras of finite GK dimension via finite Drinfeld quantizations

The classification problem for Hopf Algebras of finite GK dimension has attracted a lot of interest in recent years. We will describe a new perspective to it via deformation theory. In 1983 Drinfeld constructed quantizations of all triangular r-matrices. We expand on work of Etingof and Gelaki showing that the ones that are finite define connected Hopf algebras of finite GK dimension. Hopf algebras constructed in this way are isomorphic, as algebras, to universal enveloping algebras. This construction recovers almost all of the known connected Hopf algebras of finite GK dimension, leads to many new examples from the general point of view of quasi-Frobenius Lie algebras, and enables preexisting Lie theoretic classification results to be brought to bear on the question at hand. This is a joint work with Milen Yakimov.

Posted January 22, 2016
Last modified January 27, 2016

VIGRE@LSU: Student Colloquium Questions or comments?

5:30 pm Keisler Lounge (321 Lockett)

Actuarial Club meeting

Winnie Sloan, Travelers Insurance and former ASA president, will speak and answer questions through Skype.

Wednesday, January 27, 2016

Posted January 22, 2016

3:00 pm – 3:50 pm Lockett 232

Tom Braden, University of Massachusetts, Amherst
Deformations in topology and algebra

Abstract:

The idea of deformation appears all over mathematics. In its most basic form, one takes an object and fits it into a family of related objects parametrized by some auxiliary variables. When the family varies nicely enough, the entire family can have nicer properties than the original object did.

This talk will present a few interesting settings from topology and algebra in which this idea works nicely. In the realm of topology, the equivariant cohomology ring of a space with a torus action is a deformation of the ordinary cohomology ring. In algebra, one can view polynomial differential operators as a deformation of ordinary polynomial functions, and a useful way to study certain representations of Lie algebras is by deforming the action of a Cartan subalgebra. These ideas will be presented via concrete examples and a minimum of technical machinery.

Refreshments will be served in the Keisler Lounge at 2:30pm.

Monday, February 1, 2016

Posted January 29, 2016

3:30 pm – 4:20 pm Lockett 285

Brian Street, University of Wisconsin-Madison
The Frobenius Theorem

We present a quantitative version of the classical Frobenius theorem from differential geometry. This theorem can be seen as providing scaling maps which can be used to study a range of problems in analysis. We present two such applications: a theory of singular Radon transforms (joint with E. M. Stein) and a theory of multi-parameter singular integrals which has applications to PDEs and several complex variables.

Tuesday, February 2, 2016

Posted January 21, 2016

3:30 pm – 4:30 pm Digital Media Center 1034

Jennifer Ryan, University of East Anglia, UK
Exploiting Approximation Properties in the Discontinuous Galerkin Scheme for Improved Trouble Cell Indication

Abstract: In this talk, we present a generalized discussion of discontinuous Galerkin methods concentrating on a basic concept: exploiting the existing approximation properties. The discontinuous Galerkin method uses a piecewise polynomial approximation to the variational form of a PDE. It uses polynomials up to degree k for a k+1 order accurate scheme. Using this formulation, we concentrate on nonlinear hyperbolic equations and specifically discuss how to obtain better discontinuity detection during time integration by rewriting the approximation using a multi-wavelet decomposition. We demonstrate that this multi-wavelet expansion allows for more accurate detection of discontinuity locations. One advantage of using the multi-wavelet expansion is that it allows us to specifically relate the jumps in the DG solution and its derivatives to the multi-wavelet coefficients. This is joint work with Thea Vuik, TU Delft.

Friday, February 5, 2016

Posted January 29, 2016
Last modified January 30, 2016

1:30 pm – 2:20 pm Lockett 241

Jing Tao, University of Oklahoma
Stable commutator lengths in right-angled Artin groups

The commutator length of an element g in the commutator subgroup [G,G] of a group G is the smallest k such that g is the product of k commutators. When G is the fundamental group of a topological space, then the commutator length of g is the smallest genus of a surface bounding a homologically trivial loop that represents g. Commutator lengths are notoriously difficult to compute in practice. Therefore, one can ask for asymptotics. This leads to the notion of stable commutator length (scl) which is the speed of growth of the commutator length of powers of g. It is known that for n > 2, SL(n,Z) is uniformly perfect; that is, every element is a product of a bounded number of commutators, and hence scl is 0 on all elements. In contrast, most elements in SL(2,Z) have positive scl. This is related to the fact that SL(2,Z) acts naturally on a tree (its Bass-Serre tree) and hence has lots of nontrivial quasimorphisms. In this talk, I will discuss a result on the stable commutator lengths in right-angled Artin groups. This is a broad family of groups that includes free and free abelian groups. These groups are appealing to work with because of their geometry; in particular, each right-angled Artin group admits a natural action on a CAT(0) cube complex. Our main result is an explicit uniform lower bound for scl of any nontrivial element in any right-angled Artin group. This work is joint with Talia Fernos and Max Forester.

Posted January 29, 2016
Last modified January 30, 2016

3:30 pm – 4:20 pm Lockett 277

Roi Docampo Álvarez, Instituto de Ciencias Matemáticas (ICMAT)
The Nash problem for arc spaces

Algebraic varieties (zeros of polynomial equations) often present singularities: points around which the variety fails to be a manifold, and where the usual techniques of calculus encounter difficulties. The problem of understanding singularities can be traced to the very beginning of algebraic geometry, and we now have at our disposal many tools for their study. Among these, one of the most successful is what is known as resolution of singularities, a process that transforms (often in an algorithmic way) any variety into a smooth one, using a sequence of simple modifications.

In the 60's Nash proposed a novel approach to the study of singularities: the arc space. These spaces are natural higher-order analogs of tangent spaces; they parametrize germs of curves mapping into the variety. Just as for tangent spaces, arc spaces are easy to understand in the smooth case, but Nash pointed out that their geometric structure becomes very rich in the presence of singularities.

Roughly speaking, the Nash problem explores the connection between the topology of the arc space and the process of resolution of singularities. The mere existence of such a connection has sparked in recent years a high volume of activity in singularity theory, with connections to many other areas, most notably birational geometry and the minimal model program.

The objective of this talk is to give an overview of the Nash problem. I will give a precise description of the problem, and discuss the most recent developments, including a proof of the Nash conjecture in dimension two, and a partial solution to the Nash problem in arbitrary dimension.

Wednesday, February 10, 2016

Posted January 26, 2016

4:30 pm Lockett 285

Noah Winslow, Louisiana State University
Forbidden Minors for d-Realizability

Abstract: Call a generic placement of the vertices of a graph in an N-dimensional Euclidean space an N-realization. We say G is d-realizable if for any N-realization of a graph G, d is the smallest value for which there exists a d-realization of G with the same edge lengths. Formally, Belk and Connelly determined the set of all forbidden minors for d-realizability for d at most 3. Expanding on this work, we determine a large family of forbidden minors for each dimension greater than 3. At the heart of this graph family is a new concept, spherical realizability, which generically places the vertices of a graph on a d-sphere rather than in Euclidean space.

Thursday, February 11, 2016

Posted January 29, 2016
Last modified January 30, 2016

LSU AWM Student Chapter LSU AWM Student Chapter Website

3:30 pm – 4:20 pm Lockett 277

Jiuyi Zhu, LSU
Nodal geometry of Steklov eigenfunctions

The eigenvalue and eigenfunction problem is fundamental and essential in mathematical analysis. The Steklov problem is an eigenvalue problem with its spectral parameter at the boundary of a compact Riemannian manifold. Recently the study of Steklov eigenfunctions has been attracting much attention. We consider the quantitative properties: Doubling inequality and nodal sets. We obtain the sharp doubling inequality for Steklov eigenfunctions on the boundary and interior of manifolds using delicate Carleman estimates. We can ask Yau's type conjecture for the Hausdorff measure of nodal sets of Steklov eigenfunctions on the boundary and interior of the manifold. I will describe some recent progress about this challenging direction. Part of work is joint with C. Sogge and X. Wang.

Friday, February 12, 2016

Posted February 11, 2016

9:00 am – 10:00 am Keisler Lounge

A Conversation with Dr. Carol Woodward (LLNL)

Posted February 9, 2016

11:00 am – 12:00 pm Keisler Lounge

A Conversation with Professor James Nagy (Emory University)

Posted November 2, 2015

1:00 pm – 5:00 pm Sunday, March 13, 2016 Digital Media Center Theatre

Scientific Computing Around Louisiana (SCALA) 2016

https://www.cct.lsu.edu/SCALA

Monday, February 15, 2016

Posted January 29, 2016
Last modified September 17, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 243

Fang-Ting Tu, National Center for Theoretical Sciences, Taiwan
Modular Forms on Shimura Curves and Hypergeometric Functions

Tuesday, February 16, 2016

Posted December 2, 2015
Last modified February 15, 2016

3:30 pm – 4:20 pm Lockett 277

Mehmet Kıral, Texas A&M University
The Voronoi formula and double Dirichlet series

A Voronoi formula is an identity where on one side, there is a weighted sum of Fourier coefficients of an automorphic form twisted by additive characters, and on the other side one has a dual sum where the twist is perhaps by more complicated exponential sums. It is a very versatile tool in analytic studies of L-functions. In joint work with Fan Zhou we come up with a proof of the identity for L-functions of degree N. The proof involves an identity of a double Dirichlet series which in turn yields the desired equality for a single Dirichlet coefficient. The proof is robust and applies to L-functions which are not yet proven to come from automorphic forms, such as Rankin-Selberg L-functions.

Posted January 30, 2016
Last modified February 11, 2016

3:30 pm – 4:30 pm Digital Media Center 1034

Gang Bao, Zhejiang University
Inverse Problems for PDEs: Analysis, Computation, and Applications

Abstract: Inverse problems for PDEs arise in diverse areas of industrial and military applications, such as nondestructive testing, seismic imaging, submarine detections, near-field and nano optical imaging, and medical imaging. A model problem in wave propagation is concerned with a plane wave incident on a medium enclosed by a bounded domain. Given the incident field, the direct problem is to determine the scattered field for the known scatterer. The inverse problem is to determine the scatterer from the boundary measurements of near field currents densities. Although this is a classical problem in mathematical physics, mathematical issues and numerical solution of the inverse problems remain to be challenging since the problems are nonlinear, large-scale, and most of all ill-posed! The severe ill-posedness has thus far limited in many ways the scope of inverse problem methods in practical applications. In this talk, the speaker will first introduce inverse problems for PDEs and discuss the state of the arts of the inverse problems. Our recent progress in mathematical analysis and computational studies of the inverse boundary value problems will be reported. Several classes of inverse problems will be studied, including inverse medium problems, inverse source problems, inverse obstacle problems, and inverse waveguide problems. A novel stable continuation approach based on the uncertainty principle will be presented. By using multi-frequency or multi-spatial frequency boundary data, our approach is shown to overcome the ill-posedness for the inverse problems. New stability results and techniques for the inverse problems will be presented. Related topics will be highlighted.

Wednesday, February 17, 2016

Posted January 7, 2016
Last modified February 8, 2016

3:30 pm – 4:20 pm

Abhijit Champanerkar, CSI NY/CUNY
Virtual Seminar: "Densities and semi-regular tilings"

Abstract: For a hyperbolic knot or link $K$ the volume density is a ratio of hyperbolic volume to crossing number, and the determinant density is the ratio of 2\pi\log(det(K)) to the crossing number. We explore limit points of both densities for families of links approaching semi-regular biperiodic alternating links. We explicitly realize and relate the limits for both using techniques from geometry, topology, graph theory, dimer models, and Mahler measure of two-variable polynomials. This is joint work with Ilya Kofman and Jessica Purcell.

Thursday, February 18, 2016

Posted February 11, 2016

3:30 pm – 4:20 pm Lockett 277

Thomas Parker, Michigan State University
Holomorphic curves, strings, and the GV conjecture

This is a talk on counting solutions of non-linear elliptic PDEs. After presenting the basic idea, I will explain, from two completely different perspectives, how the search for simple examples leads -- rather surprisingly -- to considering holomorphic maps into Calabi-Yau 3-folds X. Such maps are counted by the Gromov-Witten invariants of X, which are an infinite set of rational numbers. In 1998, physicists R. Gopakumar and C. Vafa conjectured that these Gromov-Witten invariants have a hidden structure: they are obtained, by a specific transform, from a set of more fundamental \"BPS numbers\", which are integers. The talk will conclude with a pictorial proof of the GV conjecture (joint work with E. Ionel) based on the idea of using deformations of almost complex structures to count the contributions of \"clusters of curves\".

Posted February 17, 2016

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

4:30 pm – 5:30 pm Lockett 233

Bach Nguyen, LSU
Poisson Structures arising from Noncommutative Algebras I

Wednesday, February 24, 2016

Posted January 26, 2016
Last modified February 23, 2016

9:00 am – 10:00 am Digital Media Center 1034
(Originally scheduled for Tuesday, February 23, 2016, 3:30 pm)

Alexandre Madureira, Laboratorio Nacional de Computacao Cientifica, Brazil
Hybrid Finite Element Methods for Multiscale Problems

Abstract: In this talk we discuss the use of hybrid methods for multiscale partial differential equations, in particular concerning the development of a hybrid scheme to solve the linear elasticity system. The unknowns are the displacements and the boundary tractions at each element. Starting from a primal hybrid formulation, the method has a domain decomposition flavor, and the displacements can be discontinuous, with continuous tractions. A decomposition of the primal space allows the reformulation of the continuous problem as a coupled system of elementwise equations, and a global mixed system posed on the mesh skeleton. The scheme is embarrassingly parallel, where the local problems are solved independently. We shall discuss the connections between this and some other methods.

Thursday, February 25, 2016

Posted February 12, 2016

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm Lockett 277

Meeting of the professorial faculty

Posted February 23, 2016

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:40 pm – 4:40 pm Lockett 233

Bach Nguyen, LSU
Poisson Structures arising from Noncommutative Algebras II

We will continue to discuss examples of Poisson Structures coming from noncommutative algebras such as Lie algebra, algebra of polynomial differential, and algebra of quantum matrices.

Monday, February 29, 2016

Posted February 26, 2016

1:30 pm – 2:20 pm Lockett 114

Sara Billey, University of Washington
Trees, Tanglegrams, and Tangled Chains

Abstract: Tanglegrams are a special class of graphs appearing in applications concerning cospeciation and coevolution in biology and computer science. They are formed by identifying the leaves of two rooted binary trees. We give an explicit formula to count the number of distinct binary rooted tanglegrams with n matched vertices, along with a simple asymptotic formula and an algorithm for choosing a tanglegram uniformly at random. The enumeration formula is then extended to count the number of tangled chains of binary trees of any length. This includes a new formula for the number of binary trees with n leaves. We also give a conjecture for the expected number of cherries in a large randomly chosen binary tree and an extension of this conjecture to other types of trees. This talk is based on recent joint work with Matjaz Konvalinka and Frederick (Erick) Matsen IV posted at http://arxiv.org/abs/1507.04976 .

A light lunch will be served at 1pm.

Posted February 26, 2016

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:20 pm Lockett 114

Sara Billey, University of Washington
Enumeration of Parabolic Double Cosets for Coxeter Groups

Abstract: Parabolic subgroups WI of Coxeter systems (W,S) and their ordinary and double cosets W/WI and WI∖W/WJ appear in many contexts in combinatorics and Lie theory, including the geometry and topology of generalized flag varieties and the symmetry groups of regular polytopes. The set of ordinary cosets wWI, for I⊆S, forms the Coxeter complex of W, and is well-studied. In this talk, we look at a less studied object: the set of all parabolic double cosets WIwWJ for I,J⊆S.

Each double coset can be presented by many different triples (I,w,J). We describe what we call the lex-minimal presentation and prove that there exists a unique such choice for each double coset. Lex-minimal presentations can be enumerated via a finite automaton depending on the Coxeter graph for (W,S).

In particular, we present a formula for the number of parabolic double cosets with a fixed minimal element when W
is the symmetric group Sn. In that case, parabolic subgroups are also known as Young subgroups. Our formula is almost always linear time computable in n, and the formula can be generalized to any Coxeter group.

This talk is based on joint work with Matjaz Konvalinka, T. Kyle Petersen, William Slofstra and Bridget Tenner.

Refreshments will be served at 3pm in the Keisler lounge.

Tuesday, March 1, 2016

Posted February 21, 2016

5:30 pm Keisler Lounge (321 Lockett)

Actuarial Club meeting

Discussion of the concentration requirements and options.

Wednesday, March 2, 2016

Posted November 21, 2015
Last modified February 25, 2016

3:30 pm – 4:20 pm 233 Lockett

Max Forester, University of Oklahoma
Virtual Seminar: "The geometry of Stallings-Bieri groups"

Abstract: The Stallings-Bieri groups are a family of finitely presented groups that have exotic homological finiteness properties, while also being quite easy to define and describe. They occur naturally as subgroups of non-positively curved groups (products of free groups, in fact). They are not non-positively curved themselves, however, and their large-scale geometry is quite interesting. I will discuss recent work with Will Carter in which we determine the large-scale isoperimetric behavior of these groups.

Tuesday, March 8, 2016

Posted March 7, 2016

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm Digital Media Center 1034

Mayank Tyagi, Mechanical Engineering Department, Louisiana State University.
Insights into Complex Wellbore Construction Processes and Completions Performance using Computation Fluid Dynamics (CFD) Simulations

Multiphysics CFD simulations on HPC platforms provide a great opportunity to learn about the complex processes during drilling and completions operations of oil & gas wells. Several computational fluid dynamics (CFD) models with different features are presented for cuttings transport, cement placement, and production through completions in this presentation. All simulation cases are both verified and validated against available experimental data for their corresponding physics. In order to get accurate flow predictions while optimizing computational resources requirements, unsteady shear stress transport (SST) k-ω turbulence model is used to model turbulence closure while solving Reynolds-averaged Navier-Stokes (RANS) equations using unstructured finite volume method (FVM) for discretization. Discrete phase is modeled with discrete element method (DEM) by including particle-particle and particle-fluid interactions with two-way coupling in Eulerian-Lagrangian simulations. Volume of Fluid (VOF) model is used to model displacement of different fluid types with non-Newtonian fluid rheology for cement placement applications. Specifically, during the drilling of highly deviated wellbores, the cuttings transport becomes difficult due to the rolling/sliding transport of the cuttings due to settling around the lower side of the annular region between wellbore and drillpipe. Inefficient cuttings transport may lead to several critical problems such as stuck pipe, increased torque and drag, damaged material and poor quality of cementing jobs. Increasing mud flowrates and improving mud properties for a proper wellbore cleaning is usually limited due to the hydraulic and mechanical thresholds for wellbore formation integrity. Further, understanding of cement placement process remains a critical step in achieving zonal isolation between casings and hydrocarbon bearing formations in all types of well construction operation. Lastly, a gravel-packed completion is modeled to showcase the capabilities of CFD simulations by gaining new insights into modeling and representation of high-rate producer wells in reservoir simulators.

Wednesday, March 9, 2016

Posted March 7, 2016

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:40 pm – 4:10 pm Lockett 233

Neal Livesay, LSU
Regular filtrations on the symplectic loop algebra

Filtrations on the symplectic loop algebra can give explicit normal forms for formal flat $Sp$-bundles with ``toral\'\' singularities. Conjecturally, these filtrations will be useful for constructing well-behaved moduli spaces, generalizing the work of Bremer and Sage on flat $GL$-bundles. I will discuss what is meant by a ``toral\'\' singularity and illustrate the theory for some small rank examples.

Posted March 7, 2016

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

4:10 pm – 4:40 pm Lockett 233

Lucius Schoenbaum, LSU
Introduction to Topos Theory

What does left exactness of a left R-module over a commutative ring have to do with the existence of atoms in a Boolean algebra? We will learn about this and more in a leisurely, very short introduction to topos theory.

Monday, March 14, 2016

Posted March 8, 2016

2:30 pm – 3:20 pm Lockett 114

Tadele Mengesha, The University of Tennessee, Knoxville
Integration by parts, local and nonlocal

Abstract:

In this talk, I will review the impact of integration by parts on our understanding of the derivative of rough functions. Once a property of smooth functions, integration by parts can be used as a defining character of regular functions as well as their derivative in the broader sense. As a consequence, a renewed notion of solution to ordinary and partial differential equations, especially those with irregular source term or irregular coefficients can be formulated. I will discuss some frequently used spaces of functions that can be described with the new notion of regularity. Extension of the definition and application of integration by parts to integral equations, also know as, nonlocal equation will be presented.

A light lunch will be served in the Keisler lounge at 2:00 pm

Tuesday, March 15, 2016

Posted February 2, 2016
Last modified March 14, 2016

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 277

Stefan Kolb, Newcastle University
Universal K-matrix for coideal subalgebras

Quantum groups provide a uniform setting for solutions of the quantum Yang-Baxter equation. These solutions are realized via a universal R-matrix which lies at the heart of the origins of quantum groups in the theory of quantum integrable systems. For systems with boundary, additionally, the reflection equation enters the picture. It is expected that solutions of the reflection equation are obtained via a universal K-matrix. A general construction of a universal K-matrix for Hopf algebras was given by Donin, Kulish, and Mudrov. In this talk I will suggest to base the construction of a universal K-matrix on coideal subalgebras of Hopf algebras. I will then discuss examples from the theory of quantum symmetric pairs, based on joint work with Martina Balagovic.

Posted March 14, 2016

VIGRE@LSU: Student Colloquium Questions or comments?

3:30 pm – 4:30 pm 244 Locket

Arnab Ganguly, LSU
An introduction to large deviation principle

In this talk, I will present a weak convergence based approach to large deviation principle. This approach uses appropriate variational representations of certain functionals and has also connections to control theory. The talk will illustrate the main ideas through a proof of the classical Sanov\'s theorem.

Wednesday, March 16, 2016

Posted March 8, 2016

3:30 pm – 4:20 pm Lockett 114

Tadele Mengesha, The University of Tennessee, Knoxville
Averaged directional difference quotients

Abstract: We study averaged directional difference quotients of vector fields and their continuity property over several function spaces. A third order tensor field will be used to distinguish appropriate directions in which slopes are averaged. The averaged directional derivatives will be shown to approximate classical notions of derivatives. We will use this approximation property to characterize vector fields in the space of Sobolev, bounded variation, and bounded deformation functions in a unified way.

Refreshments will be served in the Keisler lounge at 3:00pm

Posted March 9, 2016
Last modified March 2, 2021

3:30 pm – 4:20 pm

Roland van der Veen, Universiteit Leiden
Virtual Seminar: "Shadows, spines and gluing equations"

Ideal triangulations were applied very effectively to understand 3-manifolds. For example Thurston set up a system of gluing equations to produce hyperbolic structures from the ideal triangulation. I will argue that their dual 2-complexes, known as spines, are both easier to visualize and more flexible than ideal triangulations. We will reformulate Thurston's construction in terms of spines and show how one proves their symplectic properties first found by Neumann and Zagier. Time permitting we will also mention relations to four-manifolds and the Andrews-Curtis conjecture that become apparent in terms of spines.

Thursday, March 17, 2016

Posted March 14, 2016

3:30 pm – 4:20 pm Lockett 277

Barbara Rüdiger, Bergische Universität Wuppertal, Germany
Exponential ergodicity of jump-diffusion CIR processes

We analyze exponential ergodicity properties of affine term structure models. For some (Jump -) diffusion CIR processes, in particular the CIR process and the basic affine jump diffusion process (BAJD), we prove Harris recurrence properties. This permits in particular to calibrate the parameters of the model. These results are based on joint articles with V. Mandrekar, Peng Jin, Chiraz Trabelsi, and Jonas Kremer . All models will be introduced in this talk.

Tuesday, March 29, 2016

Posted March 28, 2016

3:30 pm – 4:30 pm 244 Lockett

Arnab Ganguly, LSU
An introduction to large deviation principle - Part II

This will be a continuation of my previous talk. In this talk, I will continue with a weak convergence based approach to large deviation principle. This approach uses appropriate variational representations of certain functionals and has also connections to control theory. The talk will illustrate the main ideas through a proof of the classical Sanov\'s theorem.

Wednesday, March 30, 2016

Posted January 26, 2016

3:30 pm – 4:30 pm Digital Media Center 1034

Robert Falgout, Lawrence Livermore National Lab
Space-time Multigrid Solvers for Extreme-scale Scientific Computing

Abstract: Multigrid methods are important techniques for efficiently solving huge systems and they have already been shown to scale effectively on millions of cores. However, one of the major challenges facing computational science with future architectures is that faster compute speeds will be achieved through greater concurrency (more cores), since clock speeds are no longer increasing. Current petascale computers already have millions of cores, but future exascale machines are expected to have billions. This immense degree of parallelism requires a similar level of concurrency in the algorithms that run on them. One consequence of this is that time integration by traditional time marching will become a sequential bottleneck.

In this talk, we will first introduce the multigrid method, discuss its essential features, and provide basic information on its benefits for parallel scientific computing. We will then discuss our efforts to develop multigrid methods for parallel time integration. The approach we use is based on multigrid reduction (MGR) techniques and has the advantage of being easily integrated into existing codes because it builds directly on the original time-stepping scheme. Results for a variety of applications will also be presented. LLNL-ABS-681196.

Posted March 13, 2016

4:30 pm – 5:30 pm Lockett 285

Kevin Grace, LSU
Templates for Minor-Closed Classes of Binary Matroids

The concept of a template was recently introduced by Jim Geelen, Bert Gerards, and Geoff Whittle as a tool to describe some of their results in matroid structure theory. Matroids that conform to a frame template are obtained by altering a graphic matroid in a certain way. We introduce a partial order on binary frame templates and a list of minimal templates in this partial order. An application of this result is that all sufficiently highly connected 1-flowing matroids are either graphic or cographic. Other applications can be made to growth rates of minor-closed classes of binary matroids.

Tuesday, April 5, 2016

Posted March 31, 2016

VIGRE@LSU: Student Colloquium Questions or comments?

5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial club meeting

Dr. Shreve from the department of analytics will coming to speak about the graduate program and the field of analytics. The Society of Actuaries will be expanding their requirements to include analytics in the next few years.

Pizza will be served.

Wednesday, April 6, 2016

Posted March 31, 2016

2:30 pm – 3:30 pm Lockett 136

Mark Reeder, Boston College
Understanding the Hypersphere

Abstract: A Hypersphere is a sphere in four dimensions. It controls motion in our three dimensional world. Though we feel the effects of the hypersphere, our brains cannot easily visualize the whole of it. In this talk, Algebra, Geometry and Topology will unite to help us understand the Hypersphere.

A light lunch will be served in Keisler Lounge at 2:00pm.

Thursday, April 7, 2016

Posted March 31, 2016

VIGRE@LSU: Student Colloquium Questions or comments?

12:30 pm – 1:30 pm Lockett 136

Mark Reeder, Boston College
From the Hypersphere to E8

Abstract: This talk will be an introduction to compact groups G of continuous symmetries. We will see that Hyperspheres are the bricks in the construction of G, and also that G contains a \"principal hypersphere\" which knows way more than it should about the topology and group theory of G.

Refreshments will be served at 12:00pm in the Keisler Lounge.

Posted March 31, 2016
Last modified April 5, 2016

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 277

Mark Reeder, Boston College
Adjoint Swan Conductors

Langlands parameters may be regarded as arithmetically enhanced elements in complex Lie groups. The Adjoint Swan Conductor of a parameter is an arithmetic analogue of the dimension of a Springer fiber. The latter satisfy an inequality which becomes an equality for regular elements. I will discuss the analogue of this inequality for Langlands parameters.

Monday, April 11, 2016

Posted March 21, 2016
Last modified April 5, 2016

3:30 pm – 4:30 pm Lockett 233

Gianni Royer Carfagni, Università degli Studi Di Parma, Department of Civil Engineering, Environmental Engineering, and Architecture
Phase-field description of structured deformations in plasticity

Abstract: A variational approach to determine the deformation of an ideally plastic substance is proposed by solving a sequence of energy minimization problems under proper conditions to account for the irreversible character of plasticity. The flow is driven by the local transformation of elastic strain energy into plastic work on slip surfaces, once that a certain energetic barrier for slip activation has been overcome. The distinction of the elastic strain energy into spherical and deviatoric parts can also be used to incorporate in the model the idea of von Mises plasticity and isochoric plastic strain. This is a "phase field mode" because the matching condition at the slip interfaces are substituted by the evolution of an auxiliary phase field that, similarly to damage theory, is unitary on the elastic phase and null on the yielded phase. The slip lines diffuse in bands whose width depends upon a material length-scale parameter. Numerical experiments on representative problems in plane strain give solutions with striking similarities with the results from classical slip-line field theory of plasticity, but the proposed model is much richer because, accounting for elastic deformations, it can describe the formation of slip bands at the local level, which can nucleate, propagate, widen and diffuse by varying the boundary conditions.

Tuesday, April 12, 2016

Posted March 15, 2016

Algebra and Number Theory Seminar Questions or comments?

2:00 pm – 3:00 pm 138 Lockett Hall

Troy Schaudt, Wolfram Research
Mathematica 10 in Education and Research

This talk illustrates capabilities in Mathematica 10 and other Wolfram technologies that are directly applicable for use in teaching and research on campus. Topics of these technical talks include:

* Enter calculations in everyday English, or using the flexible Wolfram Language
* Visualize data, functions, surfaces, and more in 2D or 3D
* Store and share documents locally or in the Wolfram Cloud
* Use the Predictive Interface to get suggestions for the next useful calculation or function options
* Access trillions of bits of on-demand data
* Use semantic import to enrich your data using Wolfram curated data
* Easily turn static examples into mouse-driven, dynamic applications
* Access 10,000 free course-ready applications
* Utilize the Wolfram Language\'s wide scope of built-in functions, or create your own
* Get deep support for specialized areas including machine learning, time series, image processing, parallelization, and control systems, with no add-ons required

Current users will benefit from seeing the many improvements and new features of Mathematica 10 (http://www.wolfram.com/mathematica/new-in-10/), but prior knowledge of Mathematica is not required.

Posted February 22, 2016
Last modified May 8, 2021

3:30 pm – 4:20 pm Lockett 277

Peng Yu, University of Wisconsin-Madison
Special Cycles on Shimura Varieties of Orthogonal Type

I will start with describing the famous Gross-Zagier formula as a relation between Néron-Tate height of Heegner points and central derivative of L-functions. Then I will define special cycles on Shimura variety constructed by Kudla in the setting of orthogonal type. And in the special case of O(1,2), I will show how these cycles be viewed as a generalization of Heegner points and Bruinier, Kulda, Yang and other authors' works on finding Faltings height of these cycles as a generalization of Gross-Zagier formula.

Posted April 11, 2016

3:30 pm – 4:30 pm 244 Lockett

Hui-Hsiung Kuo, Mathematics Department, LSU
Some ideas on extending the Ito theory of stochastic integration

Thursday, April 14, 2016

Posted March 15, 2016
Last modified March 30, 2016

3:30 pm Lockett B16

Faculty Meeting to discuss IRC recommendations

Posted April 13, 2016

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:40 pm – 4:40 pm Lockett 233

Cris Negron, Mathematics Department, LSU
A Suprised Talk

Tuesday, April 19, 2016

Posted January 26, 2016
Last modified February 11, 2016

3:30 pm – 4:30 pm Digital Media Center 1034

Haomin Zhou, Georgia Tech University
Stochastic Differential Equations and Optimal Control with Constraints

Abstract: We design a new stochastic differential equation (SDE) based algorithm to efficiently compute the solutions of a class of infinite dimensional optimal control problems with constraints on both state and control variables. The main ideas include two parts. 1) Use junctions to separate paths into segments on which no constraint changes from active to in-active, or vice versa. In this way, we transfer the original infinite dimensional optimal control problems into finite dimensional optimizations. 2) Employ the intermittent diffusion (ID), a SDE based global optimization strategy, to compute the solutions efficiently. It can find the global optimal solution in our numerical experiments. We illustrate the performance of this algorithm by several shortest path problems, the frogger problem and generalized Nash equilibrium examples. This talk is based on joint work with Shui-Nee Chow (Math, Georgia Tech), Magnus Egerstedt (ECE, Georgia Tech). Wuchen Li (Math, Georgia Tech), and Jun Lu (Wells Fargo).

Posted April 17, 2016

5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial club meeting

Christopher Mai will be giving a presentation on Mixed Probability Distributions. This topic is on the actuarial Exam P/Exam1 syllabus, but it is not covered in Math 3355, probability.

Thursday, April 21, 2016

Posted March 15, 2016
Last modified March 30, 2016

3:30 pm Lockett B 16

Spring Faculty meeting

Posted April 20, 2016
Last modified March 2, 2021

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:40 pm – 4:40 pm Lockett 233

Maitreyee Kulkarni, LSU
Introduction to Nakajima's quiver varieties

Kashiwara's crystals give a combinatorial description of characters of irreducible finite dimensional U_q(g)-modules. The situation gets much more complicated in the case of the quantum loop algebras U_q(Lg), as the characters are now polynomials in terms of q. Nakajima has given a geometric description of the irreducible q-characters of U_q(Lg) using his graded quiver varieties. In this talk, we will define these quiver varieties, compute some examples and see how they are related to the q-characters.

Posted April 5, 2016

Algebra and Number Theory Seminar Questions or comments?

4:30 pm Keisler Lounge, 3rd Floor, Lockett Hall

Kimberly D'souza, Louisiana State University
An Introduction to Neural Networks

A neural network is a programming tool used to try to enable machines to more effectively perform tasks that are solved by humans. This involves both an initial 'teaching' of the machine as well as one or more algorithms so that it will 'learn' continuously. The goal of these networks is to mimic (as closely as possible) the functionality of the human brain. You may recall the supercomputer Watson which had a quite successful run on Jeopardy. Part of Watson's design included neural networking. In this talk we will provide an introduction to what a neural network is and how they are initially taught and continue to learn. Finally, we will look at implementation of some simple neural networks using built-in functionality in both R and Python.

Tuesday, April 26, 2016

Posted February 24, 2016
Last modified April 25, 2016

2:30 pm – 3:20 pm Lockett 276

Viswambhara Makam, University of Michigan
Polynomial degree bounds for matrix semi-invariants

Even though the invariant ring for a representation of a reductive group is finitely generated, finding strong bounds for the degree of generators has proved to be extremely difficult. We focus on the left-right action of SL(n) x SL(n) on m-tuples of n-by-n matrices. We show that invariants of degree at most n(n-1) define the null cone, and that consequently invariants of degree at most n^6 generate the invariant ring in characteristic 0. If time permits, we shall discuss the ramifications of our bound to algebraic complexity theory, such as a poly-time algorithm for non-commutative rational identity testing.

Posted April 4, 2016
Last modified April 18, 2016

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 277

Nick Ramsey, DePaul University
p-adic modular forms of half-integral weight and applications to L-values

I'll survey my work on p-adic modular forms of half-integral weight. In particular, I'll explain how to interpolate the Shimura lifting across the eigencurve and give an application to the p-adic interpolation of square roots of special values of L-functions.

Posted January 21, 2016

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Digital Media Center 1034

Francisco Javier Sayas, University of Delaware
Hybridizable Discontinuous Galerkin Methods for Elastodynamics

Abstract: In this talk I will present some preliminary results on the use of an Hybridizable Discontinuous Galerkin method for the simulation of elastic waves. I will show how the Qiu and Shi choice of spaces and stabilization parameters for an HDG scheme applied to quasi-static elasticity also apply for time harmonic elastic waves, providing a superconvergent method. I will next discuss a conservation of energy property that holds in the transient case when the elasticity equations are semidiscretized in space with the same HDG strategy. This work is a collaboration with Allan Hungria (University of Delaware) and Daniele Prada (Indiana University Purdue University at Indianapolis)

Thursday, April 28, 2016

Posted April 27, 2016

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

1:30 pm – 2:20 pm Lockett 233

Sean Taylor, LSU
An Introduction to Algebraic Stacks

Algebraic stacks constitute an often over-looked area of modern algebraic geometry, because of the seeming abstractness of the subject. In this talk, I will attempt to give a (very) brief and hopefully gentle introduction to stacks and what makes a stack \"algebraic.\" This will hopefully be approachable even for those who do not know what a scheme is, since the audience will be encouraged to think about the geometric objects in their favorite categories (manifolds, complex analytic spaces, etc.). In short, these are powerful geometric (!) objects that are becoming more and more fundamental to algebraic geometry and representation theory among other subjects.

Posted April 15, 2016
Last modified April 25, 2016

2:30 pm – 3:20 pm Lockett 277

Ivan Losev, Northeastern University
Deformations of symplectic singularities and the orbit method

Symplectic singularities were introduced by Beauville in 2000. These are especially nice singular Poisson algebraic varieties that include symplectic quotient singularities and the normalizations of orbit closures in semisimple Lie algebras. Poisson deformations of conical symplectic singularities were studied by Namikawa who proved that they are classified by points of a vector space. Recently I have proved that quantizations of conical symplectic singularities are still classified by the points of the same vector spaces. I will explain these results and then apply them to establish a version of Kirillov's orbit method for semisimple Lie algebras.

Posted March 30, 2016

3:30 pm Lockett B 16

Math faculty meeting with Dean Peterson

Friday, April 29, 2016

Posted April 7, 2016

3:00 pm Keisler lounge

Spring Awards Ceremony

Posted April 15, 2016
Last modified March 3, 2021

4:00 pm – 4:50 pm Lockett 277

Adimurthi, TIFR Bangalore
Structure of Entropy solutions of Hyperbolic conservation laws in space dimension

Hyperbolic Conservation laws in one space dimension has been studied for quite a long time starting from Lax and Oleinik. Main questions related to the existence of numbers shocks and nature of the solutions was not well understood. In this talk I will discuss these questions when the flux is convex.

Monday, May 2, 2016

Posted April 28, 2016

2:30 pm Room 233, Lockett Hall

Alex Dunkel, Louisiana State University Graduate Student
Introduction to Remote Access

Using a remote server instead of your own computer for your computations can be more efficient and time-effective. This talk demonstrates how to use a command line interface to create an SSH connection to a remote server and make use of this shared resource. We will also explore how to make use of parallelization through a simple introduction to OpenMP, a method for multithreaded programming.

Tuesday, May 3, 2016

Posted May 2, 2016

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

1:30 pm – 2:30 pm Lockett 233

Sean Taylor, LSU
Introduction to Algebraic Stacks Part 2

After introducing what a Grothendieck topology was last week, we will be able to proceed to actually define stacks - which are higher analogues of sheaves - and then algebraic stacks. If time provides, we will look at common examples of these beautiful and powerful geometric objects.

Wednesday, May 4, 2016

Posted May 2, 2016

Pasquale Porcelli Lecture Series Special Lecture Series

1:30 pm – 2:30 pm Lockett 233

Kim Pham, ENSTA ParisTech
Construction of a macroscopic model of phase-transformation for the modeling of superelastic Shape Memory Alloys

Abstract: Shape Memory Alloys (SMA) e.g. NiTi display a superelastic behavior at high temperature. Initially in a stable austenite phase, SMA can transform into an oriented martensite phase under an applied mechanical loading. After an unloading, the material recovers its initial stress-free state with no residual strain. Such loading cycle leads to an hysteresis loop in the stress-strain diagram that highlights the dissipated energy for having transformed the material. In a rate-independent context, we first show how a material stability criterion allows to construct a local one-dimensional phase transformation model. Such models relies on a unique scalar internal variable related to the martensite volume fraction. Evolution problem at the structural scale is then formulated in a variational way by means of two physical principles: a stability criterion based on the local minima of the total energy and an energy balance condition. We show how such framework allows to handle softening behavior and its compatibility with a regularization based on gradient of the internal variable. We then extend such model to a more general three dimensional case by introducing a tensorial internal variable. We derive the evolution laws from the stability criterion and energy balance condition. Second order conditions are presented. Illustrations of the features of such model are shown on different examples.

Posted June 26, 2015
Last modified March 17, 2016

3:30 pm – 4:20 pm DMC Theatre

Maria Chudnovsky, Princeton University MacArthur Foundation Fellowship recipient 2012.
Perfection and Beyond

About 10 years ago one of the central open problems in graph theory at the time, the Strong Perfect Graph Conjecture, was solved. The proof used structural graph theory methods, and spanned 155 journal pages. The speaker was part of the team of authors of this mathematical beast. In this talk we will explain the problem, describe some of the ideas of the proof (that has since been shortened somewhat), and discuss related problems that have been a subject of more recent research.

Thursday, May 5, 2016

Posted January 22, 2016
Last modified March 17, 2016

Pasquale Porcelli Lecture Series Special Lecture Series

10:30 am – 11:20 am DMC Theatre

Maria Chudnovsky, Princeton University MacArthur Foundation Fellowship recipient 2012.
Coloring some perfect graphs

Perfect graphs are a class of graphs that behave particularly
well with respect to coloring. In the 1960's Claude Berge made two
conjectures about this class of graphs, that motivated a great deal of
research, and by now they have both been solved.

The following remained open however: design a combinatorial algorithm that
produces an optimal coloring of a perfect graph. Recently, we were able to
make progress on this question, and we will discuss it in this talk. Last
year, in joint work with Lo, Maffray, Trotignon and Vuskovic we were able
to construct such an algorithm under the additional assumption that the
input graph is square-free (contains no induced four-cycle). More
recently, together with Lagoutte, Seymour and Spirkl, we solved another
case of the problem, when the clique number of the input graph is fixed
(and not part of the input).

Posted January 22, 2016
Last modified March 17, 2016

Pasquale Porcelli Lecture Series Special Lecture Series

3:30 pm – 4:20 pm DMC Theatre

Maria Chudnovsky, Princeton University MacArthur Foundation Fellowship recipient 2012.
Induced cycles and coloring

The Strong Perfect Graph Theorem states that graphs with no no induced odd cycle of length at least five, and no complements of one behave very well with respect to coloring. But what happens if only some induced cycles (and no complements) are excluded? Gyarfas made a number of conjectures on this topic, asserting that in many cases the chromatic number is bounded by a function of the clique number. In this talk we discuss recent progress on some of these conjectures. This is joint work with Alex Scott and Paul Seymour.

Tuesday, May 17, 2016

Posted April 15, 2016

3:30 pm – 4:20 pm TBA

Ben Schweizer, Technische Universität Dortmund
Resonance phenomena of small objects and the construction of meta-materials with astonishing properties

We know resonance effects from daily life: In a classical instrument, vibrations of some part of the instrument are amplified by resonance in the sound body. Typically, the resonator has a size that is related to the frequency: the larger the instrument, the lower the tone. In this talk we discuss resonators for light and sound waves that are small in size, much smaller than the wave-length. The assembly of many small resonators can act as a meta-material with astonishing properties: As a sound absorber or as a material with negative index. Our first example are small Helmholtz resonators, we investigate their frequency and the behavior of the corresponding meta-material. The second example are split-ring resonators for Maxwell\'s equations and the negative refraction of light. We conclude with some comments on negative index cloaks: These resonators lead to the invisibility of small objects in their vicinity.

Thursday, July 21, 2016

Posted July 11, 2016

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

2:00 pm – 3:00 pm Lockett 233

Cris Negron, Mathematics Department, LSU
Gauge invariants from the antipode for a Chevalley Hopf algebras

The antipode of a given Hopf algebra is an easily overlooked, yet mysteriously informative, part of the Hopf algebra structure. (For the uninitiated, the antipode of a Hopf algebra is an algebra anti-automorphism which acts like the inversion operator of a group.) For example, a result of of Larson and Radford states that a finite dimensional Hopf algebra in characteristic 0 is a semisimple ring if and only if the square of the antipode is the identity. For a finite dimensional non-semisimple Hopf algebra we only know that the order of the antipode is some positive even integer. This number can be seen as a measure of non-semisimplicity. In this talk I will discuss gauge invariance of the order of the antipode for a certain class of finite dimensional Hopf algebras, and some other related invariants. Rather, I will discuss how the order of the antipode for a given Hopf algebra can, in some cases, be extricated from its associated tensor category of representations.

Monday, August 15, 2016

Posted April 22, 2016
Last modified December 13, 2022

1:00 pm – 4:00 pm 232 Lockett

Comprehensive/PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, August 17, 2016

Posted April 22, 2016
Last modified December 13, 2022

1:00 pm – 4:00 pm 232 Lockett

Comprehensive/PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, August 19, 2016

Posted April 22, 2016
Last modified December 13, 2022

1:00 pm – 4:00 pm

Comprehensive/PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Thursday, August 25, 2016

Posted August 23, 2016

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:35 pm – 4:35 pm Lockett 233

Emily Cowie, LSU
Introduction to Lie algebras and their representations

This talk is intended to give an introduction to the basics of Lie algebra representation theory. This talk will provide the necessary background and definitions before describing the combinatorics of the most fundamental Lie algebra, sl(2, C).

Tuesday, September 6, 2016

Posted August 30, 2016

Algebra and Number Theory Seminar Questions or comments?

5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial club meeting

Discussion about preparing for a career as an actuary and planning the fall semester\'s activities. Pizza will be served.

Wednesday, September 7, 2016

Posted August 24, 2016
Last modified September 1, 2016

Graduate Student Colloquium

3:00 pm – 4:00 pm Lockett 243

Shawn Walker, LSU
Analysis and Numerics for Liquid Crystals

Abstract:

I will present an overview of recent research in liquid crystals. After a

brief review of what liquid crystals are, I will present a numerical

method for solving the Ericksen model of liquid crystals. The model is

rather non-trivial because of non-linearities and a critical degeneracy

that is key to the model. I will show a music video that summarizes some

of our recent results, and I will give an overview of the analysis needed

to justify the method (namely Gamma-convergence). I will then show some

simulations and applications of the method.

In addition, I will summarize my research program, and provide a list of

research topics of interest to graduate students.

Tuesday, September 13, 2016

Posted August 11, 2016
Last modified September 6, 2016

3:30 pm – 4:20 pm Lockett 284

Holly Swisher, Oregon State University
Quantum mock modular forms arising from eta-theta functions

In 2013, Lemke Oliver classified all eta-quotients which are theta functions. In this work we construct mock modular forms from the eta-theta functions with even characters, such that the shadows of these mock modular forms are given by the eta-theta functions with odd characters. We further prove that the constructed mock modular forms are quantum modular forms. As corollaries, we establish simple finite hypergeometric expressions which may be used to evaluate Eichler integrals of the odd eta-theta functions, as well as some curious algebraic identities. If time allows, we will address some recent extensions of this work from our recent summer REU project.

This work is joint with: Amanda Folsom, Sharon Garthwaite, Soon-Yi Kang, Stephanie Treneer (AIM SQuaRE project) and Brian Diaz, Erin Ellefsen (OSU REU project).

Monday, September 19, 2016

Posted September 9, 2016

Graduate Student Colloquium

12:30 pm – 1:20 pm Lockett 137

Kiran Kedlaya, University of California, San Diego
The ABC conjecture

Abstract: The ABC conjecture asserts that if A, B, C are three positive integers such that A + B = C, then these three integers cannot between them have \"too many\" repeated prime factors. The precise statement of the conjecture explains the difference between the fact that there are lots of such triples consisting of perfect squares (Pythagorean triples) but not consisting of higher perfect powers (Fermat\'s Last Theorem). I\'ll discuss the precise statement of the conjecture, some appealing consequences of this conjecture in various parts of number theory, and the status of a recent (2012) announcement of a proof.

A light lunch will be served in the Keisler lounge at 12:00 pm.

Posted September 9, 2016

Graduate Student Colloquium

2:30 pm – 3:20 pm Keisler Lounge

Kiran Kedlaya, University of California, San Diego
Budapest Semesters in mathematics

Study abroad opportunities in mathematics: The Budapest Semesters in Mathematics (BSM) program has been providing North American students the opportunity to spend one or two semesters learning mathematics in the \"Hungarian style\" for over 30 years. Recently, the Budapest Semesters in Mathematics Education (BSME) was launched to provide similar opportunities for those interested in Hungarian pedagogy. This information session will describe both programs, their similarities and differences, and how to participate.

Tuesday, September 20, 2016

Posted September 9, 2016

Graduate Student Colloquium

12:30 pm – 1:20 pm Coates 103

Kiran Kedlaya, University of California, San Diego
Computational Number Theory Online: SMC and LMFDB

Abstract: This is more of a demonstration than a talk: I will indicate how to get started with two different but complementary online tools. SageMathCloud (SMC) is a cloud-based version of the Sage computer algebra system, which includes extensive number-theoretic functionality (and plenty of coverage in other areas of mathematics also). The L-Functions and Modular Forms Database (LMFDB) is a website that assembles various tables of number-theoretic objects, like elliptic curves and modular forms, in an easily browsable format that highlights the deep relationships among these objects.

A light lunch will be served in the Keisler lounge at 12:00 pm.

Posted September 13, 2016

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 284

Kiran Kedlaya, University of California, San Diego
Multiplicities of mod 2 Hecke algebras

Abstract:
This is a report on joint work in progress with Anna Medvedovsky (MPI, Bonn). Motivated by computational issues arising in the tabulation of rational newforms (as in Cremona\'s tables of elliptic curves), we ask about the extent to which the multiplicity of eigenvalues of the Hecke operator T_2 on a space of newforms of odd level is explained by known facts (e.g., Serre\'s conjecture). In weight 2, we have compiled a massive data set and compared it against known results; this yields partial agreement, but there is still some room for improvement.

Posted September 14, 2016

LSU AWM Student Chapter LSU AWM Student Chapter Website

3:30 pm – 4:30 pm 1034 Digital Media Center

Susanne Brenner, Louisiana State University
Computational Mathematics

Abstract. This is a talk for a general audience. We will first take a look at computational instruments and mathematical algorithms from ancient times to the twenty-first century. We will then discuss the role of mathematics in computing and present some real life examples of computational mathematics in action. Finally, we will provide some information on career opportunities.

(Refreshments will be served at 3pm in 1034 DMC.)

Wednesday, September 21, 2016

Posted September 19, 2016

3:00 pm – 4:30 pm Keisler Lounge (Lockett 321)

AWM Welcome Tea

Thursday, September 22, 2016

Posted September 7, 2016
Last modified September 21, 2016

3:30 pm – 4:20 pm Lockett 9

Karl Mahlburg, Department of Mathematics, LSU
Classical partition identities and automorphic forms

I will discuss my work on the deep connections between automorphic forms and partition identities. These include classical results such as the famous "sum-product" identities of Euler, Rogers-Ramanujan, Andrews-Gordon, and Schur, as well as more recent identities arising from affine Lie algebras and Lepowsky-Wilson's program of vertex operator algebras; a prominent example is due to Capparelli. Although these identities are of interest due to their intrinsic combinatorics and algebraic applications, they also often display automorphic properties, with examples of theta functions, modular functions, mock modular forms, and false theta functions. Some of these connections were only discovered recently, and have led to applications including asymptotic formulas, algebraicity, congruences, and probabilistic interpretations.

Tuesday, September 27, 2016

Posted September 14, 2016

3:30 pm – 4:30 pm 1034 Digital Media Center

Runchang Lin, Texas A&M International University
A discontinuous Galerkin least-squares finite element method for reaction-diffusion problems with singular perturbation

Abstract: A discontinuous Galerkin least-squares finite element method is proposed to solve reaction-diffusion equations with singular perturbations. This method produces solutions without numerical oscillations when uniform meshes are used, where neither special treatments nor manually adjusted parameters are required. This method can be applied to linear and nonlinear reaction-diffusion problems with strong reactions. Numerical examples are provided to demonstrate the efficiency of the method.

Wednesday, September 28, 2016

Posted September 23, 2016
Last modified March 3, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 233

Viktoria Kuehner, University of Tübingen
Semiflows and Koopman semigroups

We characterize Koopman semigroups $(T(t))_{t\geq 0}$ on $\mathrm{L}^1(X,\Sigma,\mu)$, where $(X,\Sigma,\mu)$ is a standard probability space, induced by a measurable semiflow $(\varphi_t)_{t\geq 0}$ on $X$, by means of their generator $(A,D(A))$. We then construct a topological model $(\psi_t)_{t\geq 0}$ of that semiflow on a compact space $K$ such that the Koopman semigroup induced by the continuous semiflow $(\psi_t)_{t\geq 0}$ is isomorphic to the original semigroup.

Thursday, September 29, 2016

Posted September 27, 2016
Last modified March 2, 2021

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:30 pm – 4:30 pm Lockett 233

Bach Nguyen, LSU
Orders: "You are out of order!"

We will define orders and discuss examples and some of their important properties.

Tuesday, October 4, 2016

Posted September 13, 2016
Last modified September 28, 2016

3:30 pm – 4:20 pm Lockett 284

Fang-Ting Tu, LSU Mathematics Department
Hypergeometric functions over finite fields and their applications

Abstract: For a hypergeometric algebraic variety, we can express the number of it rational points over finite fields in terms of the so-called hypergeometric functions over finite fields. We have many transformation and evaluation formulas of finite field hypergeometric functions, which are parallel to the results of the classical case. As applications, we can study the arithmetic of hypergeometric varieties using these formulas.

Wednesday, October 5, 2016

Posted September 22, 2016
Last modified October 5, 2016

3:30 pm – 4:20 pm Lockett 233

Fang Sun, Tulane University
Topological Symmetries of R^3

The absence of geometric rigidity regarding topological actions of finite group on R^3 drives us into looking for possible algebraic rigidity. The outcome is positive: If a finite group G acts topologically and faithfully on R^3, then G is isomorphic to a subgroup of O(3).

Monday, October 10, 2016

Posted September 28, 2016

5:30 pm James E. Keisler Lounge (321 Lockett)

Actuarial club meeting

Rod Friedy from the Louisiana Dept of Insurance will be our guest.

Tuesday, October 11, 2016

Posted September 29, 2016
Last modified October 10, 2016

3:30 pm – 4:30 pm 1034 Digital Media Center

Xiaoliang Wan, Louisiana State University
On Small Random Perturbations of Elliptic Problems

Abstract: The large deviation principle (LDP) plays an important role for studying rare events induced by small random noise. One challenging task of applying the LDP is to minimize the rate functional numerically, especially when a spatially extended system is considered. Many numerical issues arise depending on the properties of the system and the noise. In this talk we discuss the regularization for the spatial covariance operator using Poisson's equation perturbed by small random forcing. The Euler-Lagrange (E-L) equation suggests that it is critical to approximate a nonlocal biharmonic-like operator, which is ill-posed due to the inverse of the covariance operator. We first study the properties of the nonlocal biharmonic-like operator and then consider the Lavrentiev regularization. The convergence of the approximated minimizer is established in terms of Gamma-convergence. Furthermore, we construct an LDP-based importance sampling estimator, and provide a sufficient condition for such an estimator to be asymptotically efficient. The effect of the regularization parameter on the importance sampling estimator is studied numerically.

Thursday, October 13, 2016

Posted October 6, 2016

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:30 pm – 4:30 pm Lockett 233

Lucius Schoenbaum, LSU
Cartesian Closed Categories and Lambda Calculus

During the 1960\'s and 1970\'s, connections between logic and category theory were discovered through the work of Grothendieck, Lawvere, Lambek, Benabou, and others. In the 1980\'s, these developments made an impact on areas of computer science, such as functional programming and the design of many functional programming languages. In this talk, I will focus on cartesian closed categories and the (simply-typed) lambda calculus, which are related via the Curry-Howard-Lambek correspondence (I will explain what this is). Prerequisites: No category theory other than a basic idea of what categories and functors are.

Monday, October 17, 2016

Posted October 1, 2016
Last modified October 12, 2016

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm 9 Lockett

Meeting of Tenured Faculty

Tuesday, October 18, 2016

Posted September 13, 2016
Last modified March 3, 2021

3:30 pm – 4:20 pm Lockett 284

Xingting Wang, Temple University
Quantum groups associated to a pair of preregular forms

In this talk, we study universal quantum groups that simultaneously coact on a pair of N-Koszul Artin-Schelter regular algebras. This work leads to a recovery of many well-known examples of quantum groups defined by various authors in the literature. Moreover, we show these quantum groups have surprisingly nice presentations in terms of the twisted superpotentials associated to the underlining graded algebras, respectively. In particular, we will discuss the universal quantum group associated to a pair of three-dimensional Sklyanin algebras, whose ring-theoretic and homological behaviors need further investigation. This is a joint work with Alexandru Chirvasitu and Chelsea Walton.

Wednesday, October 19, 2016

Posted September 22, 2016
Last modified October 11, 2016

3:30 pm – 4:20 pm Lockett 233

Rafal Komendarczyk, Tulane University
Ropelength, crossing number and finite-type invariants

Ropelength and embedding thickness are related measures of geometric complexity of classical knots and links in Euclidean space. In their recent work, Freedman and Krushkal posed a question regarding lower bounds for embedding thickness of n-component links in terms of Milnor linking numbers (mu-invariants). In this talk we will show how to obtain such estimates, generalizing the known linking number bound. In the process, we generalize the results of Kravchenko and Polyak on the arrow polynomial formulas of mu-invariants of string links. We also collect several facts about finite type invariants and ropelength/crossing number of knots giving examples of families of knots, where estimates via the finite type invariants outperform the well-known knot--genus estimate. This is joint work with Andreas Michaelides.

Tuesday, October 25, 2016

Posted September 24, 2016

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Dongbin Xiu, Ohio State University
Approximation Algorithms for Big Data

Abstract: One of the central tasks in scientific computing is to accurately approximate unknown target functions. This is typically done with the help of data samples of the unknown functions. In statistics this falls into the realm of regression and machine learning. In mathematics, it is the central theme of approximation theory. The emergence of Big Data presents both opportunities and challenges. On one hand, big data introduces more information about the unknowns and, in principle, allows us to create more accurate models. On the other hand, data storage and processing become highly challenging. Moreover, data often contain certain corruption errors, in addition to the standard noisy errors. In this talk, we present some new developments regarding certain aspects of big data approximation. More specifically, we present numerical algorithms that address two issues: (1) how to automatically eliminate corruption/biased errors in data; and (2) how to create accurate approximation models in very high dimensional spaces using stream/live data, without the need to store the entire data set. We present both the numerical algorithms, which are easy to implement, as well as rigorous analysis for their theoretical foundation.

Posted September 28, 2016
Last modified October 20, 2016

3:30 pm – 4:20 pm Lockett 284

Simon Riche, Université Clermont Auvergne
Character formulas in the modular representation theory of reductive algebraic groups

Abstract
In this talk I will present a project (including joint works with Pramod
Achar, Shotaro Makisumi, Carl Mautner, and Geordie Williamson) which
aims at providing a character formula for simple representations of
reductive algebraic groups over fields of positive characteristic. This
formula is inspired by Lusztig's conjecture, but different, and is
expected to hold in all characteristics bigger than the Coxeter number.
We expect to prove this formula using a geometric approach involving
coherent sheaves on the Springer resolution and constructible sheaves on
the affine flag variety and the affine Grassmannian of the Langlands
dual group.

Thursday, October 27, 2016

Posted September 26, 2016
Last modified October 12, 2016

3:30 pm – 4:30 pm 277 Lockett

Workshop: Math Communications

The workshop targeted towards mathematics will be organized by the College of Science: Dawn Jenkins and Paige Jarreau

Tuesday, November 1, 2016

Posted September 16, 2016
Last modified October 20, 2016

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 284

Nathan Green, Texas A&M
Special Values of L-functions and the Shtuka Function

Abstract: We study the arithmetic of coordinate rings of elliptic curves in finite characteristic and analyze their connection with Drinfeld modules. Using the functional equation for the shtuka function, we find identities for power sums and twisted power sums over these coordinate rings which allow us to express function field zeta values in terms of the shtuka function and the period of the exponential function. Joint with M. Papanikolas.

Posted October 18, 2016

LSU AWM Student Chapter LSU AWM Student Chapter Website

3:30 pm – 4:30 pm Digital Media Center 1034

Huan Lei, Pacific Northwest National Laboratory
Quantifying Quasi-equilibrium and Non-equilibrium Properties for Complex Multiphysics Systems

Abstract: We propose a data-driven method to quantify quasi-equilibrium and non-equilibrium properties for complex physical systems with high dimensional stochastic space based on generalize polynomial chaos (gPC) expansion and Mori-Zwanzig projection method. For quasi-equilibrium properties, we demonstrate that sparse grid method suffers instability problem due to the high-dimensionality. Alternatively, we propose a numerical method to enhance the sparsity by defining a set of collective variables within active subspace, yielding more accurate surrogate model recovered by compressive sensing method. Moreover, non-equilibrium properties further depends on the non-local memory term representing the high-dimensional unresolved states. We propose a data-driven method based on appropriate parameterization to compute the memory kernel of the generalized Langevin Equation (GLE) by merely using trajectory data. The approximated kernel formulation satisfies the second fluctuation-dissipation conditions naturally with invariant measure. The proposed method enables us to characterize transition properties such as reaction rate where Markovian approximation shows limitation.

Wednesday, November 2, 2016

Posted October 31, 2016

9:30 am – 11:00 am Keisler Lounge (Locket 321)

Chelsea Walton, Temple University
AWM Breakfast with Chelsea Walton

A round table discussion with Chelsea Walton. Breakfast foods to be provided.

Posted October 19, 2016
Last modified March 2, 2021

Graduate Student Colloquium

12:30 pm – 1:20 pm 239 Lockett

Chelsea Walton, Temple University
Undergraduate Talk: Hamilton's Quaternions

In this talk I will discuss the last great achievement of Sir William Rowan Hamilton- the discovery of the quaternion number system. This discovery was very controversial for its time and nearly drove Hamilton mad! The talk will be full of drama, intrigue, and wonderful mathematics. Some familiarity with complex numbers would help, but is not needed.

Refreshments will be served in the Keisler Lounge at 12:00 pm.

Thursday, November 3, 2016

Posted September 23, 2016
Last modified October 28, 2016

Graduate student/Faculty Colloquium

3:30 pm – 4:20 pm Lockett 9

Chelsea Walton, Temple University
Quantum Symmetry

Abstract: Like Hopf algebras? You will after this talk! The aim of this lecture is to motivate and discuss \"quantum symmetries\" of quantum algebras (i.e. Hopf co/actions on noncommutative algebras). All basic terms will be defined, examples will be provided, along with a brief survey of recent results.

Refreshments will be served in the Keisler Lounge at 3:00 pm.

Friday, November 4, 2016

Posted September 13, 2016
Last modified October 20, 2016

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 277

Chelsea Walton, Temple University
PBW deformations of braided doubles

Abstract: I'll present new examples of deformations of smash product algebras that arise from Hopf algebra actions on pairs of Koszul module algebras. This construction generalizes several 'double' constructions appearing in the literature, including Weyl algebras and some types of Cherednik algebras, and it complements the braided double construction of Bazlov and Berenstein. There will probably be more questions than answers in this talk. This is joint work with Sarah Witherspoon.

Tuesday, November 8, 2016

Posted October 18, 2016

3:30 pm – 4:30 pm Digital Media Center 1034

Xiao Wang, Chinese Academy of Sciences
Inexact Proximal Stochastic Gradient Method for Convex Composite Optimization

Abstract: We study an inexact proximal stochastic gradient (IPSG) method for convex composite optimization, whose objective function is a summation of an average of a large number of smooth convex functions and a convex, but possibly nonsmooth, function. The variance reduction technique is incorporated in the method to reduce the stochastic gradient variance. The main feature of this IPSG algorithm is to allow solving the proximal subproblems inexactly while still keeping the global convergence with desirable complexity bounds. Different accuracy criteria are proposed for solving the subproblem, under which the global convergence and the component gradient complexity bounds are derived for the both cases when the objective function is strongly convex or generally convex. Preliminary numerical experiment shows the overall efficiency of the IPSG algorithm.

Thursday, November 10, 2016

Posted November 9, 2016

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:30 pm – 4:30 pm Lockett 233

Sean Taylor, LSU
Algebraic Geometry over Fields of Characteristic p

Over fields of characteristic p there exist new phenomena that arise. One important example of this is the action of the Galois group, and in particular the Frobenius element, on the geometric points of a scheme and on the etale cohomology groups. In this talk we will discuss some of these structures and more.

Monday, November 14, 2016

Posted November 8, 2016
Last modified November 9, 2016

Algebra and Number Theory Seminar Questions or comments?

5:00 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial club meeting

Winnie Sloan from Travelers Insurance and an LSU alumna will visit via skype.

Tuesday, November 15, 2016

Posted October 17, 2016
Last modified January 11, 2017

3:30 pm – 4:20 pm

Shotaro Makisumi, Stanford University
A new approach to modular Koszul duality

The Koszul duality of Beilinson-Ginzburg-Soergel is a derived equivalence involving the BGG category O, which plays a central role in the study of highest weight modules of a semisimple complex Lie algebra. Geometrically, this may be viewed as a derived equivalence relating Langlands dual flag varieties. In this talk, I will discuss a new approach to a modular (positive characteristic) analogue of this result proved by Pramod Achar and Simon Riche.
Prerequisites will be kept to a minimum: once I have motivated the result, I will not work with representations or perverse/parity sheaves, instead giving an algebraic/combinatorial model (moment graph sheaves, Soergel bimodules) for these objects, focusing on the case of SL2. This will be enough for illustrating the key ingredient, a new construction of a left monodromy action.

I will also briefly report on joint work in progress with Pramod Achar, Simon Riche, and Geordie Williamson, in which we plan to extend the result to Kac-Moody flag varieties. The latter result would imply the Riche-Williamson conjecture on characters of tilting modules of reductive groups.

Wednesday, November 16, 2016

Posted November 4, 2016
Last modified November 7, 2016

Joint Harmonic analysis and Applied analysis seminar

3:30 pm – 4:20 pm Lockett 276

Jiuyi Zhu, LSU
Quantitative uniqueness of elliptic equations

Abstract: Motivated by the study of eigenfunctions, we consider the quantitative uniqueness of elliptic equations. The quantitative uniqueness is characterized by the order of vanishing of solutions, which describes quantitative behavior of strong unique continuation property. Strong unique continuation property states that if a solution that vanishes of infinite order at a point vanishes identically. It is interesting to know how the norm of the potential functions and gradient potentials control the order of vanishing. We will report some recent progresses about quantitative uniqueness in different spaces for second order elliptic equations. Carleman estimates play an important role in the strong unique continuation property. By using some delicate quantitative Carleman estimates, we obtain some Hadamard three-sphere theorems which lead to the order of vanishing of solutions. Part of work is joint with Blair Davey.

Posted November 16, 2016

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

4:30 pm – 5:30 pm Lockett 233

Shotaro Makisumi, Stanford University
Introduction to Soergel Bimodules

Thursday, November 17, 2016

Posted November 10, 2016
Last modified November 15, 2016

3:30 pm – 4:30 pm 139 Allen Hall

Meeting of Faculty

Tuesday, November 29, 2016

Posted October 31, 2016
Last modified November 27, 2016

3:30 pm – 4:30 pm Digital Media Center 1034

Yi Zhang, University of Notre Dame
Error Analysis of C0 Interior Penalty Methods for An Elliptic State-Constrained Optimal Control Problem

We study C0 interior penalty methods for an elliptic optimal control problem with pointwise state constraints on two and three dimensional convex polyhedral domains. The approximation of the optimal state is solved by a fourth order variational inequality and the approximation of the optimal control is computed by a post-processing procedure. To circumvent the difficulty caused by the low regularity of the optimal solutions, we carried out an a priori error analysis based on the complementarity form of the variational inequality. Furthermore, we develop an a posteriori analysis using a residual based error estimator. Numerical experiments are provided to gauge the performance of the proposed methods. This is joint work with Susanne Brenner and Li-yeng Sung.

Wednesday, November 30, 2016

Posted November 24, 2016
Last modified March 2, 2021

Joint Harmonic Analysis and Applied Analysis Seminar

3:30 pm – 4:20 pm 113 Lockett

Phuc Nguyen, Department of Mathematics, Louisiana State University
Local energy bounds and $\epsilon$-regularity criteria for the 3D Navier-Stokes system

The system of three dimensional Navier-Stokes equations is considered. We obtain some new local energy bounds that enable us to improve several $\epsilon$-regularity criteria. They key idea here is to view the head pressure as a sign distribution belonging to certain fractional Sobolev space of negative order. This talk is based on joint work with Cristi Guevara.

Thursday, December 1, 2016

Posted October 25, 2016
Last modified November 29, 2016

3:30 pm – 4:20 pm Lockett 9

Christof Geiss, UNAM Mexico
Geometric construction of semisimple Lie algebras - the non simply laced cases.

Abstract: After an unpublished manuscript by Schofield it is nowadays folklore
how to construct the universal enveloping algebra U(n) of the positive part
n of a symmetric Kac-Moody Lie algebra in terms of constructible functions
on the complex representation spaces of a quiver of the corresponding type.
This fails in the non-symmetric cases because the corresponding weighted quivers
can not be realized over an algebraically closed field.

In joint work with B. Leclerc and J. Schroeer we remedy this situation partially
by considering constructible functions on the representations of projective
dimension on certain 1-Iwanaga-Gorenstein algebras. However, for now this
approach works only in the Dynkin cases since we need to construct explicitly
for each root vector a non-vanishing constructible function.

Wednesday, January 4, 2017

Posted November 10, 2016
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, January 6, 2017

Posted November 10, 2016
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 240

Comprehensive/PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Monday, January 9, 2017

Posted November 10, 2016
Last modified December 13, 2022

Informal Geometry and Topology Seminar Questions or comments?

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, January 11, 2017

Posted January 11, 2017

10:00 am Lockett 233

Organizational meeting

Posted November 1, 2016
Last modified January 3, 2017

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm Lockett 233

Sam Nelson, Claremont McKenna College
Biquasiles and Dual Graph Diagrams

Dual graph diagrams are an alternate way to present oriented knots and links in R^3. In this talk we will see how to turn dual graph Reidemeister moves into an algebraic structure known as biquasiles and use this structure to define new integer-valued counting invariants of oriented knots and links.

Thursday, January 12, 2017

Posted January 11, 2017

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:00 pm – 4:00 pm Lockett 233

Jacob Matherne, University of Massachusetts at Amherst
Combinatorial Fourier transform for quiver representation varieties in type A

Wednesday, January 18, 2017

Posted January 17, 2017

10:30 am – 12:00 pm Lockett 233

Shea Vela-Vick, Louisiana State University
A brief introduction to Heegaard Floer invariants

In this talk, we introduce some of the basic definitions and tools used in Heegaard Floer theory, with an emphasis on applications to knot theory.

Thursday, January 19, 2017

Posted January 17, 2017

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

10:00 am – 11:00 am Lockett 233

Sean Taylor, LSU
Perverse Sheaves on Toric Varieties

Toric varieties (or \"torus embeddings\" as they were originally known) are defined as algebraic varieties that have an algebraic torus as an open dense subset such that the natural action of the torus on itself extends smoothly to the whole variety. They have slowly become of more and more interest to both algebraic geometers and combinatorists. The reason for this is that a large class of toric varieties can be functorially associated to several combinatorial objects, the most well known of which are called combinatorial fans. They are also of interest to algebraic geometers for their own sake - much in the way that algebraic curves or surfaces are - and because, though they obey a whole host of interesting and powerful geometric, topological, and combinatorial properties, they paradoxically turn out to be a fantastic place to test new theorems in algebraic geometry. In this talk, we will discuss recent research associated with the speaker\'s thesis with Pramod Achar. The ultimate goal is to finish creating a mixed category of perverse sheaves on toric varieties in the sense of Beilinson, Ginzburg, and Soergel. Along the way, however, it has become necessary to make an extended study of perverse sheaves on toric varieties and the special properties that they possess. We will begin with some basic definitions and arrive at some fascinating decompositions of Ext groups on toric varieties.

Posted January 17, 2017
Last modified March 2, 2021

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:00 pm – 4:00 pm Lockett 233

Sean Taylor, LSU
Representations of SO(∞)

One of the primary goals of representation theory and harmonic analysis is to decompose "natural" representations into irreducible pieces. In the 20th century, the regular representation of semisimple Lie groups on symmetric spaces stood out as both an example of extraordinary success of this task and as a model of beauty. In the study of symmetric spaces and their connections to representation theory, we find an interaction between algebra, geometry, and analysis. Since the introduction of Kac-Moody Lie algebras and Kac-Moody Lie groups, infinite-dimensional Lie theory has been an important area of exploration for representation theorists. It is a vista that is still very open, however, and it turns out to be important to consider even "simple" examples of infinite-dimensional Lie groups. In this talk, we will explore recent research of the speaker along with Matthew Dawson, Stephan Merignon, and Gestur Olafsson on a "replacement" for the regular representation of SO(∞) and a construction of new representations on these spaces.

Friday, January 20, 2017

Posted January 13, 2017
Last modified January 18, 2017

3:30 pm – 4:20 pm Lockett 277

Priyam Patel, UC Santa Barbara, Department of Mathematics
Quantitative methods in hyperbolic geometry

Abstract: Peter Scott\'s famous result states that the fundamental groups of hyperbolic surfaces are subgroup separable, which has many powerful consequences. For example, given any closed curve on such a surface, potentially with many self-intersections, there is always a finite cover to which the curve lifts to an embedding. It was shown recently that hyperbolic 3-manifold groups share this separability property, and this was a key tool in Ian Agol\'s resolution to the Virtual Haken and Virtual Fibering conjectures for hyperbolic 3-manifolds.
I will begin this talk by giving some background on separability properties of groups, hyperbolic manifolds, and these two conjectures. There are also a number of interesting quantitative questions that naturally arise in the context of these topics. These questions fit into a recent trend in low-dimensional topology aimed at providing concrete topological and geometric information about hyperbolic manifolds that often cannot be gathered from existence results alone. I will highlight a few of them before focusing on a quantitative question regarding the process of lifting curves on surfaces to embeddings in finite covers.

Monday, January 23, 2017

Posted January 15, 2017
Last modified January 17, 2017

3:30 pm – 4:20 pm Lockett 277

Vu Hoang, Rice University, Department of Mathematics
Singularity formation for equations of fluid dynamics

The basic equations of fluid mechanics were written down about 200 years
ago by Euler. To this day, they present a challenge for mathematical analysis and
many basic questions are still unsolved. One of these basic concerns the issue
of finite-time singularity formation versus global regularity. A great obstacle
for mathematical analysis is the fact that these equations involve both nonlinear
and non-local interactions. In my talk, I will describe recent efforts to understand the
mechanisms that are behind the singularity formation in fluid equations, starting from simple
model equations.

Tuesday, January 24, 2017

Posted December 2, 2016
Last modified March 2, 2022

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm Lockett 233

Malcolm Brown, Department of Computer Science & Informatics, Cardiff University
Scattering and inverse scattering for a left-definite Sturm–Liouville problem

This talk reports on recent work which develops a scattering and an inverse scattering theory for the Sturm–Liouville equation $u'' + qu = \lambda w u$, where $w$ may change sign but $q$ is positive. Thus the left-hand side of the equation gives rise to a positive quadratic form, and one is led to a left-definite spectral problem. The crucial ingredient of the approach is a generalised transform built on the Jost solutions of the problem and hence termed the “Jost transform” and the associated Paley–Wiener theorem linking growth properties of transforms with support properties of functions. One motivation for this investigation comes from the Camassa–Holm equation for which the solution of the Cauchy problem can be achieved by the inverse scattering transform for $u'' + qu = \lambda w u$.

This is joint work with Christer Bennewitz (Lund, Sweden) and Rudi Weikard (Birmingham, AL).

Wednesday, January 25, 2017

Posted January 25, 2017

10:30 am – 12:00 pm Lockett 233

Kyle Istvan, Louisiana State University
Invariants of Singular Knots

Posted January 16, 2017
Last modified March 2, 2021

3:30 pm – 4:20 pm Lockett 277

Aynur Bulut, Princeton University, Department of Mathematics
Recent developments on deterministic and probabilistic well-posedness for nonlinear Schrödinger and wave equations.

Dispersive equations such as nonlinear Schrödinger and wave equations arise as mathematical models in a variety of physical settings, including models of plasma physics, the propagation of laser beams, water waves, and the study of many-body quantum mechanics. They also serve as model equations for studying fundamental issues in many aspects of nonlinear partial differential equations. Key questions in the analysis of these equations include issues of well-posedness (for instance, existence of solutions, uniqueness of these solutions, and their continuous dependence on initial data in appropriate topologies) locally in time, long-time existence and behavior of solutions, and, conversely, the possible existence of solutions which blow-up in finite time. In this talk, we will give an overview of several recent results concerning the local and global (long-time) theory, including some results where probabilistic tools are used to obtain estimates for randomly chosen initial data which are not available in deterministic settings. A recurring theme (and oftentimes obstacle) is the notion of supercriticality arising from the natural scaling of the equation — seeking to characterize long-time behavior of solutions when the relevant scale-invariant norms are not controlled by the conserved energy, or for initial data of very low regularity. The techniques involved include input from several areas of mathematics, including ideas arising in many areas of PDE, harmonic analysis, and probability.

Friday, January 27, 2017

Posted January 16, 2017
Last modified January 18, 2017

3:30 pm – 4:20 pm Lockett 277

Marcel Bischoff, Vanderbilt
Subfactors, Fusion Categories and Conformal Nets

Abstract: Von Neumann algebras were mainly introduced to understand quantum theory and group representations. A factor is a von Neumann algebra with trivial center and an inclusion of two factors is called a subfactor. Finite index subfactors, in some sense, describe quantum symmetries which generalize finite groups. Similarly, fusion categories generalize the representation categories of finite groups. One can use von Neumann algebras to study chiral conformal field theory via so-called conformal nets. It turns out that conformal nets are a natural source of subfactors and fusion categories. It is an exciting open question if all fusion categories and subfactors come from conformal nets. I will introduce these three concepts and their interaction and discuss some recent results on the structure of inclusions of conformal nets and their representation theory.

Monday, January 30, 2017

Posted January 19, 2017
Last modified October 4, 2021

3:30 pm – 4:20 pm TBA

Tian Yang, Stanford University
Mapping class group action on character varieties and the ergodicity

Character varieties of a surface are central objects in several branches of mathematics, such as low dimensional topology, algebraic geometry, differential geometry and mathematical physics. On the character varieties, there is a tautological action of the mapping class group - the group of symmetries of the surface, which is expected to be ergodic in certain cases. In this talk, I will review related results toward proving the ergodicity and introduce two long standing and related conjectures: Goldman's Conjecture and Bowditch's Conjecture. It is shown by Marche and Wolff that the two conjectures are equivalent for closed surfaces. For punctured surfaces, we disprove Bowditch's Conjecture by giving counterexamples, yet prove that Goldman's Conjecture is still true in this case.

Tuesday, January 31, 2017

Posted January 26, 2017
Last modified January 27, 2017

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 15

Meeting of Tenure-track/Tenured Faculty

Wednesday, February 1, 2017

Posted February 3, 2017

10:30 am – 12:30 pm Lockett 233

Ryan Leigon, Louisiana State University
First Examples in Bordered Floer Homology

Posted January 24, 2017

5:00 pm James E. Keisler Lounge (room 321 Lockett)

Meeting of student actuarial club

We have a guest speaker, David Ellsworth and/or Gino Pagano from Startmount Insurance Co. Pizza will be served.

Friday, February 3, 2017

Posted January 15, 2017

3:30 pm – 4:20 pm

Cheng Yu, UT Austin
Weak solutions to the compressible Navier-Stokes equations

In this talk, we will discuss the construction of weak solutions for 3D compressible Navier-Stokes equations with degenerate viscosity. The method is based on the Bresch and Desjardins entropy conservation. The main contribution is to derive the Mellet-Vasseur type inequality for the weak solutions, even if it is not verified by the first level of approximation. This provides existence of global solutions for the compressible Navier-Stokes equations with large data. This is a joint work with A. Vasseur.

Monday, February 6, 2017

Posted January 30, 2017
Last modified March 2, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 277

Anton Zeitlin, Columbia University
Generalized Teichmüller Spaces, Spin Structures and Ptolemy Transformations

Teichmüller space, which parameterizes surfaces, is a fundamental space that is important in many areas of mathematics and physics. In recent times generalizations of this space have been intensely studied. The examples of such higher Teichmüller spaces are given by the so-called super-Teichmüller spaces. These appear as a natural object when studying a combinatorial approach to spin structures on Riemann surfaces and the generalization to supermanifolds. Super means that the structure sheaf is Z/2Z graded and contains odd or anti-commuting coordinates. The super-Teichmüller spaces are higher Teichmüller spaces corresponding to supergroups, which play an important role in geometric topology, algebraic geometry and mathematical physics. There the anti-commuting variables correspond to Fermions. After the introduction of these spaces, I will provide the solution of a long-standing problem of describing the analogue of Penner coordinates on super-Teichmüller space and its generalizations. The importance of these coordinates is justified by two remarkable properties: the action of the mapping class group, expressed via the so-called Ptolemy transformations, is rational, and the Weil-Petersson form is given by a simple explicit formula. I will end outlining some of the many emerging applications of this theory.

Tuesday, February 7, 2017

Posted January 15, 2017
Last modified February 5, 2017

3:30 pm – 4:20 pm Lockett 277

William Hardesty, Louisiana State University
Support varieties for algebraic groups and the Humphreys conjecture

Abstract: In this talk I will begin by recalling the notion of a support variety
for a module over a finite group scheme. This will be followed by a
brief overview of classical results and calculations in the case when
the finite group scheme is the first Frobenius kernel of a reductive
algebraic group G. In 1997, J. Humphreys conjectured that the support
varieties of indecomposable tilting modules for G (a very important
class of modules) is controlled by a combinatorial bijection, due to G.
Lusztig, between nilpotent orbits and a certain collection of subsets of
the affine Weyl group called "canonical cells". This later became known
as the "Humphreys conjecture". I will discuss my proof of this
conjecture for when G=GL(n). If time permits, I may also present some of
my recent joint work with P. Achar and S. Riche concerning the Humphreys
conjecture in other types.

Wednesday, February 8, 2017

Posted February 3, 2017

Informal Geometry and Topology Seminar Questions or comments?

10:30 am – 12:30 pm Lockett 233

Jose Ceniceros, Louisiana State University
Open Books and Contact Geometry

Thursday, February 9, 2017

Posted February 8, 2017

3:00 pm – 4:30 pm Lockett 276

Meeting of the Tenure-Track/Tenured Faculty

Monday, February 13, 2017

Posted February 2, 2017

3:30 pm – 4:20 pm Lockett 233 (Note: *different* date and room for the Comp. Math Seminar)

David Shirokoff, New Jersey Institute of Technology
Approximate global minimizers to pairwise interaction problems through a convex/non-convex energy decomposition: with applications to self-assembly

Abstract: A wide range of particle systems are modeled through energetically driven interactions, governed by an underlying non-convex and often non-local energy. Although numerically finding and verifying local minima to these energies is relatively straight-forward, the computation and verification of global minimizers is much more difficult. Here computing the global minimum is important as it characterizes the most likely self-assembled arrangement of particles (in the presence of low thermal noise) and plays a role in computing the material phase diagram. In this talk I will examine a general class of model functionals: those arising in non-local pairwise interaction problems. I will present a new approach for computing approximate global minimizers based on a convex/non-convex splitting of the energy functional that arises from a convex relaxation. The approach provides a sufficient condition for global minimizers that may in some cases be used to show that lattices are exact, and also be used to estimate the optimality of any candidate minimizer. Physically, the approach identifies the emergence of new length scales seen in the collective behavior of interacting particles. (This is a joint Applied Analysis/Computational Mathematics Seminar.)

Posted September 28, 2016
Last modified February 1, 2017

3:30 pm – 4:20 pm Lockett 233

David Shirokoff, New Jersey Institute of Technology
Approximate global minimizers to pairwise interaction problems through a convex/non-convex energy decomposition: with applications to self-assembly

Thursday, February 16, 2017

Posted October 11, 2016
Last modified February 13, 2017

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 277

Christopher Sogge, Johns Hopkins University J. J. Sylvester Professor of Mathematics
On the concentration of eigenfunctions

I shall present some results in global harmonic analysis that concern properties of eigenfunctions on compact Riemannian manifolds. Using local arguments we can show that $L^p$ norms of eigenfunctions over the entire manifold are saturated if and only if there are small balls (if $p$ is large) or small tubular neighborhoods of geodesics (if $p$ is small) on which the eigenfunctions have very large $L^p$ mass. Neither can occur on manifolds of nonpositive curvature, or, more generally, on manifolds without conjugate points.

Wednesday, February 22, 2017

Posted February 3, 2017

10:30 am – 12:30 pm Lockett 233

Federico Salmoiraghi, Department of Mathematics, LSU
TBD

Posted February 22, 2017

3:30 pm – 4:30 pm Lockett 240

Josh Fallon, LSU
A family of 2-crossing-critical graphs on the projective plane

A graph G is said to be 2-crossing-critical if it has crossing number at least two and every proper subgraph of G has crossing number less than two. Bokal, Oporowski, Richter, and Salazar recently determined all the 3-connected 2-crossing-critical graphs containing a subdivision of the Mobius Ladder V10. These graphs are members of a family generated by joining certain tiles in sequence. We show a closely related family of tile joins that are 2- crossing-critical on the real projective plane. Analogous to the plane case, these graphs have projective crossing number at least two and each proper subgraph has projective crossing number less than two. We also discuss ongoing work toward extending this family to all non-orientable surfaces.

Thursday, February 23, 2017

Posted January 31, 2017
Last modified February 15, 2017

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Locket 277

Barbara Rüdiger, Bergische Universität Wuppertal - Germany
The Enskog process and its relation to the Boltzmann equation

Abstract: The existence of a weak solution to a McKean-Vlasov type stochastic differential system corresponding to the Enskog equation of the kinetic theory of gases is established under suitable hypotheses. The distribution of any solution to the system at each fixed time is shown to be unique when the density exists. The existence of a probability density for the time-marginals of the velocity is verified in the case where the initial condition is Gaussian, and is shown to be the density of an invariant measure. This is a joint work with S. Albeverio and P. Sundar.

Thursday, March 2, 2017

Posted February 28, 2017

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:00 pm – 4:00 pm Lockett 233

Bach Nguyen, LSU
Quantum Groups: Definitions, Motivations/ History and Applications

The term quantum groups is often used in a loosed way to describe objects in mathematics which may or may not related to each other. To clear up some confusion, we will discuss the definitions of quantum groups in various settings such as: universal enveloping algebra of semisimple lie algebras/ Kac-Moody algebras, coordinate ring of simple algebraic groups, C^*- algebras, and infinite dimension quantum groups. If time permits, the history/ motivation and applications of these objects will also be mentioned.

Tuesday, March 7, 2017

Posted March 3, 2017
Last modified March 6, 2017

Undergraduate Student Colloquium

2:30 pm – 3:30 pm Lockett 244

Richard Hammack, Virginia Commonwealth University in Richmond
Integrate THIS: The mathematics of planimeters

Abstract: A planimeter is a mechanical analog device that evaluates definite integrals. A typical planimeter features a dial and a stylus attached to an arm. As the stylus traverses the boundary of a region, the dial reads off the enclosed area. Planimeters have been mostly forgotten since the advent of computers, but at one time they were fairly commonplace.

I will explain the history and mathematics of planimeters, and I will demonstrate one that I made from two pieces of cast-off junk. It has only one moving part, but it can evaluate any definite integral that it can reach.

Posted January 15, 2017
Last modified March 6, 2017

3:30 pm – 4:20 pm Lockett 277

Kenny De Commer, Vrije Universiteit Brussel
Heisenberg algebras of quantized enveloping type

Abstract: To any semisimple complex Lie algebra and generic complex number q can be associated two Hopf algebras: the QUEA (quantized universal enveloping algebra) and its dual QFA (quantum function algebra). The first of these can be constructed from a simpler algebra, the QUEA of a Borel subalgebra, by a general process known as the Drinfeld double construction. On the other hand, there exists an intermediate algebra, known as Heisenberg double, linking the Drinfeld double to a tensor product of two Borel QUEA. In this talk, I will explain how the Heisenberg double and the QFA are related, and will explain briefly how this observation can be used to find different spectral realizations of Borel QUEA as (unbounded) operators on a Hilbert space in the case of q real.

Wednesday, March 8, 2017

Posted March 1, 2017

2:30 pm – 3:20 pm Lockett 136

Kenny De Commer, Vrije Universiteit Brussel
Central approximation properties for quantum groups

Abstract: Several approximation properties for discrete groups (Haagerup property, weak amenability, property (T), ...) can be formulated also for discrete quantum groups, which are Hopf algebras with an involution and integral, to be seen as the group algebra of the discrete quantum group. In this talk, I will explain how one can formulate an extra condition on the approximation properties called centrality, which is automatically satisfied in the discrete group case. We will then show how these central approximation properties have good permanence properties for discrete quantum groups, and will illustrate the theory by showing that the free orthogonal quantum groups of Wang and Van Daele have the Haagerup property and are weakly amenable. If time permits, we will also comment on recent results by Y. Arano and by S. Popa and S. Vaes. This is joint work with A. Freslon and M. Yamashita.

Posted March 5, 2017

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 240

Richard Hammack, Virginia Commonwealth University in Richmond
Neighborhood reconstruction and cancellation of graphs

This talk connects two seemingly unrelated problems in graph theory. Any graph G has an associated neighborhood multiset N (G) = {N(x) | x in V (G)} whose elements are precisely the open vertex-neighborhoods of G. In general there exist non isomorphic graphs G and H for which N (G) = N (H). We say G is neighborhood reconstructible if it is uniquely determined by its neighborhood multiset, that is, if N (G) = N (H) implies G ~= H. The cancellation problem for the direct product of graphs seeks the conditions under which G x K ~= H x K implies G ~= H. Lovasz proved that this is indeed the case if K is not bipartite. A second instance of the cancellation problem asks for conditions on G that assure G x K ~= H x K implies G ~= H for any bipartite graph K. A graph G for which this is true is called a cancellation graph. We will see that the neighborhood-reconstructible graphs are precisely the cancellation graphs. Some new results on cancellation graphs are given, with corresponding implications for neighborhood reconstruction.

Thursday, March 9, 2017

Posted March 3, 2017

Graduate Student Colloquium

2:30 pm – 3:20 pm

Richard Hammack, Virginia Commonwealth University in Richmond
Not every graph has a robust cycle basis

Abstract: The cycle space of a graph G is the vector space (over the 2-element field) whose vectors are the spanning eulerian subgraphs of G, and addition is symmetric difference on edges. As any eulerian subgraph is a sum of edge-disjoint cycles, the cycle space is spanned by the cycles in G, so one can always find a basis of cycles. Such a basis is called a cycle basis for G. Because their vectors carry combinatorial information, cycle spaces have many applications, and different kinds of cycle bases cater to different kinds of problems. A lot of recent attention has focused on so-called robust cycle bases. Robust cycle bases are known to exist only for a few classes of graphs. Despite this, previously no graph was known to not have a robust cycle basis. We will see that the complete bipartite graphs K_{n,n} have no robust cycle basis when n ≥ 8. This leads to some tantalizingly open questions, particularly for the range 4 < n < 8, but also for general graphs.

Tuesday, March 14, 2017

Posted January 11, 2017
Last modified May 8, 2021

3:00 pm – 3:50 pm Lockett 277

Nicholas Cooney, Univ. Clermont-Ferrand
Quantizations of Multiplicative Quiver Varieties at Roots of Unity

To a quiver Q with dimension vector d, one can associate an algebra Dq(Q), which is a flat q-deformation of the algebra of differential operators on the space of d-dimensional representations of the quiver, D(Matd(Q)). There is also a quantum moment map q compatible with various degenerations of the source and target to their classical analogues. These algebras and the map q were first constructed by David Jordan, who then studied them in the case where q 2 C is not a root of unity. I will discuss the case where q is a root of unity. Here, the algebra Dq(Q) attains a large centre. For dimension d equal to 1 at each vertex of Q, Dq(Q) is locally a matrix algebra generically on Spec(Z). One can associate quiver varieties to Q with this dimension vector that are multiplicative versions of hypertoric varieties. In this case, quantum Hamiltonian reductions of Dq(Q) along q are quantizations of these multiplicative hypertoric varieties which are again locally matrix algebras. The category of coherent sheaves of modules for these algebras is derived equivalent to that of modules over the global sections algebra—an instance of derived Beilinson-Bernstein localisation. In the first part of the talk, I will give the necessary background and context, explaining how this work can be framed as an instance of a paradigm which is prevalent in geometric representation theory. The second part will consist of a more detailed treatment of the root of unity case, including a discussion of possible extensions of some of these results to higher dimension vectors. This is joint work with Iordan Ganev and David Jordan.

Wednesday, March 15, 2017

Posted February 3, 2017

Informal Geometry and Topology Seminar Questions or comments?

10:30 am – 12:30 pm Lockett 233

Andrew Holmes, Louisiana State University
TBD

Posted March 8, 2017
Last modified March 13, 2017

3:30 pm – 4:30 pm Lockett 237

Parisa Fatheddin, Air Force Institute of Technology
Asymptotic Behavior of a Class of SPDEs

Abstract: We consider a class of stochastic partial differential equations (SPDEs) that can be used to represent two commonly studied population models: super-Brownian motion and Fleming-Viot Process. After introducing these models, we establish their asymptotic limits by means of Large and Moderate deviations, Central Limit Theorem and Law of the Iterated Logarithm. These results were achieved by joint work with Prof. P. Sundar and Prof. Jie Xiong.

Posted March 14, 2017

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

4:30 pm – 5:30 pm Lockett 233

Trey Trampel, LSU
Computing Noncommutative Discriminants via Poisson Primes

We will present a general method for computing discriminants of noncommutative algebras obtained from specialization at roots of unity. This method builds a connection with Poisson geometry and will express the discriminants as products of Poisson primes. The method will be used to compute the discriminants of specializations at roots of unity of algebras of quantum square matrices. We will also evaluate the more general case of specialization of any quantum Schubert cell algebra.

Friday, March 17, 2017

Posted November 3, 2016

Algebra and Number Theory Seminar Questions or comments?

1:00 pm – 5:00 pm Saturday, March 18, 2017 Tulane University

Scientific Computing Around Louisiana (SCALA 2017)

http://www2.tulane.edu/sse/ccs/news/scala-2017.cfm

Saturday, March 18, 2017

Posted March 1, 2017

High School Math Contest

Tureard Hall 200

Schedule:

Algebra/Geometry Session 10 am - 11:30 am Tureaud Hall Open Session 10 am - 11:30 am Tureaud Hall Teacher\'s Reception 10 am - 11:20 am 206 Tureaud Hall Talk 10:20 am - 11:00 am 200 Tureaud Hall Team Session 1:00 pm - 2:15 pm Tureaud Hall Award Ceremony 2:45 pm - 3:45 pm Howe-Russell Geoscience Complex - Auditorium

Tuesday, March 21, 2017

Posted January 15, 2017
Last modified March 13, 2017

3:00 pm – 3:50 pm Lockett 277

Stefan Kolb, Newcastle University
The center of quantum symmetric pair coideal subalgebras -- revisited

Abstract: Drinfeld-Jimbo quantised enveloping algebras (QUE) have a younger sibling, the theory of quantum symmetric pairs, which is as rich in structure as QUE themselves. In finite type, the center of QUE can be described in terms of their universal R-matrix. In this talk I will explain how the recently constructed universal K-matrix for quantum symmetric pairs can be employed in a similar fashion to describe a basis of the center of quantum symmetric pair coideal subalgebras. This simplifies joint work with G. Letzter from 2006.

Wednesday, March 22, 2017

Posted March 13, 2017
Last modified March 14, 2017

3:29 pm – 4:30 pm Lockett 276

Stefan Kolb, Newcastle University
Radial part calculations for affine sl2.

Abstract: In their seminal work in the 70s Olshanetsky and Perelomov used
radial part calculations for symmetric spaces to prove integrability of
the Calogero-Moser Hamiltonian for special parameters. In this talk I will
explain these notions. Then, restricting to affine sl2, I will try to
explain what happens if one extends their argument to Kac-Moody algebras.
One obtains a blend of the KZB-heat equation with Inozemtsev\'s extension
of the elliptic Calogero-Moser Hamiltonian.

Posted February 27, 2017

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 233

Christine Lee, University of Texas at Austin
Jones slopes and Murasugi sums of links

Abstract: A Jones surface for a knot in the three-sphere is an essential surface whose boundary slopes, Euler characteristic, and number of sheets correspond to quantities defined from the asymptotics of the degrees of colored Jones polynomial. The Strong Slope Conjecture by Garoufalidis and Kalfagianni-Tran predicts that there are Jones surfaces for every knot.

A link diagram D is said to be a Murasugi sum of two links D' and D'' if a state graph of D has a cut vertex, which separates the graph into two state graphs of D' and D'', respectively. We may obtain a state surface in the complement of the link K represented by D by gluing the state surface for D and the state surface for D' along the disk filling the circle represented by the cut vertex in the state graph. The resulting surface is called the Murasugi sum of the two state surfaces.

We consider near-adequate links which are certain Murasugi sums of near-alternating link diagrams with an adequate link diagram along their all-A state graphs with an additional graphical constraint. For a near-adequate knot, the Murasugi sum of the corresponding state surface is a Jones surface by the work of Ozawa. We discuss how this proves the Strong Slope Conjecture for this class of knots and we will also discuss the stability properties of their colored Jones polynomial.

Tuesday, March 28, 2017

Posted January 15, 2017
Last modified March 22, 2017

3:00 pm – 3:50 pm Lockett 277

Peter Jorgensen, Newcastle University
Thick subcategories of d-abelian categories

Let d be a positive integer. The notion of d-abelian categories was introduced by Jasso. Such a category does not have kernels and cokernels, but rather d-kernels and d-cokernels which are longer complexes with weaker universal properties. Canonical examples of d-abelian categories are d-cluster tilting subcategories of abelian categories. We introduce the notion of thick subcategories of d-abelian categories. We show that functorially finite thick subcategories of d-cluster tilting subcategories are in bijection to so-called d-rigid epimorphisms. This generalises a classic result by Geigle and Lenzing. We apply this to show a classification of the thick subcategories of a family of d-abelian categories associated to quivers of type A_n. This is a report on joint work with Martin Herschend and Laertis Vaso.

Wednesday, March 29, 2017

Posted March 9, 2017
Last modified March 2, 2021

3:30 pm – 4:30 pm Lockett 237

Hui-Hsiung Kuo, Mathematics Department, LSU
Ito's formula for adapted and instantly independent stochastic processes

Posted March 27, 2017

3:30 pm – 4:30 pm Lockett 240

Matt Barnes, Department of Mathematics, LSU Graduate Student
Unavoidable immersions of large 3- and 4-edge connected graphs

Oporowski, Oxley, and Thomas showed that there is a function f such that every 3-connected graph of sufficient order, f(n), contains a minor isomorphic to a wheel, W_n, or K_3,n. We prove an analogous result for immersion, giving the unavoidable immersions of 3-edge-connected graphs, and a conjecture for the unavoidable immersions of 4-edge-connected graphs.

Thursday, March 30, 2017

Posted October 25, 2016
Last modified March 6, 2017

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 277

Qing Xiang, University of Delaware
Applications of Linear Algebraic Methods in Combinatorics and Finite Geometry

Abstract: Most combinatorial objects can be described by incidence, adjacency, or some other (0,1)-matrices. So one basic approach in combinatorics is to investigate combinatorial objects by using linear algebraic parameters (ranks over various fields, spectrum, Smith normal forms, etc.) of their corresponding matrices. In this talk, we will look at some successful examples of this approach; some examples are old, and some are new. In particular, we will talk about the recent bounds on the size of partial spreads of H(2d-1,q^2) and on the size of partial ovoids of the Ree-Tits octagon.

Monday, April 3, 2017

Posted March 27, 2017
Last modified March 29, 2017

Undergraduate Student Colloquium

2:30 pm – 3:20 pm Lockett 277

Dima Arinkin, University of Wisconsin
What makes a space interesting? (Intro to moduli.)

Abstract: Roughly speaking, geometry is the study of spaces. Here `space' is a placeholder: different flavors of geometry work with differentiable manifolds (differential geometry), topological spaces (topology), varieties (algebraic geometry, my favorite), and so on. This leads to a question: should we try to study all spaces, or focus on those we consider `interesting'? And what makes a space interesting? One possible answer to this question is that there are interesting spaces called moduli spaces (the word `moduli' goes back to Hilbert and basically means `parameters'). The special feature is that these spaces parametrize objects of some class: e.g., moduli space of triangles parametrizes triangles, moduli space of differential equations parametrizes differential equations, and so on.
In my talk, I will go over the basics of moduli spaces; in the (unlikely) event that there is some time left, I will talk about the Murphy Law for the moduli spaces due to Ravi Vakil.
Refreshments will be served in the Keisler lounge at 2:00 pm.

Tuesday, April 4, 2017

Posted January 15, 2017
Last modified March 29, 2017

3:00 pm – 3:50 pm Lockett 277

Dima Arinkin, University of Wisconsin
Geometry of linear ODEs

Abstract: There is a classical correspondence between systems of n linear ordinary differential equations (ODEs) of order one and linear ODEs of order n. (The correspondence may be viewed as a kind of `canonical normal form' for systems of ODEs.) The correspondence can be restated geometrically: given a Riemann surface C, a vector bundle E on C, and a connection \nabla on E, it is possible to find a rational basis of E such that \nabla is in the canonical normal form. All of the above objects have a version for arbitrary semisimple Lie group G (with the case of systems of ODEs corresponding to G=GL(n)): we can consider differential operators whose `matrices' are in the Lie algebra of G, and then try to `change the basis' so that the `matrix' is in the `canonical normal form.' However, the statement turns out to be significantly harder. In my talk, I will show how the geometric approach can be used to prove the claim for any G.

Wednesday, April 5, 2017

Posted March 27, 2017
Last modified March 29, 2017

Graduate Student Colloquium

2:30 pm – 3:30 pm Lockett 277

Dima Arinkin, University of Wisconsin
Connections with a small parameter.

Abstract: In my talk, I will start with a classical, and relatively easy, statement about differential equations with a small parameter (due to Wasow) and use a geometric point of view to translate it, first, into a claim about connections on a vector bundle on a Riemann surface, and then into a statement about the geometry of the space of such connections (their `moduli space'). The main point of the talk is the interplay between study of `individuals' (differential equations or bundles with connections) and properties of their `community' (their moduli space).
Refreshments will be served in the Keisler lounge at 2:00 pm.

Posted March 8, 2017

3:30 pm – 4:20 pm Lockett 233

Gregor Masbaum, CNRS, Institut de Mathematiques de Jussieu, Paris, France
An application of TQFT to modular representation theory

Posted April 3, 2017

3:30 pm – 4:30 pm Lockett 240

Kevin Grace, LSU
All That Glitters Is Not Golden-Mean

Three closely related classes of GF(4)-representable matroids are the golden-mean matroids, the matroids representable over all fields of size at least 4, and the matroids representable over GF(4) as well as fields of all characteristics. We characterize the highly connected matroids in each of these classes by using frame templates, which were recently introduced by Geelen, Gerards, and Whittle as tools for describing the the highly connected members of minor-closed classes of representable matroids. As a direct consequence of this characterization, we give the growth rates of these classes of matroids, including the golden-mean matroids. This proves that a conjecture made by Archer in 2005 holds for golden-mean matroids of sufficiently high rank.

Thursday, April 6, 2017

Posted April 3, 2017

3:30 pm 1034 Digital Media Center (CCT)

Yangyang Xu, University of Alabama
Primal-dual methods for affinely constrained problems

Optimization has been applied in many areas including engineering, statistics, finance, and data sciences. Modern applications often have rich structure information. Traditional methods like projected subgradient and the augmented Lagrangian can be used, but they do not utilize structures of the problems and thus are not so efficient. This talk will focus on convex optimization problems with affine constraints. The first part assumes two-block structure on the problem and presents the alternating direction method of multipliers (ADMM) and its accelerated variant. With strong convexity on one block variable, the ADMM can be accelerated from O(1/k) rate to O(1/k^2). Numerical results will be given to demonstrate the improved speed. In the second part, I will present a novel primal-dual block update method for a multi-block (at least three blocks) problem. Existing works have shown that directly extending two-block ADMM to multi-block problems may diverge. To guarantee convergence, either strong assumptions are made or updating order of the blocks has to be changed. Our method uses a simple randomization technique on choosing block variables, and it enjoys O(1/k) ergodic convergence rate and also global convergence in probability. In addition, by choosing a few blocks every time and using Jacobi-type update, the method enables parallel computing with guaranteed convergence. Numerical experiments will be shown to demonstrate its efficiency compared to other methods.

Posted March 7, 2017
Last modified March 22, 2017

3:30 pm – 4:20 pm Lockett 277

Peter Jorgensen, Newcastle University
SL_2-tilings, infinite triangulations, and continuous cluster categories

Abstract: An SL_2-tiling is an infinite grid of positive integers such that each adjacent 2x2-submatrix has determinant 1. These tilings were introduced by Assem, Reutenauer, and Smith for combinatorial purposes. We will show that each SL_2-tiling can be obtained by a procedure called Conway--Coxeter counting from certain infinite triangulations of the circle with four accumulation points. We will see how properties of the tilings are reflected in the triangulations. For instance, the entry 1 of a tiling always gives an arc of the corresponding triangulation, and 1 can occur infinitely often in a tiling. On the other hand, if a tiling has no entry equal to 1, then the minimal entry of the tiling is unique, and the minimal entry can be seen as a more complex pattern in the triangulation. The infinite triangulations also give rise to cluster tilting subcategories in a certain cluster category with infinite clusters related to the continuous cluster categories of Igusa and Todorov. The SL_2-tilings can be viewed as the corresponding cluster characters. This is a report on joint work with Christine Bessenrodt and Thorsten Holm.

Saturday, April 8, 2017

Posted April 4, 2017

Pasquale Porcelli Lecture Series Special Lecture Series

8:50 am – 4:00 pm Sunday, April 9, 2017 Lockett 233

Southern Regional Number Theory Conference

A conference in honor of Robert Perlis on the occasion of his retirement

Wednesday, April 19, 2017

Posted December 12, 2016
Last modified February 3, 2017

3:30 pm – 4:20 pm 130 Howe-Russell

Ken Ono, Emory University
Gems of Ramanujan and their Lasting Impact on Mathematics

Abstract: Ramanujan's work has has a truly transformative effect on modern mathematics, and continues to do so as we understand further lines from his letters and notebooks. In this lecture, some of the studies of Ramanujan that are most accessible to the general public will be presented and how Ramanujan's findings fundamentally changed modern mathematics, and also influenced the lecturer's work, will be discussed. The speaker is an Associate Producer of the film The Man Who Knew Infinity (starring Dev Patel and Jeremy Irons) about Ramanujan. He will share several clips from the film in the lecture.

Thursday, April 20, 2017

Posted December 12, 2016
Last modified February 3, 2017

Pasquale Porcelli Lecture Series Special Lecture Series

3:30 pm – 4:20 pm Dodson Auditorium

Ken Ono, Emory University
Cool Theorems Proved by Undergraduates

Abstract. The speaker has been organizing summer research programs for undergraduate students for many years. This lecture will give a sample of their accomplishments. The speaker will talk about partitioning integers, prime numbers, number fields, and generalizations of classical theorems of Euler, Gauss, and Jacobi.

Friday, April 21, 2017

Posted December 12, 2016
Last modified February 4, 2017

Pasquale Porcelli Lecture Series Special Lecture Series

3:30 pm – 4:20 pm Dodson Auditorium

Ken Ono, Emory University
Can't you just feel the Moonshine?

Borcherds won the Fields medal in 1998 for his proof of the Monstrous Moonshine Conjecture. Loosely speaking, the conjecture asserts that the representation theory of the Monster, the largest sporadic finite simple group, is dictated by the Fourier expansions of a distinguished set of modular functions. This conjecture arose from astonishing coincidences noticed by finite group theorists and arithmetic geometers in the 1970s. Recently, mathematical physicists have revisited moonshine, and they discovered evidence of undiscovered moonshine which some believe will have applications to string theory and 3d quantum gravity. The speaker and his collaborators have been developing the mathematical facets of this theory, and have proved the conjectures which have been formulated. These results include a proof of the Umbral Moonshine Conjecture, and Moonshine for the first sporadic finite simple group which does not occur as a subgroup or subquotient of the Monster. The most recent Moonshine (announced here) yields unexpected applications to the arithmetic elliptic curves thanks to theorems related to the Birch and Swinnerton-Dyer Conjecture and the Main Conjectures of Iwasawa theory for modular forms. This is joint work with John Duncan, Michael Griffin and Michael Mertens.

Monday, April 24, 2017

Posted April 2, 2017
Last modified April 7, 2017

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 241 Lockett

Meeting of Tenured Faculty

Tuesday, April 25, 2017

Posted January 23, 2017
Last modified March 17, 2017

3:00 pm – 3:50 pm Lockett 277

Jie Zhou, Perimeter institute
Periods and Gromov-Witten invariants

Abstract: The mirror symmetry conjectures asserts that the generating series of Gromov-Witten invariants (curve counting) of a Calabi-Yau variety are identical to some "universal" differential polynomials of period integrals of its mirror Calabi-Yau variety. I will explain in detail how these "universal" polynomials can be read off from the Picard-Fuchs system of the mirror Calabi-Yau variety, for the genus zero and one cases which are so far the only cases proved rigorously in mathematics. I will also discuss some nice ingredients (e.g., generating series of point counting, polylogarithms, Feynman diagrams and manipulation on Picard-Fuchs equations) which seem to have a motivic nature. A particularly interesting example of Calabi-Yau 3-fold will be emphasized, in which modular forms arise naturally.

Wednesday, April 26, 2017

Posted April 24, 2017
Last modified March 3, 2021

3:30 pm – 4:20 pm Lockett 285

Hongyu He, Department of Mathematics, LSU
Interlacing relations in Representation theory

Given an irreducible representation of U(n) with highest weight $\lambda$, its restriction to U(n-1) decomposes into a direct sum of irreducible representations of U(n-1) with highest weights $\mu$. It is well-known that $\lambda$ and $\mu$ must satisfy the Cauchy interlacing relations $$\lambda_1 \geq \mu_1 \geq \lambda_2 \geq \mu_2...$$ and vice versa. In this talk, I shall discuss the noncompact analogue for the discrete series of $U(p,q)$ as conjectured by Gan, Gross and Prasad. I will introduce the Gan-Gross-Prasad interlacing relations and discuss some recent progress.

Posted February 3, 2017

3:30 pm – 4:20 pm Lockett 233

Jose Ceniceros, Louisiana State University
TBD

Friday, April 28, 2017

Posted April 24, 2017

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 10

Faculty Meeting

Tuesday, May 9, 2017

Posted April 11, 2017
Last modified May 8, 2021

3:00 pm – 3:50 pm Lockett 277

Ha Tran, University of Calgary
On reduced ideals of a number field

Let F be a number field. The reduced ideals of F can be used for computing its class group and regulator. In this talk, we will introduce reduced ideals first for quadratic fields then for an arbitrary number field. Next, we will discuss a generalization of reduced ideals using the LLL-algorithm. Finally, some open problems relating to this topic will be presented.

Monday, May 15, 2017

Posted May 12, 2017

8:30 am – 4:50 pm 205 Prescott Hall

Conference on Order in Algebra and Logic (OAL 2017)

Day 1 of a 3-day conference, May 15-17, 2017:
https://www.math.lsu.edu/OAL2017

Tuesday, May 16, 2017

Posted May 12, 2017

9:00 am – 4:50 pm 205 Prescott Hall

Conference on Order in Algebra and Logic (OAL 2017)

Day 2 of a 3-day conference, May 15-17, 2017:
https://www.math.lsu.edu/OAL2017

Wednesday, May 17, 2017

Posted May 12, 2017

Algebra and Number Theory Seminar Questions or comments?

9:00 am – 11:50 am 205 Prescott Hall

Conference on Order in Algebra and Logic (OAL 2017)

Day 3 of a 3-day conference, May 15-17, 2017:
https://www.math.lsu.edu/OAL2017

Thursday, May 18, 2017

Posted April 22, 2017
Last modified May 18, 2017

3:00 pm – 3:50 pm Lockett 9

David Lax, Virginia Tech
Order Filter Model for Minuscule Plucker Relations

Abstract: The Plucker relations which define the Grassmann manifolds as projective varieties interact nicely with a natural order on the projective coordinates; the resulting homogeneous coordinate ring is an algebra with straightening law. This is a property shared by all minuscule flag manifolds. The order structures on their projective coordinates share common properties and are called minuscule lattices. We study their generalized Plucker relations independent of Lie type through the minuscule lattices. To do this we combinatorially model the Plucker coordinates based on Wildberger\'s construction of minuscule Lie algebra representations; it uses the colored partially ordered sets known as minuscule posets. We obtain, uniformly across Lie type, descriptions of the Plucker relations of ``extreme weight\'\'. We show that these are supported by ``double-tailed diamond\'\' sublattices of minuscule lattices. From this, we obtain a complete set of Plucker relations for the exceptional minuscule flag manifolds. These Plucker relations are straightening laws for their respective coordinate rings.

Monday, August 14, 2017

Posted April 27, 2017
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, August 16, 2017

Posted April 27, 2017
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, August 18, 2017

Posted April 27, 2017
Last modified December 13, 2022

Informal Geometry and Topology Seminar Questions or comments?

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, August 30, 2017

Posted August 23, 2017
Last modified August 29, 2017

10:30 am – 12:00 pm Lockett 233

Federico Salmoiraghi, Department of Mathematics, LSU
An introduction to Heegaard Floer homology

Abstract: In 2001 Ozsvath and Szabo introduced Heegaard Floer homology, an invariant of three manifolds that can be calculated from a particular class of Heegaard diagram for the manifold. In this talk, after a brief outline of the construction of the invariant, I will introduce some of the different versions of Heegaard Floer homology and compute some example.

Thursday, August 31, 2017

Posted August 29, 2017

12:00 pm – 1:00 pm Keisler Lounge (Lockett 321)

What I Did This Summer

Undergraduate and graduate students will give presentations about their
summer math experiences.

Posted August 31, 2017
Last modified March 2, 2021

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:30 pm – 4:30 pm Lockett 233

Andrew Alaniz, LSU
Hecke Operators and Ramanujan's tau function

The purpose of this talk is, primarily, to show how applying algebraic methods to situations involving analytic objects can often simplify the situation. Often, fourier coefficients encode interesting arithmetic or combinatorial information about a particular generating series considered as a holomorphic function, this is a common theme in number theory. Hecke's revolutionary insight was understanding the universial meaning of constructions like these. We will consider a certain class of operators, the so-called Hecke operators, and Ramanujan's tau function via the theory of modular forms.

Tuesday, September 5, 2017

Posted August 23, 2017
Last modified August 29, 2017

3:30 pm – 4:30 pm 1034 Digital Media Center

Jingyong Tang, Xinyang Normal University, China
Strong convergence properties of a modified nonmonotone smoothing algorithm for the SCCP

Abstract: The symmetric cone complementarity problem (denoted by SCCP) provides a simple unified framework for various existing complementarity problems and has wide applications. Smoothing algorithms have been successfully applied to solve the SCCP, which in general have the global and local superlinear/quadratic convergence if the solution set of the SCCP is nonempty and bounded. We propose a new nonmonotone smoothing algorithm for solving the SCCP and prove that the algorithm is globally and locally superlinearly/quadratically convergent if the solution set of the SCCP is only nonempty, without requiring its boundedness. This convergence result is stronger than those obtained by most smoothing-type algorithms. Finally, some numerical results are reported.

Posted August 23, 2017

5:00 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial club meeting

Discussion about preparing for a career as an actuary and planning the fall semester\'s activities. Changes in the Society of Actuaries qualification process. Pizza will be served.

Wednesday, September 6, 2017

Posted August 14, 2017
Last modified August 15, 2017

3:30 pm – 4:30 pm Lockett 233

Peter Lambert-Cole, Georgia Institute of Technology
Conway mutation and knot Floer homology

Abstract: Mutant knots are notoriously hard to distinguish. Many, but not all, knot invariants take the same value on mutant pairs. Khovanov homology with coefficients in Z/2Z is known to be mutation-invariant, while the bigraded knot Floer homology groups can distinguish mutants such as the famous Kinoshita-Terasaka and Conway pair. However, Baldwin and Levine conjectured that delta-graded knot Floer homology, a singly-graded reduction of the full invariant, is preserved by mutation. In this talk, I will give a new proof that Khovanov homology mod 2 is mutation-invariant. The same strategy can be applied to delta-graded knot Floer homology and proves the Baldwin-Levine conjecture for mutations on a large class of tangles.

Thursday, September 7, 2017

Posted September 6, 2017

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:15 pm – 4:15 pm Lockett 233

William Hardesty, Louisiana State University
Baby Verma modules for p-restricted Lie algebras

Abstract: Will give a brief introduction to the representation of theory of (semi-simple) restricted Lie algebras with an emphasis on an important class of representations called \"Baby Verma modules\". Various results concerning the structure of these modules will be presented and, if time permits, we will briefly discuss some relevant ongoing joint work between the speaker and V. Nandakumar.

Monday, September 11, 2017

Posted September 1, 2017
Last modified March 2, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett 233

Yaniv Almog, Department of Mathematics, LSU
On a Schrödinger operator with a purely imaginary potential in the semiclassical limit

We consider the operator ${\mathcal A}_h=-h^2\Delta+iV$ in the semi-classical limit $h\rightarrow 0$, where $V$ is a smooth real potential with no critical points. We obtain both the left margin of the spectrum, as well as resolvent estimates on the left side of this margin. We extend here previous results obtained for the Dirichlet realization of ${\mathcal A}_h$ by removing significant limitations that were formerly imposed on $V$. In addition, we apply our techniques to the more general Robin boundary condition and to a transmission problem which is of significant interest in physical applications.

Posted September 6, 2017

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:30 pm – 4:30 pm Lockett 233

Matt Lee, UC Riverside
Demazure Flags and q-Hypergeometric Series

Abstract: Since the current algebra of sl_2 is not semisimple, we need to understand more than just the irreducible representations. We will look at the filtration for a family of modules parametrized by a partition. Attempts to generalize this filtration to other modules leads to an interesting connection to q-Hypergeometric series and related concepts. This talk is accessible to anyone with basic knowledge of sl_2.

Tuesday, September 12, 2017

Posted August 2, 2017
Last modified September 12, 2017

3:10 pm – 4:00 pm 276 Lockett

Matthew Lee, University of California, Riverside
Global Weyl modules for non-standard maximal parabolics of twisted affine Lie algebras

Abstract: In this talk we will discuss the structure of non standard maximal parabolics of twisted affine Lie algebras, global Weyl modules and the associated commutative associative algebra, $\\mathbf{A}_\\lambda$. Since the global Weyl modules associated with the standard maximal parabolics have found many applications the hope is that these non-standard maximal parabolics will lead to different, but equally interesting applications.

Wednesday, September 13, 2017

Posted August 23, 2017
Last modified September 12, 2017

Informal Geometry and Topology Seminar Questions or comments?

10:30 am – 12:00 pm Lockett 233

Ryan Leigon, Louisiana State University
Bordered Heegaard Floer Homology

Abstract: Heegaard Floer theory yields powerful invariants of 3-manifolds, but it is often difficult to compute. Bordered Floer allows us to do computations by cutting a 3-manifold into simple pieces, where computations are easy, and then pasting the pieces back together. I will provide a brief introduction to the theory before giving an accessible yet non-trivial example.

Posted August 24, 2017
Last modified September 12, 2017

3:30 pm – 4:30 pm Lockett 233

Mike Wong, Louisiana State University
An unoriented skein exact triangle for grid homology

Abstract: Like the Jones and Alexander polynomials, Khovanov and knot Floer homology (HFK) both satisfy an oriented and an unoriented skein exact triangle. Manolescu (2007) proved the unoriented triangle for HFK over Z/2Z. In this talk, we will give a combinatorial proof of the same using grid homology (GH), which is isomorphic to knot Floer homology. This gives rise to a cube-of-resolutions complex that calculates GH-tilde. If time permits, we will outline the generalisation to the case over Z, and an application to quasi-alternating links. No prior experience with the subject is needed, as a brief introduction to grid homology will be given.

Thursday, September 14, 2017

Posted August 24, 2017
Last modified September 13, 2017

3:30 pm – 4:20 pm Lockett 277

Shea Vela-Vick, Louisiana State University
Contact geometry and Heegaard Floer theory

Abstract: Among the most transformative applications of Ozsvath and Szabo's Heegaard Floer theory is to the study of contact structures on 3-manifolds. Ozsvath and Szabo first identified an invariant of contact structures taking values in their Heegaard Floer homology in 2002. Since its definition, this invariant has been responsible for a tremendous amount of progress in our understanding of tight contact structures. A steady stream of evidence suggests subtle links between geometric characteristics of contact structures and the algebraic formalism present in Heegaard Floer theory. In this talk, we will discuss how the flow of ideas between contact geometry and Floer theory can be leveraged to establish significant results in each context.

Tuesday, September 19, 2017

Posted September 14, 2017

Informal Geometry and Topology Seminar Questions or comments?

6:00 pm Keisler Lounge (321 Lockett)

Actuarial club meeting

Matthew Arnold from Blue Cross Blue Shield of Louisiana will be our guest. Also Katelyn Kormos will be talking about her internship. Pizza will be served.

Wednesday, September 20, 2017

Posted September 20, 2017
Last modified March 2, 2021

10:30 am – 12:00 pm Lockett 233

Ryan Leigon, Louisiana State University
Federico Salmoiraghi, Department of Mathematics, LSU
Equivalence of gluing maps in Heegaard Floer theory

We show that the gluing mas in Heegaard Floer theory defined by Honda, Kazez and Matic and by Zarev are equivalent.

Posted August 25, 2017
Last modified September 8, 2017

3:30 pm – 4:20 pm Lockett 233

Changfeng Gui, University of Texas at San Antonio
The Sphere Covering Inequality and its applications

In this talk, I will introduce a new geometric inequality: the Sphere Covering Inequality. The inequality states that the total area of two {\it distinct} surfaces with Gaussian curvature less than 1, which are also conformal to the Euclidean unit disk with the same conformal factor on the boundary, must be at least $4 \pi$. In other words, the areas of these surfaces must cover the whole unit sphere after a proper rearrangement. We apply the Sphere Covering Inequality to show the best constant of a Moser-Trudinger type inequality conjectured by A. Chang and P. Yang. Other applications of this inequality include the classification of certain Onsager vortices on the sphere, the radially symmetry of solutions to Gaussian curvature equation on the plane, classification of solutions for mean field equations on flat tori and the standard sphere, etc. The resolution of several open problems in these areas will be presented. The talk is based on joint work with Amir Moradifam from UC Riverside.

Thursday, September 21, 2017

Posted August 22, 2017
Last modified August 27, 2017

3:30 pm – 4:20 pm

Hongyu He, Department of Mathematics, LSU
Branching Laws and Interlacing Relation

Abstract: Let $H$ be a subgroup of a compact group $G$. Then any irreducible unitary representation of $G$, when restricted to $H$, decomposes into a direct sum of irreducible representations of $H$. A description of such a decomposition is often called a branching law. They are important in harmonic analysis, quantum mechanics and number theory. In this talk, I shall discuss the branching laws of the discrete series of the noncompact unitary groups and the recent progress towards the local Gan-Gross-Prasad conjectures. Discrete series representations were classified by Harish-Chandra in the sixties and played a fundamental role in Langland's program.

Tuesday, September 26, 2017

Posted August 22, 2017
Last modified September 26, 2017

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Yangyang Xu, Rensselaer Polytechnic Institute
Primal-dual methods for affinely constrained problems

Abstract: Optimization has been applied in many areas including engineering, statistics, finance, and data sciences. Modern applications
often have rich structure information. Traditional methods like projected subgradient and the augmented Lagrangian can be used, but they do not utilize structures of the problems and thus are not so efficient. This talk will focus on convex optimization problems with affine constraints. The first part assumes two-block structure on the problem and presents the alternating direction method of multipliers (ADMM) and its accelerated variant. With strong convexity on one block variable, the ADMM can be accelerated from O(1/k) rate to O(1/k^2). Numerical results will be given to demonstrate the improved speed. In the second part, I will present a novel primal-dual block update method for a multi-block (at least three blocks) problem. Existing works have shown that directly extending two-block ADMM to multi-block problems may diverge. To guarantee convergence, either strong assumptions are made or updating order of the blocks has to be changed. Our method uses a simple randomization technique on choosing block variables, and it enjoys O(1/k) ergodic convergence rate and also global convergence in probability. In addition, by choosing a few blocks every time and using Jacobi-type update, the method enables parallel computing with guaranteed convergence. Numerical experiments will be shown to demonstrate its efficiency compared to other methods.

Wednesday, September 27, 2017

Posted August 23, 2017
Last modified September 11, 2017

10:20 am – 11:50 am Lockett 233

Yu-Chan Chang, Louisiana State University
Introduction to bounded cohomology of discrete groups

Abstract: In this introductory talk, we will focus on bounded cohomology of discrete groups with real or integer coefficient. I will talk about the bounded cohomology of Gromov hyperbolic groups and amenable groups. Also, we will discuss the comparison map, which is the map from the bounded cohomology to the usual cohomology.

Posted August 24, 2017
Last modified September 20, 2017

3:30 pm – 4:30 pm Lockett 233

John Etnyre, Georgia Institute of Technology
Contact surgeries and symplectic fillings

Abstract: It is well known that all contact manifolds can be obtained from the standard contact structure on the 3-sphere by contact surgery on a Legendrian link. What is not so well understood is what properties of a contact structure are preserved by positive contact surgeries (the case for negative contact surgeries is fairly well understood now). In this talk we will discuss some new results about positive contact surgeries and in particular completely characterize when contact r surgery is symplectically fillable when r is in (0,1].

Thursday, September 28, 2017

Posted August 25, 2017
Last modified September 19, 2017

3:30 pm – 4:20 pm Lockett 277

John Etnyre, Georgia Institute of Technology
Curvature and contact topology

Abstract: Contact geometry is a beautiful subject that has important interactions with topology in dimension three. In this talk I will give a brief introduction to contact geometry and discuss its interactions with Riemannian geometry. In particular I will discuss a contact geometry analog of the famous sphere theorem and more generally indicate how the curvature of a Riemannian metric can influence properties of a contact structure adapted to it. This is joint work with Rafal Komendarczyk and Patrick Massot.

Tuesday, October 3, 2017

Posted September 14, 2017
Last modified September 26, 2017

Informal Geometry and Topology Seminar Questions or comments?

4:15 pm – 5:00 pm 1034 Digital Media Center

Computational Mathematics Presentations

In this event for a general audience, we will share information on the education and research opportunities in computational mathematics at LSU. There will be a presentation on the Concentration in Computational Mathematics and several faculty members will talk about their current research. All are welcome.

Wednesday, October 4, 2017

Posted October 3, 2017

10:20 am – 11:20 am Lockett 233

Yu-Chan Chang, Louisiana State University
Introduction to bounded cohomology of discrete groups II

Abstract: We continue our discussion from last week. In this talk, I will describe the construction of non-trivial quasimorphisms on free groups. This shows that free groups have non-trivial second bounded cohomology groups while the usual cohomology groups are trivial. We will also discuss the quasi-morphism on abelian groups. If time permits, I will talk about Gromov hyperbolic groups.

Posted August 9, 2017
Last modified September 21, 2017

3:30 pm – 4:20 pm Lockett 233

Giles Auchmuty, University of Houston
The SVD of the Poisson kernel

The Poisson kernel provides a representation for the solution operator for the Dirichlet problem for Laplace's equation on a bounded region. It is usually treated as an integral operator and this talk will describe spectral representations of this operator when the boundary data is in L^2(\partial\Omega). For this problem Fichera (1955) proved, under strong regularity conditions on the boundary, that the Poisson kernel is a continuous linear transformation of L^2(\partial\Omega) to L^2(\Omega) and that it has norm related to the first eigenvalue of a Steklov eigenproblem for the biharmonic operator on \Omega. In this talk two quite different representations of this operator using Steklov eigenfunctions and Hilbert space theory will be outlined. The first is based on the use of harmonic Steklov eigenfunctions. They may be used to develop a different theory of boundary trace spaces such as H^s(\partial\Omega). This yields spectral representation of solutions of Robin and Neumann boundary value problems for Laplace's equation as well as the Dirichlet problem. There are associated approximation theories and generalizations of results such as the mean value theorem to rectangles and boxes. When the domain is a ball, the results provide an analysis in terms of classical spherical harmonics. A weak version of the Dirichlet Biharmonic Steklov eigenproblem that Fichera studied will be described using Hilbert-Sobolev space methods. It can be shown that the normal derivatives of these eigenfunctions provide an orthonormal basis of L^2(\partial \Omega) while their Laplacians provide an L^2 orthogonal basis of harmonic functions on \Omega. This yields an SVD of the Poisson kernel and the norm of the operator is related to the first Steklov eigenvalue of the problem.

Posted August 24, 2017
Last modified September 19, 2017

3:30 pm – 4:30 pm Lockett 233

Mike Wong, Louisiana State University
TBD

Friday, October 6, 2017

Posted November 1, 2017

4:30 pm – 5:30 pm Lockett 276

Zachary Gershkoff, Mathematics Department, LSU
Characterization and enumeration of 3-regular permutation graphs

By taking a permutation in line notation, drawing a vertex for every letter in the permutation, and adding edges between vertices if and only if the corresponding letters are inverted, we obtain a type of graph called a permutation graph. We give a construction to show that there are infinitely many k-regular permutation graphs for k greater than two. For 3-regular permutation graphs, we characterize their structure, and we give a formula for counting them.

Tuesday, October 10, 2017

Posted August 22, 2017
Last modified November 29, 2022

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Xiang Xu, Old Dominion University
Eigenvalue preservation for the Beris-Edwards system modeling nematic liquid crystals

The Beris-Edwards equations are a hydrodynamic system modeling nematic liquid crystals in the setting of Q-tensor order parameter. Mathematically speaking it is the incompressible Navier-Stokes equations coupled with a Q-tensor equation of parabolic type.

In this talk we first consider the simplified Beris-Edwards system that corresponds to the co-rotational case, and study the eigenvalue preservation property for the initial Q-tensor order parameter. Then we show that for the full system that relates to the non-rotational case, this property is not valid in general.

Wednesday, October 11, 2017

Posted August 23, 2017
Last modified October 3, 2017

10:30 am – 12:00 pm Lockett 233

Kent Vashaw, Louisiana State University
TBD

Posted August 7, 2017
Last modified October 7, 2017

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 134

Keng Deng, University of Louisiana at Lafayette
Global existence and blow-up for nonlinear diffusion equations with boundary flux governed by memory

In this talk, we introduce the study of global existence and blow-up in finite time for nonlinear diffusion equations with flux at the boundary governed by memory. Via a simple transformation, the memory term arises out of a corresponding model introduced in previous studies of tumor-induced angiogenesis. The study is also in the spirit of extending work on models of the heat equation with local, nonlocal, and delay nonlinearities present in the boundary flux. Specifically, we establish an identical set of necessary and sufficient conditions for blow-up in finite time as previously established in the case of local flux conditions at the boundary.

Wednesday, October 18, 2017

Posted October 6, 2017
Last modified October 16, 2017

10:30 am – 12:00 pm Lockett 233

Robin Koytcheff, University of Louisiana, Lafayette
Finite-type invariants of knots, links, and string links

Abstract: Finite-type knot invariants (a.k.a. Vassiliev invariants) are an important class of invariants in that they conjecturally approximate all knot invariants and hence separate knots. They may also be defined for (closed) links and string links, and they are known to separate string links up to link homotopy. In other words, they are a complete invariant of string links where each component may pass through itself. This parallels (and is related to) a story about the kappa invariant, which conjecturally separates closed links up to link homotopy. In joint work with F. Cohen, Komendarczyk, and Shonkwiler, we showed that the kappa invariant separates string links up to link homotopy. In this talk, we will focus on the elementary, purely combinatorial description of finite-type invariants.

Posted August 25, 2017
Last modified October 10, 2017

3:30 pm – 4:20 pm Lockett 134

Ryan Hynd, University of Pennsylvania
Partial regularity for doubly nonlinear parabolic systems

We will present a regularity result for solutions of a PDE system which is a model for general doubly nonlinear evolutions. The system we focus on a particular case of a general class of flows that arise in the study of phase transitions.

Posted August 27, 2017
Last modified October 16, 2017

3:30 pm – 4:30 pm Lockett 233

Robin Koytcheff, University of Louisiana, Lafayette
Homotopy string links, configuration spaces, and the kappa invariant

Abstract: A link is an embedding of disjoint circles in space. A link homotopy is a path between two links where distinct components may not pass through each other, but where a component may pass through itself. In the 1990s, Koschorke conjectured that link homotopy classes of n-component links are distinguished by the kappa invariant. This invariant is essentially the map that a link induces on configuration spaces of n points. In joint work with F. Cohen, Komendarczyk, and Shonkwiler, we proved an analogue of this conjecture for string links. A key ingredient is a multiplication on maps of configuration spaces, akin to concatenation of loops in a space. This approach is related to recent joint work with Budney, Conant, and Sinha on finite-type knot invariants and the Taylor tower for the space of knots.

Monday, October 23, 2017

Posted October 4, 2017
Last modified October 17, 2017

4:30 pm – 5:30 pm 241 Lockett

Faculty Meeting

Meeting of the tenured faculty, followed by a meeting of the full professors

Tuesday, October 24, 2017

Posted September 13, 2017

2:30 pm – 3:20 pm Lockett 233

Jiahong Wu, Oklahoma State University
Partial differential equations related to fluids with partial or fractional dissipation

There have been substantial recent developments on several partial differential equations from fluid dynamics with partial or fractional dissipation. This talk summarizes results on the global existence and regularity problem for the 3D Navier-Stokes equations with partial hyperdissipation, the surface quasi-geostrophic equation, the 2D Boussinesq equations with partial or fractional dissipation and the 2D magnetohydrodynamic equations with partial or fractional dissipation.

Posted August 15, 2017
Last modified October 11, 2017

3:30 pm – 4:20 pm Lockett 233

Kun Zhao, Tulane University
Analysis of a System of Parabolic Conservation Laws Arising From Chemotaxis

In contrast to random diffusion without orientation, chemotaxis is the biased movement of organisms toward the region that contains higher concentration of beneficial or lower concentration of unfavorable chemicals. The former often refers to the attractive chemotaxis and latter to the repulsive chemotaxis. Chemotaxis has been advocated as a leading mechanism to account for the morphogenesis and self-organization of a variety of biological coherent structures such as aggregates, fruiting bodies, clusters, spirals, spots, rings, labyrinthine patterns and stripes, which have been observed in many laboratory experiments. Mathematical modeling of chemotaxis was initiated more than half a century ago. The Keller-Segel type model has provided a corner for much of the works investigating chemotaxis, its success being its intuitive simplicity, analytical tractability and capability of modeling the basic phenomena in chemotactic populations. In this talk, I will present a group of results concerning the rigorous analysis of a system of parabolic conservation laws derived from a Keller-Segel type chemotaxis model with singular sensitivity. In particular, global well-posedness, long-time asymptotic behavior, zero chemical diffusion limit and boundary layer formation of classical solutions will be discussed.

Posted August 22, 2017
Last modified September 26, 2017

3:30 pm – 4:30 pm 1034 Digital Media Center

Joscha Gedicke, Universität Wien
Numerical homogenization of heterogeneous fractional Laplacians

Abstract: In this talk, we develop a numerical multiscale method to solve the fractional Laplacian with a heterogeneous diffusion coefficient. The fractional Laplacian is a non-local operator in its standard form, however the Caffarelli-Silvestre extension allows for a localization of the equation. This adds a complexity of an extra spacial dimension and a singular/degenerate coefficient depending on the fractional order. Using a sub-grid correction method, we correct the basis functions in a natural weighted Sobolev space and show that these corrections are able to be truncated to design a computationally efficient scheme with optimal convergence rates. We further show that we can obtain a greater rate of convergence for sufficient smooth forces, and utilizing a global projection on the critical boundary. We present some numerical examples, utilizing our projective quasi-interpolation in dimension 2+1 for analytic and heterogeneous cases to demonstrate the rates and effectiveness of the method. (This is joint work with Donald L. Brown and Daniel Peterseim.)

Posted October 21, 2017

Informal Geometry and Topology Seminar Questions or comments?

5:00 pm Lockett Math Lounge

Winnie Sloan LSU alumna Senior Actuarial Assistant for Travelers in St. Paul, MN
ASA Club Meeting

Skype call with Winnie Sloan. This meeting will be geared towards informing students about internships, resumes, industry practices with an emphasis on the casualty pathway for actuaries. This meeting is open to anyone interested in actuarial science.

Wednesday, October 25, 2017

Posted October 24, 2017

10:30 am – 12:00 pm Lockett 233

Kent Vashaw, Louisiana State University
TBD

Posted September 13, 2017
Last modified September 20, 2017

3:30 pm – 4:30 pm Lockett 233

Yilong Wang, The Ohio State University
Integrality for SO(p)_2-TQFTs

Abstract: Representation theory of quantum groups at roots of unity give rise to modular tensor categories hence TQFTs, and the 3-manifold invariants from such constructions are known to be algebraic integers. In this talk, I will introduce the SO(p)_2-TQFT as an example of the above construction, and I will present our results on the integral lattices of the SO(p)_2-TQFT in genus 1 and one-punctured torus.

Posted September 27, 2017
Last modified October 16, 2017

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 285
(Originally scheduled for Wednesday, October 18, 2017)

Reflection Positivity; Representation Theory meets CQFT

Moved by one week: We will give an overview over our work with K-H. Neeb on reflection positivity. We start with recalling the Osterwalder-Schrader Axioms for Constructive Quantum Field Theory and the Osterwalder-Schrader (OS) quantization. We then point out the natural generalization and discuss some examples. We then discuss reflection positive representations, in particular reflection positive 1-parameter subgroups. In the second part we discuss OS quantization related to the sphere.

Tuesday, October 31, 2017

Posted October 21, 2017

3:10 pm – 4:00 pm 276 Lockett

Bach Nguyen, Louisiana State University
Noncommutative discriminants via Poisson geometry and representation theory

The notion of discriminant is an important tool in number theory, algebraic geometry and noncommutative algebra. However, in concrete situations, it is difficult to compute and this has been done for few noncommutative algebras by direct methods. In this talk, we will describe a general method for computing noncommutative discriminants which relates them to representation theory and Poisson geometry. As an application we will provide explicit formulas for the discriminants of the quantum Schubert cell algebras at roots of unity. If time permits, we will also discuss this for the case of quantized coordinate rings of simple algebraic groups and quantized universal enveloping algebras of simple Lie algebras. This is joint work with Kurt Trampel and Milen Yakimov.

Wednesday, November 1, 2017

Posted August 23, 2017
Last modified October 24, 2017

Informal Geometry and Topology Seminar Questions or comments?

10:30 am – 12:00 pm Lockett 233

Rima Chatterjee, Louisiana State University
TBD

Posted September 27, 2017
Last modified March 3, 2021

3:30 pm – 4:30 pm Lockett 285
(Originally scheduled for Tuesday, October 10, 2017)

Reflection Positivity; Representation Theory meets CQFT, part II

This is the second part of the series on Reflection positivity. Both talks are accessible for graduate students.

Monday, November 6, 2017

Posted November 1, 2017
Last modified January 7, 2025

Algebra and Number Theory Seminar Questions or comments?

1:30 pm – 2:30 pm Lockett 284

Peter Nelson, University of Waterloo
Squaring the square

Is it possible to decompose a square into smaller squares of different sizes? The solution to this problem, which has surprising links to graph theory, linear algebra and even physics, was discovered by four undergraduate students at Cambridge University in the 1930's. I will tell the interesting mathematical story that led to this discovery.

This talk will be accessible to undergraduate students.

Tuesday, November 7, 2017

Posted September 9, 2017
Last modified October 20, 2017

3:10 pm – 4:00 pm 276 Lockett

Anna Romanov, University of Utah
A Kazhdan-Lusztig algorithm for Whittaker modules

The category of Whittaker modules for a complex semisimple Lie algebra generalizes the category of highest weight modules and displays similar structural properties. In particular, Whittaker modules have finite length composition series and all irreducible Whittaker modules appear as quotients of certain standard Whittaker modules which are generalizations of Verma modules. Using the localization theory of Beilinson-Bernstein, one obtains a beautiful geometric description of Whittaker modules as twisted sheaves of D-modules on the associated flag variety. I use this geometric setting to develop an analogue of the Kazhdan-Lusztig algorithm for computing the multiplicities of irreducible Whittaker modules in the composition series of standard Whittaker modules.

Posted August 23, 2017
Last modified October 17, 2017

3:30 pm – 4:30 pm 1034 Digital Media Center

Daniele Venturi, University of California Santa Cruz
Data-driven closures for kinetic equations

Abstract: In this talk, I will address the problem of constructing data-driven closures for reduced-order kinetic equations. Such equations arise, e.g., when we coarse-grain high-dimensional systems of stochastic ODEs and PDEs. I will first review the basic theory that allows us to transform such systems into conservation laws for probability density functions (PDFs). Subsequently, I will introduce coarse-grained PDF models, and describe how we can use data, e.g., sample trajectories of the ODE/PDE system, to estimate the unclosed terms in the reduced-order PDF equation. I will also discuss a new paradigm to measure the information content of data which, in particular, allows us to infer whether a certain data set is sufficient to compute accurate closure approximations or not. Throughout the lecture I will provide numerical examples and applications to prototype stochastic systems such as Lorenz-96, Kraichnan-Orszag and Kuramoto-Sivashinsky equations.

Posted August 15, 2017
Last modified January 24, 2022

3:30 pm – 4:20 pm Lockett 233

Zhifu Xie, University of Southern Mississippi
Variational method with SPBC and Broucke-Hénon orbit and Schubart orbit

N-body problem concerns the motion of celestial bodies under universal gravitational attraction. Although it has been a long history to apply variational method to N-body problem, it is relatively new to make some important progress in the study of periodic solutions. We develop the Variational Method with Structural Prescribed Boundary Conditions (SPBC) and we apply it to study periodic solutions in the 3-body problem with equal masses. We show that under an appropriate topological constraint, the action minimizer must be either the Schubart orbit (1956) or the Broucke-Hénon orbit (1975). One of the main challenges is to prove that the Schubart orbit coincides with the action minimizer connecting a collinear configuration with a binary collision and an isosceles configuration which must be collinear. A geometric property of the action minimizer is introduced to overcome this challenge. The action minimizer without collisions can be extended to the Broucke-Hénon orbit.

Posted November 5, 2017

Informal Geometry and Topology Seminar Questions or comments?

5:00 pm – 6:00 pm Keiser Math Lounge Room 321

ASA Club Meeting

Internship presentations by Alaina Chifici and Andrew Roberts

Wednesday, November 8, 2017

Posted November 7, 2017

10:30 am – 12:00 pm Lockett 233

Nurdin Takenov, Louisiana State University
Vassiliev Invariants

Posted November 1, 2017
Last modified January 7, 2025

1:30 pm – 2:30 pm Lockett 284

Peter Nelson, University of Waterloo
How to draw a graph

Given a network of points and edges that can be drawn in the plane without crossing edges, what is the best way to actually draw it? Can such a network always be drawn with just straight lines? I will discuss and (mostly) prove a beautiful theorem of William Tutte that answers this question using intuitive ideas from physics.

Posted October 10, 2017

3:30 pm – 4:30 pm Lockett 285

Boris Rubin, Louisiana State University
Weighted Norm Estimates for Radon Transforms and Geometric Inequalities

We obtain sharp inequalities for the Euclidean k-plane transforms and the \" j-plane to k-plane\'\' transforms acting in $L^p$ spaces on $R^n$ with a radial power weight. The corresponding operator norms are explicitly evaluated. The results extend to Funk-type transforms on the sphere and Grassmann manifolds. As a consequence, we obtain new weighted estimates of measures of planar sections for measurable subsets of $R^n$. The corresponding unweighted $L^p -L^q$ estimates and related open problems will be discussed.

Posted November 7, 2017

3:30 pm – 4:30 pm Lockett 233

Mike Wong, Louisiana State University
Ends of moduli spaces in bordered Floer homology I

Abstract: Bordered Floer homology is an invariant associated to 3-manifolds with parametrized boundary, created by Lipshitz, Ozsvath, and Thurston as an extension of Heegaard Floer homology. In this framework, we associate a differential graded algebra A(F) to each surface, and an A-infinity module CF^(Y) to each bordered 3-manifold Y. The module CF^(Y) satisfies a structural equation that should be thought of as the analogue of the condition d^2=0 for chain complexes, obtained by considering ends of moduli spaces that appear in the definition of CF^(Y). In two consecutive expository talks, we will discuss specific examples that illustrate how these ends of moduli spaces match up in pairs. As a starting point, in this talk, we will first focus on the case of grid homology, a specialization of Heegaard Floer homology. No prior knowledge is necessary, as a brief introduction to grid homology will be given.

Posted November 1, 2017

4:30 pm Lockett 114

Peter Nelson, University of Waterloo
Turan problems for matroids

Given a fixed simple binary matroid $N$, we study, for large $n$, the maximum size of a simple rank-$n$ binary matroid $M$ that does not contain $N$ has a restriction. We argue that such problems closely resemble analogous extremal problems for $H$-free graphs, using a matroidal analogue of chromatic number and deep tools from arithmetic combinatorics to give surprisingly exact answers to many such questions.

Friday, November 10, 2017

Posted November 3, 2017
Last modified November 9, 2017

9:00 am – 10:00 am 321 Lockett Hall

Xiao-Chuan Cai, University of Colorado Boulder
A Conversation with Prof. Xiao-Chuan Cai

The LSU SIAM Student Chapter is pleased to invite everyone, students and faculty, to a breakfast with Prof. Xiao-Chuan Cai to have a nice conversation about his career and work. His research interests are in the area of scientific and engineering computing including domain decomposition and multigrid methods for linear and nonlinear partial differential equations.

Posted August 22, 2017
Last modified September 26, 2017

Algebra and Number Theory Seminar Questions or comments?

11:00 am – 12:00 pm 1034 Digital Media Center

Xiao-Chuan Cai, University of Colorado Boulder
Numerical Simulation of Blood Flows in Human Arteries

Abstract: We discuss a parallel multilevel domain decomposition algorithm for the simulation of blood flows in arteries by solving a system of nonlinear partial differential equations consisting of an elasticity equation for the artery and an incompressible Navier-Stokes system for the blood flow. The system is discretized with a finite element method on unstructured moving meshes in 3D and solved by a Newton-Krylov algorithm preconditioned with an overlapping Schwarz method. A non-standard, isogeometric coarse mesh is introduced to ensure that the algorithm is scalable in terms of the total compute time when the number of processors is large. Several mathematical, bio-mechanical, and supercomputing issues will be discussed in detail. Simulation of blood flows in patient-specific pulmonary and cerebral arteries will be presented.

Additional details at: https://www.cct.lsu.edu/lectures/numerical-simulation-blood-flows-human-arteries

Tuesday, November 14, 2017

Posted August 31, 2017
Last modified November 9, 2017

3:10 pm – 4:00 pm 276 Lockett

Yifan Yang, National Taiwan University
Rational torsion points on the generalised Jacobian of a modular curve with cuspidal modulus

In this talk we consider the generalised Jacobian of the modular curve X_0(N) with respect to the reduced divisor given by the sum of cusps. When N is a prime power >3, we show that the group of rational torsion points on the generalised Jacobian tends to be much smaller than the classical Jacobian. This is a joint work with Takao Yamazaki.

Posted November 3, 2017

3:30 pm – 4:30 pm Hill Memorial Library Lecture Hall

College of Science Fall Faculty & Staff Convocation

Posted September 12, 2017
Last modified October 10, 2017

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Shawn Walker, LSU
A Finite Element Scheme for a Phase Field Model of Nematic Liquid Crystal Droplets

Abstract: We present a phase field model for nematic liquid crystal droplets. Our model couples the Cahn-Hilliard equation to Ericksen's one constant model for liquid crystals with variable degree of orientation. We present a special discretization of the liquid crystal energy that can handle the degenerate elliptic part without regularization. In addition, our discretization uses a mass lumping technique in order to handle the unit length constraint. Discrete minimizers are computed via a discrete gradient flow. We prove that our discrete energy Gamma-converges to the continuous energy and our gradient flow scheme is monotone energy decreasing. Numerical simulations will be shown in 2-D to illustrate the method. This work is joint with Amanda Diegel (post-doc at LSU). Near the end of the talk, I will discuss 3-D simulations of the Ericksen model coupled to the Allen-Cahn equations (with a mass constraint). This work is joint with REU 2017 students (E. Seal and A. Morvant).

Wednesday, November 15, 2017

Posted August 25, 2017
Last modified November 15, 2017

10:30 am – 12:00 pm Lockett 233

Sudipta Ghosh, Louisiana State University
Seiberg-Witten invariants of 4-manifolds with free circle actions

Posted November 15, 2017

3:30 pm – 4:30 pm Lockett 233

Mike Wong, Louisiana State University
Ends of moduli spaces in bordered Floer homology II

Abstract: This is the second in two consecutive talks about the ends of moduli spaces in Bordered Floer homology. Bordered Floer homology is an invariant associated to 3-manifolds with parametrized boundary, created by Lipshitz, Ozsvath, and Thurston as an extension of Heegaard Floer homology. In this framework, we associate a differential graded algebra A(F) to each surface, and an A-infinity module CF^(Y) to each bordered 3-manifold Y. The module CF^(Y) satisfies a structural equation that should be thought of as the analogue of the condition d^2=0 for chain complexes, obtained by considering ends of moduli spaces that appear in the definition of CF^(Y). In the talk last week, we discussed how these ends of moduli spaces match up in pairs in grid homology. In this talk, we will focus on the situation in bordered Floer homology, for both type A and type D structures.

Thursday, November 16, 2017

Posted September 1, 2017
Last modified November 8, 2017

3:30 pm – 4:20 pm Lockett 277

Yifan Yang, National Taiwan University
Some evaluations of hypergeometric functions from theory of Shimura curves

Abstract: Shimura curves are generalizations of classical modular curves. Because of the lack of cusps on Shimura curves, most of the methods for classical modular curves cannot possibly be extended to the case of Shimura curves. However, in recent years, there have been some methods for Shimura curves emerging in literature. Among them, one method is to realize modular forms in terms of solutions of the so-called Schwarzian differential equations. In the case where a Shimura curve has genus 0 and exactly three elliptic points, this means that modular forms can be expressed in terms of hypergeometric functions. In this talk, we will explain how this idea, together with arithmetic properties and CM theory of Shimura curves, leads to some beautiful evaluations of hypergeometric functions.

Friday, November 17, 2017

Posted November 15, 2017

4:30 pm – 5:30 pm Lockett 276

Josh Fallon, LSU
Criticality of Counterexamples to Edge-hamiltonicity on the Klein Bottle

Tutte and Thomas and Yu proved that 4-connected planar and projective-planar graphs, respectively, are hamiltonian. Grunbaum and Nash-Williams conjecture that 4-connected toroidal and Klein bottle graphs are hamiltonian. Thomassen constructed counterexamples to edge-hamiltonicity of four-connected toroidal and Klein bottle graphs. Ellingham and Marshall contribute to the characterization of four-connected toroidal graphs in which some edge is not on a hamilton cycle, showing a sort of criticality of Thomassen\'s counterexamples and their generalizations. In this talk, I will discuss the progress made toward determining hamiltonicity of 4-connected graphs on the torus and Klein bottle and show in Thomassen\'s Klein bottle counterexamples a criticality similar to that in toroidal graphs.

Tuesday, November 21, 2017

Posted November 19, 2017

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:30 pm – 4:20 pm Lockett 233

Sean Taylor, LSU
Mixed Categories of Sheaves on Toric Varities

Monday, November 27, 2017

Posted November 14, 2017

3:30 pm – 4:30 pm Lockett 241

Faculty Meeting

Monday, December 4, 2017

Posted November 30, 2017
Last modified December 3, 2017

3:30 pm Lockett 233

Michael Malisoff, LSU Roy P. Daniels Professor
Stability And Robustness Analysis For A Multispecies Chemostat Model With Delays

Abstract: The chemostat is a laboratory device and a mathematical model for the continuous culture of microorganisms. Chemostat models have been studied extensively, because of their importance in biotechnology and ecology. This talk will discuss a chemostat model with an arbitrary number of competing species, one substrate, and constant dilution rates. We allow delays in the growth rates and additive uncertainties. Using constant inputs of certain species as controls, we derive bounds on the sizes of the delays that ensure asymptotic stability of an equilibrium when the uncertainties are zero, which can allow persistence of multiple species. Under delays and uncertainties, we provide bounds on the delays and on the uncertainties that ensure input-to-state stability with respect to uncertainties. No prerequisite background in biology or control theory will be necessary to understand and appreciate this talk.

Wednesday, December 6, 2017

Posted November 14, 2017

3:30 pm – 4:20 pm Lockett 285

Anton Zeitlin, LSU
Enumerative geometry and quantum integrable systems

Abstract: The miraculous correspondence between 3-dimensional Gauge theory and integrable models based on quantum groups was observed by Nekrasov and Shatashvili in 2009. That discovery led to a lot of interesting developments in mathematics, in particular in enumerative geometry, bringing a new life to older ideas of Givental, and enriching it with flavors of geometric representation theory via the results of Braverman, Maulik, Okounkov and many others. In this talk I will focus on recent breakthroughs, originating from the work of Okounkov on the subject, leading to proper mathematical understanding of Nekrasov-Shatashvili original papers.

Posted November 14, 2017

3:30 pm – 4:20 pm Lockett 285

Anton Zeitlin, LSU
Enumerative geometry and quantum integrable systems

Thursday, December 7, 2017

Posted December 7, 2017

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:30 pm

Bach Nguyen, Louisiana State University
Hecke algebra and its interesting applications

Wednesday, December 13, 2017

Posted December 7, 2017
Last modified March 3, 2021

3:30 pm – 4:20 pm Lockett 285

Kenny De Commer, Vrije Universiteit Brussel
Three categorical pictures for quantum symmetric spaces

Using Tannaka-Krein methods, a duality can be constructed between actions of a compact quantum group on the one hand, and module C*-categories over its representation category on the other. In this talk, we will construct three module C*-categories for the q-deformed representation category of a compact semisimple Lie group G, starting from a compact symmetric space G/K for G. The first construction is based on the theory of cyclotomic KZ-equations developed by B. Enriquez. The second construction uses the notion of quantum symmetric pair as developed by G. Letzter. The third construction uses the notion of twisted Heisenberg algebra. In all cases, we show that the module C*-category is twist-braided — this is due to B. Enriquez in the first case, S. Kolb in the second case, and closely related to work of J. Donin, P. Kulish and A. Mudrov in the third case. We formulate a conjecture concerning equivalence of these twist-braided module C*-categories, and prove the equivalence in the simplest case of quantum SU(2). This is joint work with S. Neshveyev, L. Tuset and M. Yamashita.

Thursday, January 4, 2018

Posted October 24, 2017
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, January 5, 2018

Posted October 24, 2017
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 138

Comprehensive/PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Tuesday, January 9, 2018

Posted October 24, 2017
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Thursday, January 11, 2018

Posted December 17, 2017
Last modified October 4, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 277

Susanna Dann, Technical University of Vienna
Bounding marginal densities via affine isoperimetry

Let $\mu$ be a probability measure on $R^n$ with a bounded density $f$. We prove that the marginals of $f$ on most subspaces are well-bounded. For product measures, studied recently by Rudelson and Vershynin, our results show there is a trade-off between the strength of such bounds and the probability with which they hold. Our proof rests on new affinely-invariant extremal inequalities for certain averages of $f$ on the Grassmannian and affine Grassmannian. These are motivated by Lutwak's dual affine quermassintegrals for convex sets. We show that key invariance properties of the latter, due to Grinberg, extend to families of functions. The inequalities we obtain can be viewed as functional analogues of results due to Busemann–Straus, Grinberg and Schneider. As an application, we show that without any additional assumptions on $\mu$, any marginal $\pi_E(\mu)$, or a small perturbation thereof, satisfies a nearly optimal small-ball probability.

Tuesday, January 16, 2018

Posted December 11, 2017
Last modified January 14, 2018

3:10 pm – 4:00 pm 285 Lockett

Yinhuo Zhang, Universiteit Hasselt
Finite-dimensional quasi-Hopf algebras of Cartan type

In this talk, we present a general method for constructing finite-dimensional quasi-Hopf algebras from finite abelian groups and braided vector spaces of Cartan type. The study of such quasi-Hopf algebras leads to the classification of finite-dimensional radically graded basic quasi-Hopf algebras over abelian groups with dimensions not divisible by 2,3,5,7 and associators given by abelian 3-cocycles. As special cases , the small quasi-quantum groups are introduced and studied. Many new explicit examples of finite-dimensional genuine quasi-Hopf algebras are obtained.

Friday, January 19, 2018

Posted January 12, 2018
Last modified October 4, 2021

3:30 pm – 4:20 pm Lockett 241

Jake Fillman, Virginia Tech
Spectral properties of quasicrystals

Discovered in the early 1980s by Dan Shechtman, quasicrystals are solids that simultaneously exhibit aperiodicity (a lack of translation symmetries) and long-range order (quantified by the presence of Bragg peaks in their diffraction patterns). We will discuss almost-periodic Schrödinger operators, which supply a rich family of operator-theoretic models of quasicrystals. Our discussion will center around the spectral properties of the underlying operator and transport properties of the associated quantum dynamics. We will discuss how some of our results may be viewed as an inverse spectral theoretic obstruction to solving Deift's conjecture for the KdV equation with current technology. We will conclude with a discussion of results in higher dimensions that are motivated by the Bethe–Sommerfeld conjecture.

Monday, January 22, 2018

Posted January 13, 2018
Last modified January 19, 2018

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 241

Galyna Dobrovolska, Columbia University
A geometric Fourier transform, noncommutative resolutions, and Hilbert schemes

Abstract: I will start by defining and computing an example of a geometric Fourier transform for constructible functions, and more generally for constructible sheaves. Next I will explain how geometric representation theory can be used to study categories of modules over Lie algebras and more general algebras which quantize symplectic resolutions. Lastly I will apply the above techniques in the case of the Hilbert scheme of points in the plane. (This talk is based on a joint work in progress with R. Bezrukavnikov and I. Loseu and on my Ph.D. thesis)

Tuesday, January 23, 2018

Posted November 30, 2017
Last modified January 23, 2018

3:10 pm – 4:00 pm 285 Lockett

William Casper, Louisiana State University
Algebras of Differential Operators and Algebraic Geometry with Applications

The algebro-geometric structure of the centralizer of a differential operator has a strong influence over the value of the operator itself. This principle serves as the basis of the theory of soliton solutions of the Korteweg-de Vries equation. Furthermore, these ideas have been shown to have purely algebraic applications in the context of the Schottky's problem of characterizing Jacobian varieties. In this talk, we relate some of the historical highlights in the study of centralizers of differential operators. Following this, we describe some recent applications in the classification of bispectral differential operators. (The latter is based on joint work with Milen Yakimov and results from the author's Ph.D. thesis)

Posted January 16, 2018
Last modified November 29, 2022

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Amanda Diegel, Louisiana State University
The Cahn-Hilliard Equation, a Robust Solver, and a Phase Field Model for Liquid Crystal Droplets

We begin with an introduction to the Cahn-Hilliard equation and some motivations for the use of phase field models. We will then go on to describe a first order finite element method for the Cahn-Hilliard equation and the development of a robust solver for that method. The key ingredient of the solver is a preconditioned minimal residual algorithm (with a multigrid preconditioner) whose performance is independent of the spatial mesh size and the time step size for a given interfacial width parameter.

In the second part of the talk, we present a novel finite element method for a phase field model of nematic liquid crystal droplets. The model considers a free energy comprised of three components: the Ericksen's energy for liquid crystals, the Cahn-Hilliard energy for phase separation, and an anisotropic weak anchoring energy that enforces a boundary condition along the interface between the droplet and surrounding substance. We present the key properties of the finite element method for this model including energy stability and convergence and conclude with a few numerical experiments.

Wednesday, January 24, 2018

Posted August 23, 2017
Last modified January 23, 2018

10:30 am – 12:00 pm Lockett 233

Rob Quarles, Louisiana State University
The Alexander module

Posted January 12, 2018
Last modified January 17, 2018

3:30 pm – 4:20 pm Lockett 241

Christine Lee, University of Texas at Austin
Understanding quantum link invariants via surfaces in 3-manifolds

Abstract: Quantum link invariants lie at the intersection of hyperbolic geometry, 3-dimensional manifolds, quantum physics, and representation theory, where a central goal is to understand its connection to other invariants of links and 3-manifolds. In this talk, we will introduce the colored Jones polynomial, an important example of quantum link invariants. We will discuss how studying properly embedded surfaces in a 3-manifold provides insight into the topological and geometric content of the polynomial. In particular, we will describe how relating the definition of the polynomial to surfaces in the complement of a link shows that it determines boundary slopes and bounds the hyperbolic volume of many links, and we will explore the implication of this approach on these classical invariants.

Friday, January 26, 2018

Posted January 19, 2018
Last modified January 21, 2018

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 241

Shawn X. Cui, Stanford, Institute for Theoretical Physics
Four Dimensional Topological Quantum Field Theories

Abstract: We give an introduction to topological quantum field theories (TQFTs), which have wide applications in low dimensional topology, representation theory, and topological quantum computing. In particular, TQFTs provide invariants of smooth manifolds. We give an explicit construction of a family of four dimensional TQFTs. The input to the construction is a class of tensor categories called $G$-crossed braided fusion categories where $G$ is any finite group. We show that our TQFTs generalize most known examples such as Yetter's TQFT and the Crane-Yetter TQFT. It remains to check if the resulting invariant of 4-manifolds is sensitive to smooth structures. It is expected that the most general four dimensional TQFTs should arise from spherical fusion 2-categories, the proper definition of which has not been universally agreed upon. Indeed, we prove that a $G$-crossed braided fusion category corresponds to a 2-category which does not satisfy the criteria to be a spherical fusion 2-category as defined by Mackaay. Thus the question of what axioms properly define a spherical fusion 2-category is open.

Tuesday, January 30, 2018

Posted November 30, 2017
Last modified January 26, 2018

3:10 pm – 4:00 pm 285 Lockett

William Casper, Louisiana State University
The Prolate Spheroidal Phenomenon, Bispectrality, and Growth of Algebras

The prolate spheroidal phenomenon is the property that certain integral operators possess commuting differential operators. It has been long conjectured that integral operators possessing the prolate spheroidal property are closely related to bispectral functions. In this talk we demonstrate a general connection between the two topics by establishing a natural bi-filtration on the algebra of bispectral operators and measuring the growth rate. By obtaining an estimate for the growth rate, we are able to show that the bispectral operator algebra contains a differential operator commuting with an integral operator.

Wednesday, January 31, 2018

Posted January 24, 2018
Last modified January 30, 2018

Informal Geometry and Topology Seminar Questions or comments?

10:00 am – 12:00 pm Lockett 233

Rima Chatterjee, Louisiana State University
Transverse universal links

Posted January 22, 2018
Last modified October 4, 2021

3:30 pm – 4:20 pm Lockett 241

Larry Rolen, Trinity College Dublin & Georgia Tech
Jensen–Pólya Criterion for the Riemann Hypothesis and Related Problems

In this talk, I will summarize forthcoming work with Griffin, Ono, and Zagier. In 1927 Pólya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann's $\Xi$-function. This hyperbolicity has been proved for degrees $d <= 3$. We obtain an arbitrary precision asymptotic formula for the derivatives $\Xi^{(2n)}(0)$, which allows us to prove the hyperbolicity of 100 % of the Jensen polynomials of each degree. We obtain a general theorem which models such polynomials by Hermite polynomials. In the case of Riemann's $\Xi$-function, this proves the GUE random matrix model prediction for the distribution of zeros in derivative aspect. This general condition also confirms a conjecture of Chen, Jia, and Wang on the partition function.

Friday, February 2, 2018

Posted January 29, 2018

11:00 am – 12:00 pm Keisler Lounge, Room 321

A Conversation with Prof. Howard Elman

Posted September 14, 2017
Last modified January 29, 2018

12:30 pm – 3:30 pm Saturday, February 3, 2018 Digital Media Center Theatre

Scientific Computing Around Louisiana (SCALA) 2018

Posted January 21, 2018
Last modified October 4, 2021

3:30 pm – 4:20 pm Lockett 241

Chun-Hung Liu, Princeton University
Graph minors and topological minors

Minors and topological minors are two closely related graph containment relations that have attracted extensive attentions in graph theory. Though giant breakthroughs have been made over decades, several questions about these two relations remain open, especially for topological minors. This talk addresses part of our recent work in this direction, including a proof of Robertson's conjecture about well-quasi-ordering graphs by the topological minor relation, a complete characterization of the graphs having the Erdős–Pósa property with respect to topological minors which answers a question of Robertson and Seymour, and a proof of Thomas's conjecture on half-integral packing. More open questions, such as Hadwiger's conjecture on graph coloring and its variations and relaxations, will be discussed in this talk.

Monday, February 5, 2018

Posted February 4, 2018

11:00 am – 12:00 pm Lockett 239

Irfan Alam, LSU
Introduction to nonstandard methods

Abstract: This will be an expository talk on nonstandard analysis, of potential interest to all mathematicians. The framework of nonstandard analysis can be used to make rigorous the notion of infinitesimals in Leibniz'' original Calculus. The set of real numbers is extended to a larger ordered field (containing infinite and infinitesimal elements) that preserves the logical structure of the set of real numbers in some sense. This will be made precise in the talk. The tool of nonstandard extensions is not exclusive to this setting, and this talk will highlight some of the general principles that have seen applications in probability theory, combinatorial number theory, functional analysis, mathematical physics, etc. This talk will serve as background to a subsequent talk on recent work related to Gaussian measures.

Posted January 30, 2018

3:30 pm – 4:20 pm Lockett 241

Andrew Zimmer, William and Mary
Non-positive curvature in several complex variables

Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, sometimes this metric satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity) and one can then use these conditions to understand holomorphic maps.

Tuesday, February 6, 2018

Posted February 2, 2018

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 5:00 pm Lockett 232

Faculty Meeting

Wednesday, February 7, 2018

Posted January 24, 2018

10:00 am – 12:00 pm Lockett 233

Ryan Leigon, Louisiana State University
TBD

Posted February 5, 2018

3:30 pm – 4:30 pm Lockett 243

Raul Quiroga, Centro de Investigacion en Matematicas (CIMAT)
K-invariant Toeplitz operators on bounded symmetric domains

Monday, February 19, 2018

Posted February 17, 2018

Algebra and Number Theory Seminar Questions or comments?

11:00 am – 12:00 pm Lockett 239

Irfan Alam, LSU
Introduction to nonstandard methods - Part 2

Abstract: I will continue the introduction to nonstandard methods started in the previous talk. The concept of saturation will be introduced before we generalize the theory to abstract nonstandard extensions (of arbitrary structures). Some applications to Topology and Functional Analysis will be described. I will end the talk with a description of proof methods used in my recent work on Gaussian measures.

Tuesday, February 20, 2018

Posted November 30, 2017
Last modified February 19, 2018

3:10 pm – 4:00 pm 285 Lockett

Peng-Jie Wong, PIMS-University of Lethbridge
Holomorphy of L-functions and distribution of primes

The analytic properties of L-functions have been one of the central topics in number theory as they have many arithmetic applications. For example, the distribution of prime numbers has a deep connection with the properties of the Riemann zeta function. In general, for any number field, there are primes and L-functions of similar nature. In this talk, we shall discuss the holomorphy of such L-functions and its applications to the distributions of the associated primes.

Posted February 19, 2018

Informal Geometry and Topology Seminar Questions or comments?

6:00 pm – 7:00 pm Keiser Math Lounge Room 321

Lawrence Steinert, Casualty Actuary, Department of Insurance
ASA Club Meeting

Guest Speaker Larry Steinert presenting on his experience as a casualty actuary for the Louisiana Department of Insurance

Wednesday, February 21, 2018

Posted February 20, 2018

10:30 am – 12:00 pm Lockett 233

Configuration Spaces and Graph Realizability

Abstract: Embed a graph G generically into R^n as a bar framework (edges are rigid straight bars which are free to rotate around vertices). Fixing the edge lengths given by the embedding, what is the smallest integer d such that G can embed into R^d with the same edge lengths? As an example, no n-simplex can be generically embedded into R^{n-1}. Viewing the n-simplex as a complete graph, we see that the non-realizability of the n-simplex is a property of the complete graph. Are simplicies the minimal objects in some sense with regards to realizability? No, we can find generic 4-dim embeddings of the octahedron which do not admit 3-dim realizations. We will demonstrate a proof of this fact and examine several different characterizations of this correspondence between graphs and certain simplicial complexes as we try to build towards more complex and higher dimensional objects. This is a work in progress.

Posted January 30, 2018
Last modified January 10, 2022

3:30 pm – 4:30 pm Lockett 233

Shea Vela-Vick, Louisiana State University
Knot Floer homology and fibered knots

We prove that the knot Floer homology of a fibered knot is nontrivial in its next-to-top Alexander grading. Immediate applications include a new proof that L-space knots prime and a classification of knots 3-manifolds with rank 3 knot Floer homology. We will also discuss a numerical refinement of the Ozsváth-Szabó contact invariant. This is joint work with John Baldwin.

Thursday, February 22, 2018

Posted January 30, 2018
Last modified February 14, 2018

3:30 pm – 4:30 pm 1034 Digital Media Center

Ellya Kawecki, Oxford University
A discontinuous Galerkin finite element method for Hamilton Jacobi Bellman equations on piecewise curved domains

Abstract: We introduce a discontinuous Galerkin finite element method (DGFEM) for Hamilton Jacobi Bellman equations on piecewise curved domains, and prove that the method is consistent, stable, and produces optimal convergence rates. Upon utilising a long standing result due to N. Krylov, we may characterise the Monge Ampere equation as a HJB equation; in two dimensions, this HJB equation can be characterised further as uniformly elliptic HJB equation, allowing for the application of the DGFEM.

Friday, February 23, 2018

Posted October 16, 2017

12:00 pm – 4:00 pm Saturday, February 24, 2018 Digital Media Center Theatre

Finite Element Rodeo

Monday, February 26, 2018

Posted February 24, 2018

11:00 am – 12:00 pm Lockett 239

Hui-Hsiung Kuo, Mathematics Department, LSU
Multiplicative renormalization method for orthogonal polynomials

Abstract: I will give a very simple talk to show how I discovered this method and how powerful it can be. The ideas will be introduced through concrete examples.

Posted January 11, 2018
Last modified February 20, 2018

3:30 pm – 4:30 pm Lockett 233

Wei Li, LSU
Fluorescence ultrasound modulated optical tomography in diffusive regime

Fluorescence optical tomography (FOT) is an imaging technology that localizes fluorescent targets in tissues. FOT is unstable and of poor resolution in highly scattering media, where the propagation of multiply-scattered light is governed by the smoothing diffusion equation. We study a hybrid imaging modality called fluorescent ultrasound-modulated optical tomography (fUMOT), which combines FOT with acoustic modulation to produce high-resolution images of optical properties in the diffusive regime. The principle of fUMOT is to perform multiple measurements of photon currents at the boundary as the optical properties undergo a series of perturbations by acoustic radiation, in which way internal information of the optical field is obtained. We set up a Mathematical model for ufUMOT, prove well-posedness for certain choices of parameters, and present reconstruction algorithms and numerical experiments for the well-posed cases.

Tuesday, February 27, 2018

Posted February 19, 2018

Informal Geometry and Topology Seminar Questions or comments?

6:00 pm – 7:00 pm Keiser Math Lounge Room 321

Jared Braud, Starmount Life
ASA Club Meeting

Senior Actuarial student, Tia Jones will be presenting about her internship experience last summer. Jared Braud ASA, will be presenting his experience in specialty insurance on the health and life side.

Wednesday, February 28, 2018

Posted January 24, 2018
Last modified February 27, 2018

10:00 am – 12:00 pm Lockett 233

Yu-Chan Chang, Louisiana State University
Simplicial Volume

Abstract: Gromov introduced the simplicial volume in 1982, it is an invariant of manifolds. While several vanishing and non-vanishing results for the simplicial volume are known by now, the exact value of non-vanishing simplicial volumes is difficult to compute. In this talk, the bounded cohomology of spaces will be defined, then we will discuss some basic properties of simplicial volume and some celebrated results by Gromov and Thurston.

Posted November 13, 2017
Last modified February 26, 2018

3:30 pm – 4:30 pm Lockett 233

Ivan Levcovitz, CUNY Graduate Center
Coarse geometry of right-angled Coxeter groups

Abstract: A main goal of geometric group theory is to understand finitely generated groups up to a coarse equivalence (quasi-isometry) of their Cayley graphs. Right-angled Coxeter groups (RACGs for short), in particular, are important classical objects that have been unexpectedly linked to the theory of hyperbolic 3-manifolds through recent results, including those of Agol and Wise. I will give a background on the relevant geometric group theory, RACGs and what is currently known regarding the quasi-isometric classification of RACGs. I will then describe a new computable quasi-isometry invariant, the hypergraph index, and its relation to other invariants such as divergence and thickness.

Friday, March 2, 2018

Posted March 5, 2018

AWM

3:30 pm Lounge

Deborah Chun, West Virginia University Institute of Technology
Chat with Deborah Chun

This is an informal time to ask questions about Deb''s career, and to get advice for current graduated students. All graduate students and professors are invited, and there will be snacks.

Monday, March 5, 2018

Posted March 3, 2018

11:00 am – 12:00 pm Lockett 239

Irfan Alam, LSU
Introduction to nonstandard methods - Part 3

Abstract: In the first half of the talk, I will finish the basic introduction to nonstandard methods with some immediate applications to Topology and Functional Analysis (prefaced in the previous talk in this series). In the second half, I will explain my work on limits of spherical integrals and their connection with Gaussian measures from a nonstandard perspective.

Posted January 10, 2018
Last modified February 12, 2018

3:30 pm – 4:30 pm Lockett 233

Masato Kimura, Kanazawa University, Japan
A phase field model for crack propagation and some applications

Tuesday, March 6, 2018

Posted February 14, 2018

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Yi Zhang, University of North Carolina at Greensboro
Numerical Approximations for a Singular Elliptic Variational Inequality

Abstract: The displacement obstacle problem of simply supported plates is an example of a fourth order variational inequality. As the bending rigidity tends to zero the problem degenerates to an elastic membrane obstacle problem which is a second order variational inequality. In this talk we will introduce C0 interior penalty methods for this singular perturbed problem with small parameter. Robust error estimates with respect to the parameter will be presented. We also discuss the convergence of numerical solutions to the unperturbed second order elliptic variational inequality. This is joint work with Susanne Brenner and Li-yeng Sung.

Posted January 15, 2018
Last modified February 22, 2018

3:30 pm – 4:20 pm

Wen-Ching Winnie Li, Pennsylvania State University
colloquium this week

Posted February 22, 2018
Last modified February 25, 2018

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 284

Wen-Ching Winnie Li, Pennsylvania State University
Distribution of primes

Abstract: The distribution of prime numbers has been one of the central topics in number theory. It has a deep connection with the zeros of the Riemann zeta function. The concept of "primes" also arises in other context. For example, in a compact Riemann surface, as introduced by Selberg, primitive closed geodesic cycles play the role of primes; while in a finite quotient of a finite-dimensional building, for each positive dimension, there are primes of similar nature. In this talk we shall discuss the distributions of such primes and their connections with the analytic behavior of the associated zeta and L-functions.

Wednesday, March 7, 2018

Posted January 24, 2018
Last modified February 27, 2018

10:00 am – 12:00 pm Lockett 233

Federico Salmoiraghi, Department of Mathematics, LSU
TBD

Posted October 18, 2017
Last modified February 27, 2018

3:30 pm – 4:30 pm Lockett 233

Bulent Tosun, University of Alabama
Obstructing Stein structures on contractible 4-manifolds

Abstract: A Stein manifold is a complex manifold with particularly nice convexity properties. In real dimensions above 4, existence of a Stein structure is essentially a homotopical question, but for 4-manifolds the situation is more subtle. An important question that has been circulating among contact and symplectic topologist for some time asks: whether every contractible smooth 4-manifold admits a Stein structure? In this talk we will provide examples that answer this question negatively. Moreover, along the way we will provide new evidence to a closely related fascinating conjecture of Gompf, which asserts that a nontrivial Brieskorn homology sphere, with either orientation, cannot be embedded in complex 2-space as the boundary of a Stein submanifold. This is a joint work with Tom Mark.

Posted March 5, 2018

3:30 pm – 4:30 pm Lockett 277

Deborah Chun, West Virginia University Institute of Technology
Three Recent Results

The first result concerns matroid connectivity and basis exchange graphs for matroids. The second result gives the bicircular matroids representable over GF(4) and GF(5). The third result is the unavoidable minors for bicircular 4-connected matroids. Basis exchange graphs and bicircular matroids are introduced. Knowledge of matroids is assumed.

Thursday, March 8, 2018

Posted March 5, 2018

Student Algebra Seminar Graduate Student Algebra and Number Theory Seminar

3:15 pm – 4:15 pm Lockett 233

Bach Nguyen, LSU
Geometric and Algebraic Approaches to Representation Theory of Algebras

Monday, March 12, 2018

Posted March 11, 2018

11:00 am – 12:00 pm Lockett 239

George Cochran, Mathematics Department, LSU
Policy Iteration for Controlled Markov Chains

Abstract: In my consulting work in the gambling industry I have had several complex projects in the past five years that were solved using the algorithm of policy iteration in a controlled Markov chain (or Markov decision process). The 1960 Ph.D. thesis of Ronald Howard first described this algorithm and proved convergence. This talk will describe the algorithm and why and how it applies to the particular application of determining the optimal strategy for playing the game "Ultimate X Streak".

Posted January 16, 2018
Last modified October 1, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 233

Tadele Mengesha, The University of Tennessee, Knoxville
Sobolev regularity estimates for solutions to spectral fractional elliptic equations

Global Calderón-Zygmund type estimates are obtained for solutions to fractional elliptic problems over smooth domains. Our approach is based on the "extension problem" where the fractional elliptic operator is realized as a Dirichlet-to-Neumann map corresponding to a degenerate elliptic PDE in one more dimension. This allows the possibility of deriving estimates for solutions to the fractional elliptic equations from that of degenerate elliptic equations. We will confirm this first by obtaining weighted estimates for the gradient of solutions to a class of linear degenerate/singular elliptic problems over a bounded, possibly non-smooth, domain. The class consists of those with coefficient matrix that symmetric, nonnegative definite, and both its smallest and largest eigenvalues are proportion to a particular weight that belongs to a Muckenhoupt class. The weighted estimates are obtained under a smallness condition on the mean oscillation of the coefficients with a weight. This is a joint work with T. Phan.

Tuesday, March 13, 2018

Posted February 27, 2018
Last modified March 3, 2021

3:10 pm – 4:00 pm 285 Lockett

Laura Rider, University of Georgia
An Iwahori-Whittaker model for the Satake category

The geometric Satake equivalence gives a topological incarnation of the representation theory of a connected, reductive algebraic group over any field. This description uses so-called "spherical" perverse sheaves on the affine Grassmannian. In my talk, I'll discuss an Iwahori-Whittaker model for this category. This model takes advantage of a cellular stratification of the affine Grassmannian, and as a result, allows for some nice applications of the equivalence. This work is joint with Roman Bezrukavnikov, Dennis Gaitsgory, Ivan Mirkovic, and Simon Riche.

Posted January 30, 2018
Last modified February 14, 2018

3:30 pm – 4:30 pm 1034 Digital Media Center

Liping Wang, Nanjing University of Aeronautics and Astronautics
A Joint Matrix Minimization Approach and the Applications in Collective Face Recognition and Seismic Wavefield Recovery

Abstract: Recently, image-set based face recognition and multi trace seismic wavefield recovery have attracted extensive attention in pattern recognition and geophysical community. Representation coding is one of popular ways for both face recognition and seismic wave reconstruction. Similar representative coding pattern among the group of samples is observed both in facial images and seismic signals. To take account of the collective correlation from a given set of testing samples as well as each individual, a matrix minimization model is presented to jointly representing all the testing samples over the coding bases simultaneously. A generalized matrix norms employed to measure the interrelation of the multiple samples and the entries of each one. For solving the involved matrix optimization problem, a unified algorithm is developed and the convergence analysis is accordingly demonstrated for the range of parameters p in (0,1]. Extensive experiments on public data of facial images and real-world seismic waves exhibit the efficient performance of the joint technique over the state-of-the-art methods in recognition or recovery accuracy and computational cost.

Wednesday, March 14, 2018

Posted March 7, 2018
Last modified March 3, 2021

3:30 pm Lockett 277

James Oxley, Mathematics Department, LSU
The mathematical contributions of W.T. Tutte

Bill Tutte was born in 1917 in Newmarket, England, a town famous for the breeding of thoroughbred racehorses. To mark the centenary of his birth, there were many mathematical celebrations around the world last year. This talk, versions of which were presented at some of those celebrations, will discuss some of Bill's many profound mathematical contributions.

Posted October 18, 2017
Last modified March 13, 2018

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm

Ina Petkova, Dartmouth College
Knot Floer homology and the gl(1|1) link invariant

Abstract: The Reshetikhin-Turaev construction for the standard representation of the quantum group gl(1|1) sends tangles to C(q)-linear maps in such a way that a knot is sent to its Alexander polynomial. After a brief review of this construction, I will give an introduction to tangle Floer homology - a combinatorial generalization of knot Floer homology which sends tangles to (homotopy equivalence classes of) bigraded dg bimodules. Finally, I will discuss how to see tangle Floer homology as a categorification of the Reshetikhin-Turaev invariant. This is joint work with Alexander Ellis and Vera Vertesi.

Thursday, March 15, 2018

Posted March 1, 2018
Last modified March 6, 2018

3:30 pm – 4:20 pm 277 Lockett

Daniel Sternheimer, Rikkyo University & Institut de Mathématiques de Bourgogne
The reasonable effectiveness of mathematical deformation theory in physics

New fundamental physical theories can, so far a posteriori, be seen as emerging from existing ones via some kind of deformation. That is the basis for Flato's "deformation philosophy", of which the main paradigms are the physics revolutions from the beginning of the twentieth century, quantum mechanics (via deformation quantization) and special relativity.

On the basis of these facts we explain how symmetries of hadrons (strongly interacting elementary particles) could "emerge" by deforming in some sense (including quantization) the Anti de Sitter symmetry (AdS), itself a deformation of the Poincare group of special relativity.

The ultimate goal is to base on fundamental principles the dynamics of strong interactions, which originated over half a century ago from empirically guessed "internal" symmetries.

We start with a rapid presentation of the physical (hadrons) and mathematical (deformation theory) contexts, including a possible explanation of photons as composites of AdS singletons and of leptons as similar composites. Then we present a "model generating" framework in which AdS would be deformed and quantized (possibly at root of unity and/or in manner not yet mathematically developed with noncommutative "parameters").

That would give (using deformations) a space-time origin to the "internal" symmetries of elementary particles, on which their dynamics were based, and either question, or give a conceptually solid base to, the Standard Model, in line with Einstein's quotation: "The important thing is not to stop questioning. Curiosity has its own reason for existing."

Monday, March 19, 2018

Posted March 14, 2018
Last modified January 7, 2025

1:30 pm – 2:20 pm tba

Renling Jin, College of Charleston
Can nonstandard analysis produce new standard theorems?

The answer is yes. Nonstandard analysis which was created by A. Robinson in 1963 incorporates infinitely large numbers and infinitesimally small positive numbers consistently in our real number system. But the strength of nonstandard analysis in the research of standard mathematics has not seemed to be sufficiently appreciated by mathematical community. In the talk, we will introduce two parts of the work done by the speaker and his collaborators on the standard combinatorial number theory using nonstandard analysis. In each of these two parts new standard theorems that were proved by nonstandard methods will be presented.

The audience is not assumed to have prior knowledge of nonstandard analysis.

Refreshments will be served in the Keisler lounge at 1:00 pm

Posted January 10, 2018
Last modified February 5, 2018

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 233

Prashant Kumar Jha, LSU
Numerical analysis of finite element approximation of nonlocal fracture models

We discuss nonlocal fracture model and present numerical analysis of finite element approximation. The peridynamic potential considered in this work is the regularized version of the bond-based potential generally considered in peridynamic literature (Silling 2000). In the limit of vanishing nonlocality, peridynamic model behaves like a elastodynamic model away from a crack zone and has a finite fracture energy associate to crack set (Lipton 2014, 2016).Using this property we relate the parameters in a peridynamic potential with given elastic constant and fracture toughness. Before we consider finite element approximation, we show that the problem is well posed. We show the existence of evolutions in H^2 space. We consider finite element discretization in space and central difference in time to approximate the problem. Approximation is shown to converge in L^2 norm at the rate Ct\triangle t+C_sh^2/s^2. Here \triangle t is the size of time step, h is the mesh size, and is the size of horizon (nonlocal scale). Constants C_t and C_s are independent of h and \triangle t. In the absence of nonlinearity, stability of approximation is shown. Numerical results are presented to verify the convergence rate. This is a joint work with Robert Lipton.

Tuesday, March 20, 2018

Posted January 16, 2018
Last modified February 25, 2018

3:10 pm – 4:00 pm 285 Lockett

Rina Anno, Kansas State University
Non-split P^n-twists

P^n-objects were introduced in 2005 by Huybrechts and Thomas as objects E in D^b(Coh X) for a smooth projective X satisfying certain conditions, one of which is Ext^*(E,E) being isomorphic as a graded ring to H^*(P^n,C). These objects induce autoequivalences of D^b(Coh X) called P^n-twists. In 2011, Addington proposed a definition for P^n-functors that also define autoequivalences of the target category. One of the requirements in his definition is that if F is a P^n-functor and R is its right adjoint, RF\simeq \oplus H^i, where H is an autoequivalence of the source category of F. We are going to introduce the definition of a P^n-functor where RF is isomorphic to a repeated extension of id by H^i (a convolution of a complex of H^i's in some DG enhancement, which generalizes the direct sum), and provide a class of examples. This is joint work with Timothy Logvinenko.

Posted March 5, 2018

3:30 pm – 3:30 pm 1034 Digital Media Center

Jun-Hong Liang, Louisiana State University
Horizontal Dispersion of Buoyant Materials in the Ocean Surface Boundary Layer 1

Abstract: In this talk I will discuss our recent study that uses a large eddy simulation model for ocean surface gravity wave filtered incompressible Navier-Stokes equation to study how buoyant material spreads in the upper ocean. The results of the study will improve the prediction of the pathway of marine pollutants such as spilled oil and microplastics.

Posted March 23, 2018

6:00 pm – 7:00 pm Keiser Math Lounge Room 321

Winnie Sloan LSU alumna Senior Actuarial Assistant for Travelers in St. Paul, MN
ASA Club Meeting

Skype call with Winnie Sloan about mock interviews, college timeline for success in the actuarial problem, and presentation of a mock actuarial problem.

Wednesday, March 21, 2018

Posted March 14, 2018
Last modified January 7, 2025

Algebra and Number Theory Seminar Questions or comments?

10:30 am – 11:20 am tba

Renling Jin, College of Charleston
A taste of Logic -- from the reasoning of a thief to a painless proof of the incompleteness theorem of Godel.

We will present some fun part of mathematical logic including a puzzle, a true paradox, and a fake paradox. The discussion will lead to Godel's Incompleteness Theorem. Godel's Incompleteness Theorem is well-known but difficult to proof. We will present a heuristic proof of the theorem which should be sufficient to understand the idea of the rigorous proof of the theorem.

This talk will be accessible to undergraduate students.

Refreshments will be served in the Keisler Lounge at 10am.

Posted March 13, 2018
Last modified March 19, 2018

3:10 pm – 4:00 pm 285 Lockett

Neal Livesay, University of California, Riverside
Moduli spaces of irregular singular connections

A classical problem in mathematics is that of classifying singular differential operators. An algebro-geometric variant of this problem involves the construction of moduli spaces of connections on vector bundles over P^1 with singularities x_1,...,x_k. Locally (i.e., around a singularity x_i), a selection of a basis for the vector bundle induces a matrix form for the connection. The study of matrices associated to connections is analogous to the study of matrices associated to linear maps. In this talk, I will discuss a construction of moduli spaces of connections on P^1 which are locally diagonalizable, along with recent generalizations made by C. Bremer, D. Sage, and N. Livesay.

Posted January 10, 2018
Last modified March 20, 2018

3:30 pm – 4:30 pm Lockett 233

Adam Levine, Duke University
Piecewise-linear disks and spheres in 4-manifolds

Abstract: We discuss a variety of problems related to the existence of piecewise-linear (PL) embedded surfaces in smooth 4-manifolds. We give the first known example of a smooth, compact 4-manifold which is homotopy equivalent to the 2-sphere but for which the homotopy equivalence cannot be realized by a PL embedding. We also show that the PL concordance group of knots in homology 3-spheres is infinitely generated and contains elements of infinite order. This is joint work with Jen Hom and Tye Lidman.

Thursday, March 22, 2018

Posted December 17, 2017
Last modified October 4, 2021

Algebra and Number Theory Seminar Questions or comments?

3:00 pm – 3:50 pm Lockett 277

Guozhen Lu, University of Connecticut
Harmonic analysis on hyperbolic spaces and Sharp geometric inequalities

Sharp geometric and functional inequalities play an important role in modern analysis, geometry and partial differential equations. We will begin the talk with some overall review on the best constants and maximizers (aka optimizers) for geometric inequalities such as Sobolev inequalities, Hardy–Trudinger–Moser inequalities, and Caffarelli–Kohn–Nirenberg inequalities, etc. Then we will briefly explain why such inequalities are useful in analysis and geometry. We will then review the Poincaré model of hyperbolic spaces. Next, we will describe some recent works using the techniques of harmonic analysis on hyperbolic spaces to establish optimal geometric inequalities. These include the sharp Hardy-Adams inequalities on hyperbolic balls and Hardy–Sobolev–Maz'ya inequalities on upper half spaces or hyperbolic balls. Using the Fourier analysis on hyperbolic spaces, we will be able to establish sharper inequalities than those known classical inequalities in the literature. This talk in intended for general audience including graduate students.

Tuesday, March 27, 2018

Posted March 1, 2018

LSU Spring Break

Monday, April 2, 2018

Posted March 18, 2018

3:30 pm – 4:30 pm Lockett 233

Stephen Shipman, Mathematics Department, LSU
Reducibility of the Fermi surface for periodic quantum-graph operators

The Fermi, or Floquet, surface for a periodic operator at a given energy level is an algebraic variety that describes all complex wave vectors admissible by the periodic operator at that energy. Its reducibility is intimately related to the construction of embedded eigenvalues supported by local defects. The rarity of reducibility is reflected in the fact that a generic polynomial in several variables cannot be factored. The "easy" mechanism for reducibility is symmetry. However, reducibility ensues in much more general and interesting situations. This work constructs a class of non-symmetric periodic Schrodinger operators on metric graphs (quantum graphs) whose Floquet surface is reducible. The graphs in this study are obtained by coupling two identical copies of a periodic quantum graph by edges to form a bilayer graph. Reducibility of the Floquet surface for all energies ensues when the coupling edges have potentials belonging to the same asymmetry class, that is, when their "spectral A-functions" are identical. If the potentials of the connecting edges belong to different asymmetry classes, then typically the Floquet surface is not reducible. Bilayer graphene is a notable exception--its Floquet surface is always reducible.

Tuesday, April 3, 2018

Posted March 23, 2018

6:00 pm – 7:00 pm Keiser Math Lounge Room 321

Rod Friedy, Director of Life Actuarial Services, Louisiana Department of Insurance
ASA Club Meeting

Rod Friedy, FSA, MAAA will be presenting on the life actuarial profession.

Wednesday, April 4, 2018

Posted March 19, 2018

Informal Geometry and Topology Seminar Questions or comments?

8:30 am – 9:30 am Keisler Lounge, Room 321

A Conversation with Prof. Irene Fonseca

(sponsored by the LSU SIAM and AWM Student Chapters)

Posted January 24, 2018

10:00 am – 12:00 pm Lockett 233

Sudipta Ghosh, Louisiana State University
TBD

Posted November 7, 2017
Last modified March 13, 2018

Pasquale Porcelli Lecture Series Special Lecture Series

2:30 pm – 3:30 pm Dodson Auditorium

Irene Fonseca, Carnegie Mellon University
Porcelli Lecture 1: Mathematics and Imaging Science

(The talk is intended to be accessible to High School Students.) In this talk, we will address the mathematical treatment of image processing, including inpainting, recolorization, denoising, and machine learning schemes.

Posted November 7, 2017
Last modified March 13, 2018

Pasquale Porcelli Lecture Series Special Lecture Series

4:10 pm – 5:10 pm Dodson Auditorium

Irene Fonseca, Carnegie Mellon University
Porcelli Lecture 2: Mathematics and Materials Science

(Intended to be accessible to Undergraduate Students.) Abstract: Quantum dots are man-made nanocrystals of semiconducting materials. Their formation and assembly patterns play a central role in nanotechnology, and in particular in the optoelectronic properties of semiconductors. Changing the dots' size and shape gives rise to many applications that permeate our daily lives, such as the new Samsung QLED TV monitor that uses quantum dots to turn "light into perfect color"! Quantum dots are obtained via the deposition of a crystalline overlayer (epitaxial film) on a crystalline substrate. When the thickness of the film reaches a critical value, the profile of the film becomes corrugated and islands (quantum dots) form. As the creation of quantum dots evolves with time, materials defects appear. Their modeling is of great interest in materials science since material properties, including rigidity and conductivity, can be strongly influenced by the presence of defects such as dislocations. In this talk, we will use methods from the calculus of variations and partial differential equations to model and mathematically analyze the onset of quantum dots, the regularity and evolution of their shapes, and the nucleation and motion of dislocations.

Thursday, April 5, 2018

Posted November 7, 2017
Last modified March 13, 2018

Pasquale Porcelli Lecture Series Special Lecture Series

10:30 am – 11:30 am Digital Media Center Theater

Irene Fonseca, Carnegie Mellon University
Porcelli Lecture 3: Homogenization of Integral Energies Under Periodically Oscillating Differential Constraints

(The talk is intended to be accessible to Graduate Students.) Abstract: A homogenization result for a family of integral energies is presented, where the fields are subjected to periodic first order oscillating differential constraints in divergence form. We will give an example that illustrates that, in general, when the operators differential operators have non constant coefficients then the homogenized functional maybe be nonlocal, even when the energy density is convex. This work is based on the theory of A-quasiconvexity with variable coefficients and on two-scale convergence techniques.

Monday, April 9, 2018

Posted April 6, 2018

Algebra and Number Theory Seminar Questions or comments?

11:00 am – 12:00 pm Lockett 239

Exponential inequality for exit probability

Abstract: Exponential upper bounds for exit from a ball of radius $r$ before time $T$ will be discussed for Brownian motion in finite and infinite dimensions, stochastic integrals, and solutions of certain stochastic partial differential equations. The role of large deviation principle in obtaining exponential bounds will be illustrated in the context of two-dimensional stochastic Navier-Stokes equations with additive noise.

Tuesday, April 10, 2018

Posted January 15, 2018
Last modified April 8, 2018

3:10 pm – 4:00 pm 285 Lockett

Li Guo, Rutgers University at Newark
A Locality Principle of Renormalization via Algebraic Birkhoff Factorization

An interpretation of the locality principle in renormalization is that a locality property is preserved in the process of renormalization. We establish such a principle in the framework of the algebraic approach of Connes and Kreimer to quantum field renormalization, by working with their algebraic Birkhoff factorization. More precisely we show that if a regularization map is a locality map, then so is the corresponding renormalization map from the algebraic Birkhoff factorization. For this purpose, we introduce locality for various algebraic structures including those of a Hopf algebra, a Rota-Baxter algebra and a regularization map between the two algebras. For applications, we consider the exponential generating function of lattice points in a convex cone, giving rise to a meromorphic function with linear poles.

Posted March 5, 2018

3:30 pm – 4:30 pm 1034 Digital Media Center

Shu Lu, Univeristy of North Carolina at Chapel Hill
Statistical inference for sample average approximation of constrained optimization and variational inequalities

Abstract: The sample average approximation is widely used as a substitute for the true expectation function in optimization and equilibrium problems. We study how to provide a confidence region or confidence intervals for the true solution, once the SAA solution is obtained. Our method is based on the asymptotic distribution of the SAA solution, and we handle polyhedral constraints by examining the nonsmooth structure of the asymptotic distribution.

Posted April 10, 2018

Informal Geometry and Topology Seminar Questions or comments?

6:00 pm – 7:00 pm 321 Lockett Keiser Math Lounge

Winnie Sloan LSU alumna Senior Actuarial Assistant for Travelers in St. Paul, MN
ASA Club Meeting

Skype call with Winnie Sloan, ACAS from Travelers about the actuarial case competition

Wednesday, April 11, 2018

Posted March 19, 2018

10:30 am – 12:00 pm Lockett 233

Kent Vashaw, Louisiana State University
TBD

Posted March 21, 2018

3:30 pm – 4:20 pm Lockett 243

Joseph Grenier, Louisiana State University
Constructive and Topological Reflection Positivities

In the 1970''s, Osterwalder and Schrader introduced an axiom for Constructive Quantum Field Theories called Reflection Positivity. The uses and consequence of Reflection Positivity have been explored by Jaffe, Neeb, Olafsson, and more with numerous interesting results. It was only recently, in 2016, that Reflection Positivity was adapted to Topological Quantum Field Theory through the use of bordisms and categories. This talk will briefly introduce the constructive form of Reflection Positivity before discussing the categorical approach taken by Freed and Hopkins. The talk will be suitable for graduate students in algebra, analysis and topology.

Thursday, April 12, 2018

Posted December 26, 2017
Last modified April 2, 2018

3:30 pm – 4:20 pm Lockett 277

Stefan Kolb, Newcastle University
Quantum symmetric pairs

Abstract: Since they arose in the 1980s, quantum groups have become an integral part of representation theory with many deep applications, including canonical bases, link invariants and quantum integrable systems. Quantum symmetric pairs were originally invented to perform quantum group analogs of harmonic analysis on symmetric spaces. Over the past five years it has become increasingly clear that many of the applications and constructions for quantum groups allow analogs for quantum symmetric pairs. In this talk I will give an introduction to the theory of quantum symmetric pairs and explain some of the recent developments, illustrating them, where possible, in the simplest example of quantum sl(2).

Monday, April 16, 2018

Posted April 6, 2018
Last modified January 7, 2025

3:30 pm Lockett 239

Ken Goodearl, UCSB
How fast does a group or an algebra grow?

An algebraic object ``grows" from a set $X$ of generators as larger and larger combinations of those generators are taken. In the case of a group $G$, this means taking longer and longer products of generators and their inverses. For an algebra $A$ (a ring containing a field), it means taking linear combinations of longer and longer products of the generators. The growth rate of $G$ is the rate at which the number of elements that can be obtained as products of at most $n$ generators and their inverses grows with increasing $n$. The growth rate of $A$ amounts to counting dimensions of subspaces spanned by products of at most $n$ generators. These rates of growth provide important measures for the ``complexities" of $G$ and $A$, respectively. They may be given by a polynomial function or an exponential function, but there are quite a few surprises -- rates like a polynomial with degree $\sqrt 5$ can occur, or rates in between polynomial and exponential functions, whereas some other potential rates are ruled out. We will discuss the basic ideas of growth for groups and algebras; the distillation of growth rate into a ``dimension" for algebras; and the values that this dimension can take.

This talk will be accessible to undergraduate students.

Refreshments will be served in the Keisler Lounge at 3:00 pm.

Posted April 2, 2018

3:30 pm – 4:30 pm Lockett 233

Ivan Gudoshnikov, The University of Texas at Dallas
Stabilization of quasistatic evolution of elastoplastic systems subject to periodic loading

We consider an arrangement of m elastoplastic springs (elastoplastic system) that are connected according to a given graph. Each spring i is described by both elastic e_i and plastic p_i strains, but only the elastic strains e_i generate stress responses s_i. We develop an analytic framework to design time-periodic loadings which make the evolution s(t) of the stress vector s = (s_1, ..., s_m) converging to a globally asymptotically stable time-periodic regime. The core of our approach is in converting the problem into a sweeping process with a moving polyhedron, which was earlier proposed by Moreau [C.I.M.E. notes, 1974]. We prove that global stability of a unique periodic regime takes place if the moving polyhedron is a simplex, which we further link to a simple topological property of the elastoplastic system under consideration. To illustrate the abstract theorem, sample sweeping processes are solved numerically by the so-called catch-up algorithm (which we implement using a constrained quadratic optimization pack-age).

The preprint is available at https://arxiv.org/abs/1708.03084.

Tuesday, April 17, 2018

Posted March 5, 2018
Last modified March 19, 2018

3:30 pm – 4:30 pm 1034 Digital Media Center

Longfei Li, University of Louisiana at Lafayette
Overcoming the added-mass instability for coupling incompressible flows and elastic beams

Abstract: A new partitioned algorithm is described for solving fluid-structure interaction (FSI) problems coupling incompressible flows with elastic structures undergoing finite deformations. The new algorithm, referred to as the Added-Mass Partitioned (AMP) scheme, overcomes the added-mass instability that has for decades plagued partitioned FSI simulations of incompressible flows coupled to light structures. Within a Finite-Difference framework, the AMP scheme achieves fully second-order accuracy and remains stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The stability and accuracy of the AMP scheme is validated through mode analysis and numerical experiments. Aiming to extend the AMP scheme to an Finite-Element framework, we also develop an accurate and efficient Finite-Element Method for solving the incompressible Navier-Stokes Equations with high-order accuracy up-to the boundary.

Posted April 16, 2018

Informal Geometry and Topology Seminar Questions or comments?

6:00 pm – 7:00 pm Keiser Math Lounge Room 321

Winnie Sloan LSU alumna Senior Actuarial Assistant for Travelers in St. Paul, MN
ASA Club Meeting

Skype call with Winnie Sloan, ACAS from Travelers on the results of the actuarial case competition

Wednesday, April 18, 2018

Posted January 24, 2018
Last modified March 19, 2018

10:00 am – 12:00 pm Lockett 233

Nurdin Takenov, Louisiana State University
TBD

Posted April 6, 2018
Last modified January 7, 2025

3:30 pm Lockett 239

Ken Goodearl, UCSB
From dimension to Grothendieck groups and monoids

In trying to generalize the concept of ``dimension'' from finite dimensional vector spaces to structural size measures for other classes of mathematical objects, one quickly arrives at the idea that such ``sizes'' should be elements of some abelian group, so that (at the very least) sizes can be added. The natural group to use in linear algebra is $\bf Z$, but in general there is no obvious group at hand. Grothendieck pointed out how to construct an appropriate group as one satisfying a certain universal property. Typically, one wants to not only add but compare ``sizes'', in the sense of inequalities. To accommodate comparisons, a combined structure is needed -- an abelian group which is equipped with a (compatible) partial order relation. On the other hand, demanding subtraction for ``sizes'' is sometimes asking too much, and ``sizes'' should take values in a monoid rather than a group. We will introduce the above concepts and constructions in the context of modules over a ring, and we will discuss various examples.

Refreshments will be served in the Keisler lounge at 3:00 pm.

Thursday, April 19, 2018

Posted January 12, 2018
Last modified April 15, 2018

3:30 pm – 4:20 pm Lockett 277

Birge Huisgen-Zimmermann, University of California, Santa Barbara
Representations of Quivers with Relations

Abstract: It is well known that the representations of a finite dimensional algebra may be viewed as representations of a certain quiver (insider jargon for a finite directed graph). We will start by outlining the ultimate goals pursued in the theory of such representations and illustrate them with classical results and examples. In particular, we will discuss and exemplify the notions of tame and wild representation type.

Then we will zero in on a geometric approach to classifying representations of a quiver. A priori, "degenerations" of a given representation appear to constitute an obstacle on the road to classification. We will explain how this negative can be turned into a positive by harnessing degeneration theory towards the classification goal.

Friday, April 20, 2018

Posted April 16, 2018

AWM

2:30 pm – 3:30 pm Lockett 381

Birge Huisgen-Zimmermann, University of California, Santa Barbara
Informal meeting with Birge Huisgen-Zimmerman

The purpose of this meeting is to give graduate students a chance to ask questions about careerer life after graduate school and in particular how being female in a male dominated field impacts that experience. The event is primarily for female graduate students but is open to all.

Posted April 20, 2018

4:00 pm – 5:30 pm Keisler Lounge, Room 321

Movie Event

Join the chapter for a screening of the documentary "Top Secret Rosies"

Monday, April 23, 2018

Posted April 21, 2018

11:00 am – 12:00 pm Lockett 239

Arnab Ganguly, LSU
Moderate deviation of occupation measures of diffusions.

We will discuss weak convergence method to prove moderate deviations asymptotics of occupation measures of ergodic diffusions. Some concepts related to ergodicity of Markov processes will be discussed before.

Posted April 12, 2018
Last modified April 19, 2018

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 276 Lockett

Meeting of Tenured Faculty

Tuesday, April 24, 2018

Posted February 27, 2018
Last modified March 3, 2021

3:10 pm – 4:00 pm 285 Lockett

Soumya (Shom) Banerjee, Tulane University
Revisiting the Variety of Complete Quadrics

The variety of complete quadrics is a family of smooth projective variety that has a long and interesting history which rivals Grassmannian variety and Flag varieties. However, surprisingly little is known about its geometric structure. In this talk, I will explain our attempts to understand the geometry of this variety in an explicit way. This is a joint work with Mahir Can and Mike Joyce.

Wednesday, April 25, 2018

Posted April 17, 2018

3:30 pm Lockett 277

James Madden, Mathematics Department, LSU
A Generating Function for the Distribution of Runs in Binary Words

Let N(n,r,k) denote the number of binary words of length n that begin with 0 and contain exactly k runs (i.e., maximal subwords of identical consecutive symbols) of length r. We show that the generating function for the sequence N(n,r,0), n=0,1,..., is (1−x)(1−2x+x^r−x^{r+1})−1 and that the generating function for {N(n,r,k)} is x^{kr} time the k+1 power of this. We extend to counts of words containing exactly k runs of 1s by using symmetries on the set of binary words.

Posted November 12, 2017
Last modified November 5, 2021

3:30 pm – 4:30 pm Lockett 233

Miriam Kuzbary, Rice University
Perspectives on Link Concordance Groups

The knot concordance group has been the subject of much study since its introduction by Ralph Fox and John Milnor in 1966. One might hope to generalize the notion of a concordance group to links; however, the immediate generalization to the set of links up to concordance does not form a group since connected sum of links is not well-defined. In this talk, I will discuss two notions of a link concordance group: the string link concordance group due to Le Dimet in 1988 and one due to Matthew Hedden and myself based on the knotification construction of Peter Ozsvath and Zoltan Szabo. I will present invariants for studying these groups coming from Heegaard Floer homology and a new group theoretic invariant for studying concordance of knots inside in certain types of 3-manifold, as well a preliminary result involving more classical link concordance invariants.

Thursday, April 26, 2018

Posted January 30, 2018
Last modified April 23, 2018

3:30 pm – 4:20 pm Lockett 277

Luis Silvestre, University of Chicago
Integro-differential equations

Abstract: Integro-differential equations have been a very active area of research in recent years. In this talk we will explain what they are and in what sense they are similar to more classical elliptic partial differential equations. We will discuss connections with problems in probability, fluids and statistical mechanics.

Monday, April 30, 2018

Posted April 26, 2018
Last modified April 27, 2018

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm 136 Prescott

Meeting of Faculty

Tuesday, May 15, 2018

Posted April 30, 2018
Last modified May 6, 2018

3:10 pm – 4:00 pm 285 Lockett

Xingting Wang, Temple University
Representations of 4-dimensional Sklyanin algebras through Poisson geometry.

In 1982, Sklyanin constructed a certain noncommutative graded algebra A(E,\tau) depending on an elliptic curve E embedded in P^3 and a point \tau in E related to the Yang-Baxter equation in "quantum inverse scattering method". It was shown by Smith and Stafford that these so-called 4-dimensional Sklyanin algebras have the same Hilbert series as the polynomial algebra on four variables and possess excellent homological property. When \tau is torsion-free, Smith and Staniszkis proved that there are exactly 4-parametric families of non-trivial irreducible representations at each dimension of k >= 1. In this talk, we give all irreducible representations of A(E, \tau) when \tau is of finite order n>4 with the help of Poisson geometry and deformation quantization. This is a joint work of Chelsea Walton and Milen Yakimov.

Monday, August 13, 2018

Posted May 8, 2018
Last modified December 13, 2022

1:00 pm – 4:00 pm 232 Lockett

Comprehensive/PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, August 15, 2018

Posted May 8, 2018
Last modified December 13, 2022

1:00 pm – 4:00 pm 232 Lockett

Comprehensive/PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, August 17, 2018

Posted May 8, 2018
Last modified December 13, 2022

Informal Geometry and Topology Seminar Questions or comments?

1:00 pm – 4:00 pm 232 Lockett

Comprehensive/PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, August 29, 2018

Posted August 27, 2018

1:30 pm – 3:00 pm Lockett 233

Ignat Soroko, Louisiana State University
Right-angled Artin groups and their subgroups

I will define right-angled Artin groups, consider few examples and talk about some interesting classes of their subgroups: special subgroups in the sense of Haglund and Wise, and Bestvina-Brady kernels.

Posted August 14, 2018
Last modified August 27, 2018

3:30 pm – 4:30 pm Lockett 233

Ignat Soroko, Louisiana State University
Dehn functions of subgroups of right-angled Artin groups

The question of what is a possible range for the Dehn functions (a.k.a. isoperimetric profile) for certain classes of groups is a natural and interesting one. Due to works of many authors starting with Gromov, we know a lot about the isoperimetric profile for the class of all finitely presented groups. Much less is known for many natural subclasses of groups, such as subgroups of right-angled Artin groups. We prove that polynomials of arbitrary degree are realizable as Dehn functions of subgroups of right-angled Artin groups. The key step is to construct for each natural k a free-by-cyclic group with the monodromy automorphism growing as n^k, which is virtually special in the sense of Haglund and Wise. Then its double will have Dehn function growing as n^{k+2}. This is a joint work with Noel Brady.

Tuesday, September 4, 2018

Posted August 20, 2018

3:30 pm – 4:30 pm 1034 Digital Media Center

Jianchao Bai, Xian Jiaotong University
Deterministic and Stochastic ADMM for Structured Convex Optimization

Abstract: The Alternating Direction Method of Multipliers (ADMM) has a long history, but its algorithmic idea can be still used to design new algorithms for the application examples involving big-data. In this talk, we show our recent work about two kinds of deterministic ADMMs and a family of stochastic ADMM for solving structured convex optimization. We also present the convergence complexity of these ADMM-type algorithms. Several further questions are discussed finally. (Refreshments at 3pm.)

Posted August 29, 2018
Last modified March 3, 2021

Informal Geometry and Topology Seminar Questions or comments?

6:00 pm Keisler Lounge (Lockett 321)

Actuarial club meeting

Introducing the new officers-
President: Sarah Davidson
Vice-President: Matt Blanchard

Welcoming new members, discussion about preparing for a career as an actuary, and planning the fall semester's agenda.

Winnie Sloan, former ASA President and current Associate Actuary at Travelers Insurance, will attend via Skype.
Pizza will be served.

Wednesday, September 5, 2018

Posted August 16, 2018
Last modified September 7, 2018

1:30 pm – 3:00 pm Lockett 233

Andrew Zimmer, Louisiana State University
Metrics in several complex variables

Abstract: In this talk I'll define three classical metrics in several complex variables: the Kobayashi metric, the Bergman metric, and the K{\"a}hler-Einstein metric. After introducing these metrics, I'll describe how their geometric properties can be used to solve problems. The talk won't assume any prior background in complex analysis.

Posted August 16, 2018
Last modified September 3, 2018

3:30 pm – 4:30 pm Lockett 233

Andrew Zimmer, Louisiana State University
Limit sets of discrete subgroups

Given a discrete group of matrices one can define an associated limit set in projective space. In this talk I'll describe some results concerning the regularity of this limit set when the discrete group satisfies certain geometric properties.

Thursday, September 6, 2018

Posted August 13, 2018
Last modified September 2, 2018

3:30 pm Lockett 232

Ian Wood, School of Mathematics, University of Kent
Boundary triples and spectral information in abstract M-functions

Abstract: The Weyl-Titchmarsh m-function is an important tool in the study of forward and inverse problems for ODEs, as it contains all the spectral information of the problem. The abstract setting of boundary triples allows the introduction of an abstract operator M-function. It is then interesting to study how much spectral information is still contained in the M-function in this more general setting. Boundary triples allow for the study of PDEs, block operator matrices and many other problems in one framework. We will discuss properties of M-functions, their relation to the resolvent and the spectrum of the associated operator, and connections to the extension theory of operators.

Friday, September 7, 2018

Posted August 29, 2018

Lockett 232

Malcolm Brown, Department of Computer Science & Informatics, Cardiff University
Spectral problems on star graphs

We report on a two-step reduction method for spectral problems on a star graph with n+1 edges and a self-adjoint matching condition at the central vertex . The first step is a reduction to the problem on a single edge but with an energy depending boundary condition at the vertex. In the second step, by means of an abstract inverse result for m-functions, , a reduction to a problem on a path graph with two edges joined by continuity and Kirchhoff conditions is given. All results are proved for symmetric linear relations in an orthogonal sum of Hilbert spaces. This ensures wide applicability to various different realisations, in particular, to canonical systems and Krein strings which include, as special cases, Dirac systems and Stieltjes strings. Employing two other key inverse results by de Branges and Krein, we answer the question: If all differential operators are of one type, when can the reduced system be chosen to consist of two differential operators of the same type? This is joint work with Heinz Langer and Christine Tretter

Monday, September 10, 2018

Posted August 30, 2018

5:00 pm – 6:00 pm Math Lounge

Karl Mahlburg, Department of Mathematics, LSU
The Putnam competition

Tuesday, September 11, 2018

Posted September 7, 2018

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett Hall Keisler Lounge (Room 321)

What We Did This Summer

The LSU SIAM Student Chapter is hosting this annual event to discuss various summer experiences. All are welcome to attend! Pizza and drinks will be served.

Wednesday, September 12, 2018

Posted August 27, 2018
Last modified September 7, 2018

1:30 pm – 3:00 pm Lockett 233

Ryan Leigon, Louisiana State University
TBA

Monday, September 17, 2018

Posted August 30, 2018
Last modified March 2, 2021

5:00 pm – 6:00 pm Math Lounge

Irfan Alam, LSU
Matthew Bertucci, Louisiana State University
Summer math experiences

Tuesday, September 18, 2018

Posted September 17, 2018

3:30 pm – 4:30 pm 1034 Digital Media Center

Jose Garay, Louisiana State University
Asynchronous Optimized Schwarz Methods for Partial Differential Equations in Rectangular Domains

https://www.cct.lsu.edu/lectures/asynchronous-optimized-schwarz-methods-partial-differential-equations-rectangular-domains

Posted September 11, 2018
Last modified September 13, 2018

Informal Geometry and Topology Seminar Questions or comments?

6:00 pm Keiser Math Lounge (Lockett 321)

Ken Alleman, Pacific Life LSU Alumnus Actuarial Assistant for Pacific Life in Orange County, CA
ASA Club Meeting

Hearing from Mr. and Mrs. Alleman, who are both practicing actuaries at Pacific Life. They will be discussing their internship program, different areas of the actuarial field, new-hire trends, and answering any questions from members. Pizza will be served.

Wednesday, September 19, 2018

Posted August 27, 2018

1:30 pm – 3:00 pm Lockett 233

Ryan Leigon, Louisiana State University
TBA

Posted September 12, 2018
Last modified February 2, 2022

3:30 pm – 4:20 pm Lockett 232

Andreas Debrouwere, LSU
Factorization of quasianalytic vectors

In 1978 [1], Dixmier and Malliavin addressed the following problem: Let $E$ be a Banach space and let $(π, E)$ be a representation of a Lie group $G$ on $E$. This representation induces a continuous action $Π$ of the algebra $C_c^∞(G)$ on $E$ given by $$Π(f)e = \int_G f(g)π(g)e\mathrm{d}g,\quad f \in \mathcal{D}(G), e \in E,$$ and it restricts to a continuous action on the space of smooth vectors $E^∞$. Dixmier and Malliavin proved the following beautiful factorization result $$E^∞ = \text{span}(Π(\mathcal{D}(G))E^∞).$$ Recently, a similar factorization result was shown for analytic vectors [2, 3].

In this talk we will generalize these results for the case $G = (\mathbb{R}^d, +)$ in the following way: We consider a representation $(π, E)$ of $(\mathbb{R}^d, +)$ on a quasicomplete locally convex space $E$, introduce the notion of a quasianalytic vector (w.r.t. a general Denjoy-Carleman class) and show a Dixmier-Malliavin type result for the space of quasianalytic vectors. As an application, we present factorization results for various weighted convolution algebras of quasianalytic functions.

This talk is based on collaborative work with Bojan Prangoski and Jasson Vindas.

References
[1] J. Dixmier, P. Malliavin, Factorisations de fonctions et de vecteurs indéfiniment différentiables, Bull. Sci. Math. 102 (1978), 307–330.
[2] H. Gimperlein, B. Krötz, C. Lienau, Analytic factorization of Lie group representations, J. Funct. Anal. 262 (2012), 667–681.
[3] C. Lienau, Analytic representation theory of $(\mathbb{R}; +)$, J. Funct. Anal. 257 (2009), 3293–3308.

Monday, September 24, 2018

Posted September 12, 2018
Last modified September 21, 2018

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 233

Aynur Bulut, LSU
Logarithmically energy-supercritical Nonlinear Wave Equations: axial symmetry and global well-posedness

In nonlinear dispersive PDE, radial symmetry often plays a key role in allowing for more refined analysis of the nonlinear interactions which could lead to possible blowup. We will describe recent work where we have recently introduced a mechanism for relaxing assumptions of radiality by considering symmetry in a subset of the variables (for instance, assuming that the initial data is axially symmetric). We applied this philosophy to show global well-posedness and scattering in for the nonlinear wave equation in the logarithmically energy-supercritical setting, generalizing a result of Tao which was established for the radial case. The uses Morawetz and Strichartz estimates that have been adapted to the new symmetry assumption. These methods in fact bring a new perspective to sharp estimates for the energy-critical problem, along the lines of the influential work of Ginibre, Soffer, and Velo. This is joint work with B. Dodson

Wednesday, September 26, 2018

Posted August 27, 2018
Last modified September 24, 2018

1:30 pm – 12:00 am Saturday, September 15, 2018 Lockett 233

Yilong Wang, Louisiana State University
TBA

Posted August 16, 2018
Last modified September 24, 2018

3:30 pm – 4:30 pm Lockett 233

Yilong Wang, Louisiana State University
Modular tensor categories and Reshetikhin-Turaev TQFTs

Abstract: In this talk, we give a detailed introduction to modular tensor categories and the Reshetikhin-Turaev TQFT associated to them. Time permitted, I will talk about algebraic properties of the RT-TQFTs.

Posted September 12, 2018
Last modified September 18, 2018

3:30 pm – 4:20 pm Lockett 232
(Originally scheduled for Tuesday, September 25, 2018, 3:20 pm)

Jiuyi Zhu, LSU
Quantitative unique continuation of partial differential equations

Abstract: Motivated by the study of eigenfunctions, we consider the quantitative unique continuation (or quantitative uniqueness) of partial differential equations. The quantitative unique continuation is characterized by the order of vanishing of solutions, which describes quantitative behavior of strong unique continuation property. Strong unique continuation property states that if a solution that vanishes of infinite order at a point vanishes identically. It is interesting to know how the norms of the potential functions and gradient potentials control the order of vanishing. We will report some recent progresses about quantitative unique continuation in different Lebesgue spaces for semilinear elliptic equations, parabolic equations and higher order elliptic equations.

Monday, October 1, 2018

Posted August 30, 2018

5:00 pm – 6:00 pm Math Lounge

Shea Vela-Vick, Louisiana State University
TBA

Tuesday, October 2, 2018

Posted August 19, 2018
Last modified September 5, 2018

3:30 pm – 4:30 pm 1034 Digital Media Center

Nicholas Zabaras, University of Notre Dame
Bayesian Deep Learning for Predictive Scientific Computing

Abstract: We will briefly review recent advances in the solution of stochastic PDEs using Bayesian deep encoder-decoder networks. These models have been shown to work remarkably well for uncertainty quantification tasks in very-high dimensions. In this talk through examples in computational physics and chemistry, we will address their potential impact for modeling dynamic multiphase flow problems, accounting for model form uncertainty in coarse grained RANS simulations and providing the means to coarse graining in atomistic models. Emphasis will be given to the small data domain using Bayesian approaches. The training of the network is performed using Stein variational gradient descent. We will show both the predictive nature of these models as well as their ability to capture output uncertainties induced by the random input, limited data and model error. In closing, we will outline the integration of these surrogate models with generative adversarial networks for the solution of inverse problems. NOTE: Reception in 1034 DMC at 3pm. Additional details at: https://www.cct.lsu.edu/lectures/bayesian-deep-learning-predictive-scientific-computing

Posted September 28, 2018

3:30 pm – 4:20 pm Lockett 232

Alexey Karapetyants, Southern Federal University, Russia and SUNY Albany
Mixed norm spaces of analytic functions as spaces of generalized fractional derivatives of functions in Hardy type spaces

We present a new general approach to the definition of a class of mixed norm spaces of analytic functions on the unit disc in complex plane. We study a problem of boundedness of Bergman projection in this general setting. We apply this general approach for the new concrete cases when the norms of variable exponent Lebesgue space, Orlicz space or generalized Morrey space are used. In general, such introduced spaces are the spaces of functions which are in a sense the generalized Hadamard type derivatives of analytic functions having lq summable Taylor coefficients.

Posted October 1, 2018

Informal Geometry and Topology Seminar Questions or comments?

6:00 pm Keiser Math Lounge (Lockett 321)

Actuarial club meeting

Alumnus and former ASA president Taylor Daigle will visit. Pizza will be served.

Wednesday, October 3, 2018

Posted August 27, 2018
Last modified March 2, 2021

1:30 pm – 3:00 pm Lockett 233

Kent Vashaw, Louisiana State University
TBA

Posted September 26, 2018
Last modified October 4, 2021

3:30 pm – 4:20 pm Lockett 232

Alexey Karapetyants, Southern Federal University, Russia and SUNY Albany
On Bergman type spaces of functions of nonstandard growth and related questions.

We study various Banach spaces of holomorphic functions on the unit disc and half plane. As a main question we investigate the boundedness of the corresponding holomorphic projection. We exploit the idea of V.P. Zaharyuta, V.I. Yudovich (1962) where the boundedness of the Bergman projection in Lebesgue spaces was proved using Calderón–Zygmund operators. We treat the cases of variable exponent Lebesgue space, Orlicz space, Grand Lebesgue space and variable exponent generalized Morrey space. The major idea is to show that the approach can be applied to a wide range of function spaces. This opens a door in a sense for introducing and studying new function spaces of Bergman type in complex analysis. We also study the rate of growth of functions near the boundary in spaces under consideration and their approximation by mollifying dilations.

Monday, October 8, 2018

Posted August 31, 2018
Last modified February 2, 2022

3:30 pm – 4:30 pm Lockett 232

Karthik Adimurthi, Seoul National University
Partial existence result for Homogeneous Quasilinear parabolic problems beyond the duality pairing

In this talk, we will discuss the existence theory of distributional solutions solving \[ \begin{cases} u_t − \text{div}\,\mathcal{A}(x, t, ∇u) = 0&\text{on } Ω × (0, T),\\ u = u_0&\text{on } ∂Ω × (0, T),\\ u = 0&\text{on } Ω × {t = 0}, \end{cases} \] on a bounded domain $Ω$. The nonlinear structure $\mathcal{A}(x, t, ∇u)$ is modeled after the standard parabolic $p$-Laplace operator. In order to do this, we develop suitable techniques to obtain a priori estimates between the solution and the boundary data. As a consequence of these estimates, a suitable compactness argument can be developed to obtain the existence result. An interesting ingredient in the proof is the careful use of the boundedness of the Hardy-Littlewood Maximal function in negative Sobolev spaces.

Tuesday, October 9, 2018

Posted August 19, 2018
Last modified September 2, 2018

3:30 pm – 4:30 pm 1034 Digital Media Center

Minah Oh, James Madison University
The Hodge Laplacian on Axisymmetric Domains

Abstract: An axisymmetric problem is a problem defined on a three-dimensional (3D) axisymmetric domain, and it appears in numerous applications. An axisymmetric problem can be reduced to a sequence of two-dimensional (2D) problems by using cylindrical coordinates and a Fourier series decomposition. A discrete problem corresponding to the 2D problem is significantly smaller than that corresponding to the 3D one, so such dimension reduction is an attractive feature considering computation time. Due to the Jacobian arising from change of variables, however, the resulting 2D problems are posed in weighted function spaces where the weight function is the radial component r. Furthermore, formulas of the grad, curl, and div operators resulting from the so-called Fourier finite element methods are quite different from the standard ones, and it is well-known that these operators do not map the standard polynomial spaces into the next one. In this talk, I will present stability and convergence results of the mixed formulations arising from the axisymmetric Hodge Laplacian by using a relatively new family of finite element spaces that forms an exact sequence and that satisfies the abstract Hilbert space framework developed by Arnold, Falk, and Winther.

Wednesday, October 10, 2018

Posted August 27, 2018

1:30 pm – 3:00 pm Lockett 233

Federico Salmoiraghi, Department of Mathematics, LSU
TBA

Posted October 1, 2018

3:30 pm – 4:30 pm Lockett 233

Yilong Wang, Louisiana State University
Modular categories and RT-TQFTs: part II

Abstract: In this talk, I will define ribbon and modular categories, and show how modular categories give rise representations of the modular group SL(2,Z) using the graphical calculus introduced last time. Time permitted, I will explain how to generalize the construction to obtain a TQFT for closed surfaces.

Thursday, October 11, 2018

Posted August 29, 2018
Last modified October 1, 2018

3:30 pm – 4:20 pm Lockett 232

Guillermo Goldsztein , School of Mathematics, Georgia Institute of Technology
Synchronization of pendula clocks and metronomes

Abstract: In 1665, Huygens discovered that, when two pendulum clocks
hanged from a same wooden beam supported by two chairs, they synchronize
in anti-phase mode. Metronomes provides a second example of oscillators
that synchronize. As it can be seen in many YouTube videos, metronomes
synchronize in-phase when oscillating on top of the same movable surface.
In this talk, we will review these phenomena, introduce a mathematical
model, and analyze the the different physical effects. We show that, in a
certain parameter regime, the increase of the amplitude of the
oscillations leads to a bifurcation from the anti-phase synchronization
being stable to the in-phase synchronization being stable. We argue that
this may explain the experimental observations.

Monday, October 15, 2018

Posted August 25, 2018
Last modified August 29, 2018

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 233

Jiuyi Zhu, LSU
Nodal sets for Robin and Neumann eigenfunctions

We investigate the measure of nodal sets for Robin and Neumann eigenfunctions in the domain and on the boundary of the domain. A polynomial upper bound for the nodal sets is obtained for the Robin eigenfunctions. For the analytic domains, we show a sharp upper bound for the nodal sets on the boundary of the Robin and Neumann eigenfunctions. Furthermore, the sharp doubling inequality and vanishing order are obtained.

Wednesday, October 17, 2018

Posted August 27, 2018

1:30 pm – 3:00 pm Lockett 233

Lucas Meyers, Louisiana State University
TBA

Posted August 14, 2018
Last modified September 17, 2018

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 233

Joshua Sabloff, Haverford College
Length and Width of Lagrangian Cobordisms

Abstract: In this talk, I will discuss two measurements of Lagrangian cobordisms between Legendrian submanifolds in symplectizations: their length and their relative Gromov width. The Gromov width, in particular, is a fundamental global invariant of symplectic manifolds, and a relative version of that width helps understand the geometry of Lagrangian submanifolds of a symplectic manifold. Lower bounds on both the length and the width may be produced by explicit constructions; this talk will concentrate on upper bounds that arise from a filtered version of Legendrian contact homology, a Floer-type invariant. This is joint work with Lisa Traynor.

Monday, October 22, 2018

Posted September 7, 2018
Last modified September 30, 2018

3:10 pm – 4:00 pm 232 Lockett

Armin Straub, University of South Alabama
The congruences of Fermat, Euler, Gauss and stronger versions thereof

The Gauss congruences are a natural generalization of the more familiar Fermat and Euler congruences. Interesting families of combinatorial and number theoretic sequences are known to satisfy these congruences. Though a general classification remains wide open, Minton characterized constant recursive sequences satisfying Gauss congruences. We consider the natural extension of this question to Laurent coefficients of multivariate rational functions. One of the motivations for studying Gauss congruences lies in the fact that a certain interesting class of sequences, related to Ap\'ery-like constructions of linear forms in zeta values, conjecturally satisfies stronger versions of these congruences. We outline this story and indicate recent developments. The first part of this talk is based on joint work with Frits Beukers and Marc Houben, while the second part includes joint work with Dermot McCarthy and Robert Osburn.

Posted September 13, 2018
Last modified October 18, 2018

3:30 pm – 4:30 pm Lockett 233

Blaise Bourdin, Department of Mathematics, Louisiana State University
Variational phase-field models of fracture

Since their inception, over 20 years ago, variational phase-field models of fracture have become widely popular. Part of their success is undoubtedly due to their ability to be efficiently implemented in two and three space dimension, and to their demonstrated ability to capture complex fracture behavior in a wide range of situations. In this presentation, I will go back to the roots of this family of models, deriving Francfort and Marigo's variational approach to fracture from Griffith's classical theory. I will construct variational phase-field models as a numerical approximation for this approach. I will present numerical simulation highlighting the properties of this approximation, as well as some that cannot be fully explained by the mathematical theory. I will then describe an alternate construction as gradient-damage models can explain this behavior and will show how this dual view can address some of the long standing issues in the modeling of brittle solids, including crack nucleation and size effect. Finally, I will discuss ongoing extensions and open issues.

Tuesday, October 23, 2018

Posted October 19, 2018

Informal Geometry and Topology Seminar Questions or comments?

6:00 pm Kiesler Math Lounge (Lockett 321)

Brian Frey, Protective Life Insurance Company Actuary at Protective Life Insurance Company in Birmingham, AL
ASA Club Meeting

Video conference with Brain Frey, an actuary at Protective Life in Birmingham, AL. Discussing his experience with the profession and possible internship opportunities. Pizza will be served.

Wednesday, October 24, 2018

Posted August 27, 2018

1:30 pm – 3:00 pm Lockett 233

Sudipta Ghosh, Louisiana State University
TBA

Posted September 14, 2018
Last modified October 18, 2018

3:30 pm – 4:30 pm Lockett 233

Scott Baldridge, Louisiana State University
A new cohomology for planar trivalent graphs with perfect matchings

Abstract: In this lecture, I will describe a simple-to-compute polynomial invariant of a planar trivalent graph with a perfect matching (think: Jones polynomial for graphs). This polynomial is interesting because of what it detects: If the polynomial is non-zero when evaluated at one, then the perfect matching is even. Such a perfect matching implies that the graph can be 4-colored. I will then show how to categorify this polynomial to get a Khovanov-like cohomology theory for planar trivalent graphs and compute a couple of simple examples. If time, I will talk about some consequences of the cohomology theory.

Thursday, October 25, 2018

Posted August 14, 2018
Last modified October 23, 2018

3:30 pm – 4:20 pm Lockett 232

Hongjie Dong, Brown University
Interior and boundary regularity for the incompressible Navier-Stokes Equations

Abstract: The regularity theory for fluid equations is at the heart of fluid flow modeling and leads to many new ideas in scientific computing, differential equations, and statistics, and has been characterized as one of the outstanding technical challenges in this era. For sufficiently regular data, the local strong solvability of the incompressible Navier-Stokes equations is well understood. Such solution is unique and locally smooth in both spatial and time variables. On the other hand, the global in time strong solvability is an outstanding open problem for d \geq 3. Another important type of solutions are called Leray-Hopf weak solutions. In the pioneering works of Leray and Hopf, it is shown that evolving from any divergence-free vector field in $L_2$, there exists at least one Leray-Hopf weak solution to the Navier-Stokes Equations. Although the problems of uniqueness and regularity of Leray-Hopf weak solutions are still open, solutions are known to be partially regular in certain cases, and fully regular under certain criteria. In this talk, I will first review some previous results on the conditional regularity of solutions to the incompressible Navier-Stokes equations in the critical Lebesgue spaces, and then discuss a recent work which mainly addressed the boundary regularity issue.

Monday, October 29, 2018

Posted August 29, 2018

3:30 pm – 4:30 pm Lockett 233

Robert Lipton, Mathematics Department, LSU
Predicting complex fracture evolution using nonlocal dynamics

The dynamic fracture of brittle solids is a particularly interesting collective interaction connecting both large and small length scales. Apply enough stress or strain to a sample of brittle material and one eventually snaps bonds at the atomistic scale leading to fracture of the macroscopic specimen. We discuss a nonlocal model for calculating dynamic fracture. The force interaction is derived from a double well strain energy density function, resulting in a non- monotonic material model. The material properties change in response to evolving internal forces eliminating the need for a separate phase field to model the fracture set. (However there is no free lunch and the discrete model is posed in terms of a dense matrix and parallel computation must be used to solve fracture problems.) The model can be viewed as a regularized fracture model. In the limit of zero nonlocal interaction, the model recovers a sharp interface evolution characterized by the classic Griffith free energy of brittle fracture with elastic deformation satisfying the linear elastic wave equation off the crack set. We conclude with a numerical analysis of the model which is joint work with Prashant Jha.

Tuesday, October 30, 2018

Posted September 5, 2018
Last modified October 18, 2018

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Shawn Walker, LSU
A Numerical Scheme for the Generalized Ericksen Model of Liquid Crystals With Applications to Virus DNA Packing

Abstract: We consider the generalized Ericksen model of liquid crystals, which is an energy with 8 independent ``elastic'' constants that depends on two order parameters n (director) and s (variable degree of orientation). In addition, we present a new finite element discretization for this energy, that can handle the degenerate elliptic part without regularization, is stable and it Gamma-converges to the continuous energy. Moreover, it does not require the mesh to be weakly acute (which was an important assumption in our previous work). A minimization scheme for computing discrete minimizers will also be discussed. Furthermore, we include other effects such as weak anchoring (normal and tangential), as well as fully coupled electro-statics with flexo-electric and order-electric effects. We also present several simulations (in 2-D and 3-D) illustrating the effects of the different elastic constants and electric field parameters. At the end of the talk, we discuss a problem about the packing of DNA inside viral capsids. We show how the generalized Ericksen model can be used to simulate the packing of DNA inside viral capsids, and to estimate packing pressures inside the capsid. This part is joint with Carme Calderer (UMN), Dmitry Golovaty (U. Akron).

Wednesday, October 31, 2018

Posted August 27, 2018

1:30 pm – 3:00 pm Lockett 233

Rima Chatterjee, Louisiana State University
TBA

Posted October 26, 2018

2:30 pm – 3:30 pm Lockett 232

Scott Baldridge, Louisiana State University
A new polynomial invariant of planar trivalent graphs

Tutte discovered a polynomial derived from graphs that gave valuable information about the graph. In this talk, I will describe a simple-to-compute polynomial invariant of a planar trivalent graph with a perfect matching (think: the formula for computing the Tutte polynomial). This polynomial invariant is conjectured to count the number of 2-factors of the graph that contain the perfect matching. We will calculate some examples and show some implications of these counts, including questions about counting k-factors of n-regular graphs. In particular, we will explain why the conjecture implies that the polynomial can be used to detect when the perfect matching is even. We will end with a discussion of why this may be a pathway to understanding a non-computer based proof of the 4-color theorem for trivalent planar graphs.

Posted August 14, 2018
Last modified October 26, 2018

3:30 pm – 4:30 pm Lockett 233

Matthew Haulmark, Vanderbilt
Non-hyperbolic groups with Menger curve boundary

Abstract: In the setting of hyperbolic groups groups with Menger curve boundary are known to be abundant. Given the prevalence of negatively curved groups, it is was a surprising observation of Ruane that there were no known examples of non-hyperbolic groups with Menger curve boundary found in the literature. Thus Ruane posed the problem (early 2000's) of finding examples (alt. interesting classes) of non-hyperbolic groups with Menger curve boundary. In this talk I will discuss the first class of such examples. This is joint work with Chris Hruska and Bakul Sathaye.

Monday, November 5, 2018

Posted August 29, 2018

3:30 pm – 4:30 pm Lockett 233

Robert Lipton, Mathematics Department, LSU
Understanding nonlocal models for fracture simulation

The peridynamic model is increasingly being used and developed for fracture simulation. In this talk we go "under the hood" to see how nonlocal models can capture the fracture process and to see how they relate to existing fracture models. Along the way we show how the peridynamic energy is related to the Griffiths fracture energy and how the nonlocal evolution satisfies the principle of least action.

Tuesday, November 6, 2018

Posted November 2, 2018

Informal Geometry and Topology Seminar Questions or comments?

6:00 pm Kiesler Math Lounge (Lockett 321)

ASA Club Meeting

Summer Internship presentations and discussion from students Matt Blanchard and Jacob Doran. Pizza will be served.

Wednesday, November 7, 2018

Posted November 8, 2018

1:30 pm – 3:00 pm

Rima Chatterjee, Louisiana State University
Branches covers of contact manifolds II

Posted September 12, 2018
Last modified March 3, 2021

3:30 pm – 4:20 pm Lockett 232

Anton Zeitlin, LSU
Thoughts on Supermoduli

I will talk about various approaches to supermoduli spaces of punctured surfaces. After short introduction, I will briefly describe earlier results, regarding the construction of Penner-like coordinates on super-Teichmüller spaces for punctured surfaces. Then I will describe a "parallel" construction explicitly describing deformations of superconformal structures via data on fatgraphs and the associated Strebel differentials.

Posted October 15, 2018
Last modified October 23, 2018

3:30 pm – 4:30 pm Lockett 233

Andrew McCullough, Georgia Institute of Technology
Legendrian Large Cables and Non-uniformly Thick Knots

Abstract: We will define the notion of a knot type having Legendrian large cables, and discuss the fact that having this property implies that the knot type is not uniformly thick. In this case, there are solid tori in this knot type that do not thicken to a solid torus with integer slope boundary torus, and that exhibit new phenomena; specifically, they have virtually overtwisted contact structures. We will give an example of an infinite family of ribbon knots that have Legendrian large cables which fail to be uniformly thick in several ways not previously seen.

Thursday, November 8, 2018

Posted October 11, 2018
Last modified November 3, 2018

3:30 pm – 4:20 pm Lockett 232

Scott Ahlgren, University of Illinois at Urbana-Champaign
Kloosterman sums, Maass cusp forms, and partitions.

Abstract: Kloosterman sums are exponential sums which appear naturally in a wide range of applications in number theory. Maass cusp forms are real-analytic automorphic forms which are eigenfunctions of the Laplace operator; they encode information about a variety of arithmetical problems. The partition function is the basic function of additive number theory: it counts the number of ways to break a natural number into parts. I will describe these objects and their history, discuss connections between them, and discuss some deep conjectures about their properties. I will also describe some recent applications to the theory of partitions.

Monday, November 12, 2018

Posted September 10, 2018
Last modified October 30, 2018

3:30 pm – 4:30 pm Lockett 233

Yuri Antipov, Mathematics Department, LSU
Method of automorphic functions for an inverse problem of antiplane elasticity

A nonlinear inverse problem of antiplane elasticity (theory of harmonic functions) for a multiply connected domain is examined. It is required to determine the profile of $n$ uniformly stressed inclusions when the surrounding infinite body is subjected to antiplane uniform shear at infinity. A method of conformal mappings for circular multiply connected domains is employed. The conformal map is recovered by solving consequently two Riemann-Hilbert problems for piecewise analytic symmetric automorphic functions. For domains associated with the first class Schottky symmetry groups a series-form representation of a ($3n-4$)-parametric family of conformal maps solving the problem is discovered. Numerical results for two and three uniformly stressed inclusions are reported and discussed.

Tuesday, November 13, 2018

Posted November 13, 2018
Last modified January 7, 2025

3:30 pm – 4:20 pm Lockett 114

Joeseph E. Bonin, George Washington University
What do lattice paths have to do with matrices, and what is beyond both?

A lattice path is a sequence of east and north steps, each of unit length, that describes a walk in the plane between points with integer coordinates. While such walks are geometric objects, there is a subtler geometry that we can associate with certain sets of lattice paths. Considering such sets of lattice paths will lead us to examine set systems and transversals, their matrix representations, and geometric configurations in which we put points freely in the faces of a simplex (e.g., a triangle or a tetrahedron). Matroid theory treats these and other abstract geometric configurations. We will use concrete examples from lattice paths to explore some basic ideas in matroid theory and some of the many intriguing problems in this field.

This talk will be accessible to undergraduate students.

Posted September 5, 2018
Last modified October 18, 2018

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Andrew Gillette, University of Arizona
Serendipity Finite Element Methods in Theory and Practice

Abstract: Serendipity finite element methods present a promising computational advantage over traditional tensor product finite elements: a significant reduction in degrees of freedom without sacrificing the order of accuracy in the computed solution. The theory of serendipity methods dates back to the 1970s but has seen a resurgence of interest in recent years within the context of finite element exterior calculus and the Periodic Table of the Finite Elements. In this talk, I will review modern perspectives on the family of serendipity elements and present the accompanying family of ``trimmed serendipity'' elements from my recent work. On the practical side, I will also discuss developments on the construction of basis functions for serendipity-type elements and their use on non-affinely mapped mesh element geometries. This is joint work with Tyler Kloefkorn and Victoria Sanders.

Wednesday, November 14, 2018

Posted August 27, 2018
Last modified November 8, 2018

1:30 pm – 3:00 pm Lockett 233

Rob Quarles, Louisiana State University
TBA

Posted November 13, 2018
Last modified January 7, 2025

1:30 pm – 2:20 pm Lockett 235

Joeseph E. Bonin, George Washington University
Old and New Connections Between Matroids and Codes: A Short Introduction to Two Field

The theory of error-correcting codes addresses the practical problem of enabling accurate transmission of information through potentially noisy channels. The wealth of applications includes getting information to and from space probes, reliably accessing information from (perhaps scratched or dirty) compact discs, and storage in the cloud. There are many equivalent definitions of a matroid, each conveying a different perspective. Matroids generalize the ideas of linear independence, subspace, and dimension in linear algebra, and cycles and bonds in graph theory, and much, much more. The wealth of perspectives reflects how basic and pervasive matroids are. Matrodis arise naturally in many applications, including in coding theory. The aim of this talk is to give a glimpse of both of these fields, with an emphasis on several ways in which matroid theory sheds light on coding theory. One of these applications of matroid theory dates back to the 1970's; another is a relatively new development that is motivated by applications, such as the cloud, that require locally-repairable codes.

Posted November 5, 2018
Last modified March 2, 2021

3:30 pm – 4:30 pm Lockett 241

Joeseph E. Bonin, George Washington University
The 𝒢-Invariant of a Matroid

The 𝒢-invariant of a matroid was introduced by Derksen (2009), who showed that it properly generalizes the Tutte polynomial. Akin to the Recipe Theorem, which says that the Tutte polynomial is universal among invariants that satisfy deletion-contraction rules, Derksen and Fink (2010) showed that the 𝒢-invariant is universal among valuations, which are invariants that satisfy an inclusion/exclusion-like property on matroid base polytopes. We give a new view of 𝒢(M) as a generating function for the flags of flats of M. We use this perspective to explore the effect of some matroid constructions on the 𝒢-invariant. We identify some of the information that the 𝒢-invariant picks up that the Tutte polynomial does not, such as the number of circuits and cocircuits of a given size, and whether (apart from free extensions and free coextensions) the matroid is a free product of two other matroids. From 𝒢(M), we can deduce whether M is connected; however, we show that for each positive integer n, there are matroids M and N with 𝒢(M) = 𝒢(N) for which their connectivities satisfy λ(M) - λ(N) ≥ n. Much of this is joint work with Joseph Kung.

Posted October 15, 2018
Last modified January 10, 2022

3:30 pm – 4:30 pm Lockett 233

Marco Marengon, UCLA
Strands algebras and Ozsváth-Szabó's Kauffman states functor

Ozsváth and Szabó introduced in 2016 a knot invariant, which they announced to be isomorphic to the usual knot Floer homology. Their construction is reminiscent of bordered Floer homology: for example, their invariant is defined by tensoring bimodules over certain algebras. During the talk I will introduce a more geometric construction, closer in spirit to bordered sutured Floer homology, based on strands on a particular class of generalized arc diagrams. The resulting strands algebras are quasi-isomorphic to the Ozsváth-Szabó's algebras, suggesting that Ozsváth and Szabó's theory may be part of a hypothetical generalization of bordered sutured Floer homology. This is a joint work with Mike Willis and Andy Manion.

Monday, November 19, 2018

Posted September 12, 2018
Last modified January 24, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 233

Wei Li, LSU
Embedded eigenvalues for the Neumann–Poincaré operator

The Neumann–Poincaré operator and its adjoint are boundary-integral operators associated with harmonic layer potentials. We proved the existence of eigenvalues in the essential spectrum for the Neumann–Poincaré operator for certain Lipschitz curves in the plane with reflectional symmetry, when considered in the functional space in which it is self-adjoint. The proof combines the compactness of the Neumann–Poincaré operator for curves of class C^2 with the continuous spectrum generated by a corner. Even (odd) eigenfunctions are proved to lie within the continuous spectrum of the odd (even) component of the operator when a C^2 curve is perturbed by inserting a small corner.

Tuesday, November 20, 2018

Posted November 10, 2018
Last modified November 15, 2018

3:10 pm – 4:00 pm 232 Lockett

Yilong Wang, Louisiana State University
Higher Gauss sums of modular categories

In this talk, we will introduce the notion of a modular category with an emphasis on the Galois group action such a category. Then we will discuss a family of categorical invariants of a modular category called the higher Gauss sums as generalizations of the classical quadratic Gauss sums.

Tuesday, November 27, 2018

Posted November 10, 2018
Last modified November 25, 2018

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm 232 Lockett

Scott Baldridge, Louisiana State University
From Spatial Trivalent Graphs with Rigid Perfect Matchings to Categories of Cobordisms and Frobenius Algebras

In the first part of this talk, we introduce the notion of an "interlocking crossbar web", which generalizes knots and links to spatial trivalent graphs with rigid perfect matchings. We then define a new cohomology theory that is invariant of these webs and show how to compute it using simple examples. When the web is a knot (i.e., no crossbars), this cohomology theory reduces to the usual Khovanov Homology of the knot. When the web is planar, this cohomology is a recently-discovered invariant of the planar trivalent graph with its perfect matching. In the second part of the talk, we attempt to interpret this cohomology in terms of TQFTs: What is the category of cobordisms (2Cob) for this theory? In particular, what are examples of generators and relations in the category? How do these generators and relations relate to Frobenius Algebras? The second part of the talk is hoped to be more of a fruitful discussion between participants than a lecture.

Wednesday, November 28, 2018

Posted August 27, 2018
Last modified November 8, 2018

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm – 3:00 pm Lockett 233

Nurdin Takenov, Louisiana State University
TBA

Posted August 27, 2018

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm – 3:00 pm Lockett 233

Natthawut Phanachet, Louisiana State University
TBA

Posted November 27, 2018

Special seminar sponsored by the Woman in Math Program

3:30 pm – 4:30 pm Lockett 285

Erin Compaan, MIT
Dynamics of dispersive differential equations

This talk will introduce dispersive partial differential equations, and give some background on where they appear and techniques used to study them. I''ll then discuss results on existence and smoothness of solutions for a Korteweg--de Vries and a Boussinesq model.

Thursday, November 29, 2018

Posted September 5, 2018
Last modified November 26, 2018

3:30 pm – 4:20 pm Lockett 232

Ko Honda, UCLA
Convex hypersurface theory in higher-dimensional contact topology

Abstract: Contact 3-manifolds occupy a central role in low-dimensional topology due to their interactions with Floer-theoretic invariants. Convex surface theory and bypasses are extremely powerful tools for analyzing contact 3-manifolds and in particular have been successfully applied to many classification problems. After reviewing convex surface theory in dimension three, we explain how to generalize many of their properties to higher dimensions. This is joint work with Yang Huang.

Friday, November 30, 2018

Posted November 26, 2018

3:30 pm – 4:30 pm TBA

Charles Semple, University of Canterbury, New Zealand
When is a phylogenetic network reconstructible from its path distances?

Phylogenetic networks are a type of leaf-labelled, acyclic, directed graph used by evolutionary biologists to represent the ancestral history of species whose past includes reticulate (non-treelike) events. To what extent is an edge-weighted phylogenetic network determined by the path-length distances between its leaves? It is well known that such distances are sufficient to (uniquely) reconstruct phylogenetic trees. This result dates back to Zaretskii (1965), and underlies many widely-used tree reconstruction methods including the popular method of Neighbor-Joining. Does this sufficiency extend to phylogenetic networks? In this talk, we explore this question and discuss some recent results for the prominent class of tree-child networks.

Tuesday, December 4, 2018

Posted December 2, 2018

3:30 pm – 4:30 pm 1034 Digital Media Center

Xin Wang, University of Maryland
Semidefinite Optimization for Quantum Information Processing

Abstract: In this talk, I will show how to apply semidefinite optimization to study two basic lines of quantum information processing: entanglement manipulation and communication over quantum channels. Novel mathematical tools improve our understanding of the structure of quantum entanglement and the limits of information processing with quantum systems. In the first part, I will discuss the fundamental features of quantum entanglement and develop quantitative approaches to better exploit the power of entanglement. I will introduce a computable and additive entanglement measure to quantify the amount of entanglement, which also plays an important role as the improved semidefinite programming (SDP) upper bound of distillable entanglement. Notably, I will demonstrate the irreversibility of asymptotic entanglement manipulation under positive-partial-transpose-preserving quantum operations, resolving a long-standing open problem in quantum information. In the second part, I will develop a framework of semidefinite programs to evaluate the classical and quantum communication capabilities of quantum channels in both the non-asymptotic and asymptotic regimes, which can be applied as benchmarks for near-term quantum codes. In particular, I will discuss the first general SDP strong converse bound on the classical capacity of an arbitrary quantum channel and give in particular the best known upper bound on the classical capacity of the amplitude damping channel. I will further establish a finite resource analysis of classical communication over basic channels such as the quantum erasure channel.

Thursday, December 6, 2018

Posted November 2, 2018
Last modified December 3, 2018

3:30 pm – 4:30 pm Lockett 232

Faculty Meeting with Dean Peterson

Thursday, January 3, 2019

Posted October 28, 2018
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, January 4, 2019

Posted October 28, 2018
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Tuesday, January 8, 2019

Posted October 28, 2018
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, January 9, 2019

Posted September 7, 2018
Last modified January 6, 2019

3:30 pm – 4:30 pm Lockett 233

Genevieve Walsh, Tufts University
Relatively hyperbolic groups with planar boundary

Abstract: I will describe what a relatively hyperbolic group is, and give a lot of examples where the boundary is planar. Furthermore, I will explore some of the interesting phenomena that can occur and explain the significance of cut points in the boundary. Lastly I will discuss restrictions on the peripheral groups when the boundary is planar and without cut points.

Friday, January 11, 2019

Posted December 4, 2018
Last modified January 7, 2019

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 232

Ruoyu Wu, University of Michigan
Weakly interacting particle systems on random graphs: from dense to sparse

Abstract: We consider the asymptotic behaviors of weakly interacting (mean-field) particle systems on random graphs that could be dense or sparse. The system consists of a large number of nodes in which the state of each node is governed by a stochastic process that has a mean-field type interaction with the neighboring nodes. Such systems arise in many areas, including but not limited to neuroscience, queueing theory and social sciences, which we will discuss in this talk.

In the dense graph case, the limiting system is described by the classic McKean--Vlasov equation. Law of large numbers, propagation of chaos, and central limit theorems are established and turn out to be the same as those in the complete graph case.

In the sparse case, the limiting system is quite different and depends heavily on the graph structure. We obtain an autonomous characterization of the local dynamics of a typical node and its neighbors when the limiting graph is a D- regular tree or a Galton--Watson tree.

If time permits, certain queueing systems with non-mean-field interactions will be discussed.

Wednesday, January 16, 2019

Posted January 16, 2019
Last modified May 8, 2021

1:30 pm – 3:00 pm Lockett 233

Shea Vela-Vick, Louisiana State University
Arnold's dream: in search for higher-order helicity invariants

Arnold dreamed of a hierarchy of helicity invariants which could provide lower bounds for the $L_2$-energy of a vector field under appropriate deformations. Ordinary helicity is a field analogue of the standard linking number between curves, and this correspondence quickly leads to an integral expression for helicity. The general expectation is that higher-order helicity invariants should be obtained as field generalizations of higher order linking invariants, of which Milnor's triple-linking number is the first in line. In this talk, I'll survey some of the history behind helicity invariant and show how one can use configuration space techniques to obtain a geometrically natural integral expression for the Milnor triple-linking number.

Posted January 27, 2019

Algebra and Number Theory Seminar Questions or comments?

5:30 pm Keiser Math Lounge (Lockett 321)

ASA Club Meeting

Our visitor is Sayi Otoikhine, FSA. She is an LSU alumna and former club president. She currently is as an actuary for IBM. She will be giving a presentation to us via Skype. Pizza will be served.

Tuesday, January 22, 2019

Posted November 3, 2018
Last modified March 3, 2021

3:10 pm – 4:00 pm 114 Lockett

Ignacio Nahuel Zurrian, Universidad Nacional de Cordoba (National University of Cordoba)
Completeness of the Bethe Ansatz for an open q-boson system with integrable boundary interaction

We employ a discrete integral-reflection representation of the double affine Hecke algebra of type $C^\V$$C$ at the critical level $q=1$, to endow the open finite q-boson system with integrable boundary interactions at the lattice ends. It is shown that the Bethe Ansatz entails a complete basis of eigenfunctions for the commuting quantum integrals in terms of Macdonald's three-parameter hyperoctahedral Hall-Littlewood polynomials. This is a joint work with J.F. van Diejen and E. Emsiz.

Wednesday, January 23, 2019

Posted January 21, 2019
Last modified January 23, 2019

SUSY and Morse Theory Seminar

10:30 am – 11:20 am Lockett 233

Rob Quarles, Louisiana State University
A Brief Introduction to the Hodge Star

In this talk we introduce the Hodge star in several different ways, and consider some practical methods of computation.

Posted January 22, 2019

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm – 3:00 pm Lockett 233

Mike Wong, Louisiana State University
GRID invariants obstruct decomposable Lagrangian cobordisms

Abstract: Ozsvath, Szabo, and Thurston defined several combinatorial invariants of Legendrian links in the 3-sphere using grid homology, which is a combinatorial version of knot Floer homology. These, collectively called the GRID invariants, are known to be effective in distinguishing some Legendrian knots that have the same classical invariants. In this talk, we describe a recent result that the GRID invariants provide an obstruction to the existence of decomposable Lagrangian cobordisms between Legendrian links. This obstruction is stronger than the obstructions from the Thurston-Bennequin and rotation numbers, and is closely related to a recent result by Golla and Juhasz. This is joint work with John Baldwin and Tye Lidman.

Posted January 11, 2019
Last modified January 14, 2019

3:30 pm – 4:30 pm Lockett 232

William Feldman, University of Chicago
Interfaces in inhomogeneous media: pinning, hysteresis, and facets

Abstract: I will discuss some models for the shape of liquid droplets on rough solid surfaces. The framework of homogenization theory allows to study the large scale effects of small scale surface roughness, including interesting physical phenomena such as contact line pinning, hysteresis, and formation of facets.

Friday, January 25, 2019

Posted January 22, 2019

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Wenqing Hu, Missouri University of Science and Technology
Stochastic Approximations, Diffusion Limit and Randomly Perturbed Dynamical Systems - a probabilistic approach to machine learning

Abstract: The remarkable empirical performance of the Stochastic Gradient Descent (SGD) algorithm with constant learning rate has led to the effective training of many large-scale machine learning models in modern data science.

In this talk, we provide a theoretical understanding of the effectiveness of the SGD algorithm from a probabilistic approach. As the learning rate tends to zero, a stochastic differential equation is introduced to describe the diffusion limit of the discrete recursive scheme used in SGD. Based on this diffusion limit, we connect SGD with a randomly perturbed gradient system. This connection enables us to understand the stochastic dynamics of SGD via delicate probabilistic techniques in stochastic analysis (stochastic calculus). As examples, we will discuss several important theoretical problems around SGD that are raised by the daily practice of data scientists: How does SGD escape from stationary points (including saddle points and local minima)? Does SGD finally choose a local minimum point that agrees with the global minimum point of the loss function? How does SGD's noise covariance structure implicitly affect the regularization properties of its solution path? Our probabilistic approach provides insights into these problems through a unified mathematical framework that can also be carried to many other stochastic approximation algorithms.

Tuesday, January 29, 2019

Posted January 28, 2019
Last modified January 10, 2022

3:10 pm – 4:00 pm 232 Lockett

Wenbin Guo, University of Science and Technology of China
Recent some progress on finite groups

In this talk, we will discuss some recent developments of the theory of finite groups, which include F-hypercenter and its generalizations, the theory of quasi-F-groups, the generalization of Schur-Zassenhaus theorem, Hall theorem and Chunihin theorem and answers to two Wielandt's open problems.

Wednesday, January 30, 2019

Posted January 27, 2019

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm – 3:00 pm Lockett 233

Scott Baldridge, Louisiana State University
TBA

Posted August 28, 2018
Last modified January 14, 2019

3:30 pm – 4:30 pm Lockett 233

Francesco Lin, Princeton University
Monopole Floer homology and spectral geometry

Abstract: By studying the Seiberg-Witten equations, Kronheimer and Mrowka defined a package of invariants of three-manifolds called monopole Floer homology. In this talk, we discuss some interactions between this topological invariant and the spectral geometry of the Laplacian on the underlying Riemannian manifold, with the goal of understanding concrete examples of hyperbolic and Solv manifolds.

Posted January 23, 2019

5:30 pm – 6:30 pm Keiser Math Lounge (Lockett 321)

ASA Club Meeting

Our speaker for the second meeting of the semester will be Mr. Nick Klinka, FCAS. He is an LSU alumnus and is currently working as a Senior Actuarial Assistant at Allstate. He will be giving a presentation to us via Skype. Pizza will be served!

Thursday, January 31, 2019

Posted January 26, 2019
Last modified October 4, 2021

3:30 pm – 4:20 pm Lockett 232

Huanchen Bao, University of Maryland
From Schur-Weyl duality to quantum symmetric pairs

The classical Schur-Weyl duality relates the representation theory of general linear Lie algebras and symmetric groups. Drinfeld and Jimbo independently introduced quantum groups in their study of exactly solvable models, which leads to a quantization of the Schur duality relating quantum groups of general linear Lie algebras and Hecke algebras of symmetric groups.

In this talk, I will explain the generalization of the (quantized) Schur-Weyl duality to other classical types. This new duality leads to a theory of canonical bases arising from quantum symmetric pairs generalizing Lusztig's canonical bases on quantum groups.

Monday, February 4, 2019

Posted January 28, 2019

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Andrei Tarfulea, University of Chicago
Existence, continuation, and lower mass bounds for the Landau equation.

Abstract: Kinetic equations model gas and particle dynamics, specifically focusing on the interactions between the micro-, meso-, and macroscopic scales. Mathematically, they demonstrate a rich variety of nonlinear phenomena, such as hypoellipticity through velocity-averaging and Landau damping. The question of well-posedness remains an active area of research.
In this talk, we look at the Landau equation, a mathematical model for plasma physics arising from the Boltzmann equation as so-called grazing collisions dominate. Previous results are in the perturbative regime, or in the homogeneous setting, or rely on strong a priori control of the solution (the most crucial assumption being a lower bound on the density, as this prevents the elliptic terms from becoming degenerate).
We prove that the Landau equation has local-in-time solutions with no additional a priori assumptions; the initial data is even allowed to contain regions of vacuum. We then prove a "mass spreading" result via a probabilistic approach. This is the first proof that a density lower bound is generated dynamically from collisions. From the lower bound, it follows that the local solution is smooth, and we establish the mildest (to date) continuation criteria for the solution to exist for all time.

Tuesday, February 5, 2019

Posted November 3, 2018
Last modified February 3, 2019

3:10 pm – 4:00 pm 232 Lockett

Iván Angiono, Universidad Nacional de Cordoba (National University of Cordoba)
On Nichols algebras

Nichols algebras appeared naturally when several authors, led by Andruskiewitsch and Schneider, looked for the classification of (a family of) non semisimple finite dimensional Hopf algebras. They are a universal quotient of the tensor algebra of a braided vector space. The aim of this talk is to introduce Nichols algebras, present several examples, and finally give some properties when the braided vector space is of diagonal type.

Posted February 4, 2019

Informal Geometry and Topology Seminar Questions or comments?

4:10 pm – 5:00 pm Lockett 232

Faculty Meeting

Wednesday, February 6, 2019

Posted January 27, 2019
Last modified February 5, 2019

1:30 pm – 3:00 pm Lockett 233

Anton Zeitlin, LSU
Hidden Homotopy Symmetries of Einstein Field Equations

Abstract: We demonstrate that the Einstein field equations with extra fields known as B-field and dilaton, have a nontrivial underlying algebraic structure, known as homotopy Gerstenhaber algebra. Such homotopy algebra is a natural object associated to Courant algebroid in the vertex algebra formalism. We show that the Einstein equations coincide with the Maurer-Cartan equations for the L-infinity part of such Gerstenhaber algebra.

Posted February 3, 2019

3:30 pm – 4:20 pm Lockett 276

Boris Rubin, Louisiana State University
Radon Transforms for Mutually Orthogonal Affine Planes

Abstract: We study a Radon-like transform that takes functions on the Grassmannian of j-dimensional affine planes in $R^n$ to functions on a similar manifold of k-dimensional planes by integration over the set of all j-planes that meet a given k-plane at a right angle. This transform has a mixed structure, combining the k-plane transform and the dual j-plane transform. The main results include action of such transforms on rotation invariant functions, sharp existence conditions, intertwining properties, connection with Riesz potentials and inversion formulas. The case j+k=n-1 for n odd was considered by S. Helgason and F. Gonzalez. This is a joint work with Yingzhan Wang (Guangzhou University).

Thursday, February 7, 2019

Posted November 21, 2018
Last modified February 3, 2019

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Daniel Nakano, University of Georgia
On Donkin's Conjectures

Abstract: Let $G$ be a simple, simply connected algebraic group over an algebraically closed field of prime characteristic. Recent work of Kildetoft and Nakano and of Sobaje has shown close connections between two long-standing conjectures of Donkin: one on tilting modules and the lifting of projective modules for Frobenius kernels of $G$ and another on the existence of certain filtrations of $G$-modules. In this talk, I will survey recent results in this area and present new results where we verify the one direction of Donkin's $(p,r)$ Filtration Conjecture for rank 2 groups for all primes. I will also show a recently discovered counterexample to the Tilting Module Conjecture. These results represent joint work with Christopher Bendel, Cornelius Pillen and Paul Sobaje.

Posted February 2, 2019
Last modified March 2, 2021

Extracurricular Mathematics Research Seminar on Flow Semigroups

4:30 pm – 5:20 pm Prescott 203
(Originally scheduled for Saturday, February 2, 2019)

Rainer Nagel, University of Tübingen
Global Linearization of Nonlinear Dynamical Systems

Posted February 6, 2019

Extracurricular Mathematics Research Seminar on Flow Semigroups

5:30 pm – 6:20 pm Prescott 203

Amy Adair, LSU
Arun Banjara, LSU
Rohin Gilman, LSU
Logan Hart, LSU
Flow Semigroups, Superstability, and Nonlinear Lie-Trotter Type Product Formulas

Tuesday, February 12, 2019

Posted November 3, 2018
Last modified February 9, 2019

3:10 pm – 4:00 pm 232 Lockett

Ignacio Nahuel Zurrian, Universidad Nacional de Cordoba (National University of Cordoba)
Time-Band-Limiting for Matrix-valued functions

The subject of time-band-limiting, originating in signal processing, is dominated by the "miracle" that a naturally appearing integral operator admits a commuting differential one allowing for a numerically efficient way to compute its eigenfunctions. Bispectrality is an effort to dig into the reasons behind this miracle. This search has revealed unexpected connections with several parts of mathematics. In this talk consider a matrix valued version of bispectrality and give a general condition under which we can display a constructive and simple way to obtain the commuting differential operator. Furthermore, we will build an operator that commutes with both the time-limiting operator and the band-limiting operators.

Wednesday, February 13, 2019

Posted January 27, 2019

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm – 3:00 pm Lockett 233

Andrew Zimmer, Louisiana State University
TBA

Posted February 12, 2019

3:00 pm – 3:30 pm Lockett 232

Faculty Meeting

Posted February 11, 2019

3:30 pm – 4:20 pm Lockett 276

Andreas Debrouwere, LSU
The solution to the first Cousin problem for classes of quasianalytic functions

The solution to the (first) Cousin problem on Stein open sets is a classical result in the theory of functions of several complex variables. As a consequence, the Cousin problem is solvable for the class of real analytic functions on an arbitrary open set of \R^d. The aim of this talk is to explain this problem and show that it is solvable for general classes of quasianalytic functions. Our solution makes use of the so-called Mittag-Leffler procedure, which will also be discussed during the talk.

Posted February 7, 2019

5:30 pm Keiser Math Lounge (Lockett 321)

ASA Club Meeting

Hearing from speaker Mr. Matthew Arnold, FSA, MAAA. He works at BlueCross BlueShield of Louisiana in Baton Rouge, LA as the Director of Actuarial Valuation and Senior Products. His presentation is on Commercial Risk Adjustment. Pizza will be served.

Thursday, February 14, 2019

Posted August 29, 2018
Last modified March 3, 2021

3:30 pm – 4:20 pm Lockett 232

Iván Angiono, Universidad Nacional de Cordoba (National University of Cordoba)
Finite-dimensional pointed Hopf algebras over abelian groups

Hopf algebras appeared in the 50s associated to algebras of functions of algebraic groups, with a well-known bijection when we restrict to commutative Hopf algebras over the complex numbers. Other classical examples of Hopf algebras are the enveloping algebras of Lie algebras, which in turn are co-commutative. In the 80s Drinfeld and Jimbo introduced quantized versions of these enveloping algebras, which are examples of non-commutative nor co-cocommutative Hopf algebras with several applications to Mathematics and Physics. Related with them, Lusztig introduced in the 90s finite-dimensional versions, the so-called small quantum groups. All these Hopf algebras are pointed: the coradical is a group algebra, which dominates the structure of the Hopf algebra and becomes a first invariant to describe it. In this talk we present the classification of finite-dimensional Hopf algebras whose group is abelian. We start from the basic definitions with the first known examples. Then we recall the Lifting Method introduced by Andruskiewitsch and Schneider, a fundamental step for their classification result when the order of the group is coprime with 210. We describe Nichols algebras of diagonal type (some kind of algebras closely related to our problem) and the classification obtained by Heckenberger. Next we give a presentation by generators and relations and the first consequences of this result. Finally we give a generalization of the Lifting Method to obtain deformations of graded Hopf algebras and the end of the classification, a result by myself, Andruskiewitsch and Garcia Iglesias, and some consequences about tensor categories attached to these Hopf algebras.

Friday, February 15, 2019

Posted August 19, 2018

Informal Geometry and Topology Seminar Questions or comments?

12:00 pm – 4:00 pm Saturday, February 16, 2019 Tulane University

Scientific Computing Around Louisiana (SCALA) 2019

Wednesday, February 20, 2019

Posted January 27, 2019

1:30 pm – 3:00 pm Lockett 233

Ryan Leigon, Louisiana State University
TBA

Thursday, February 21, 2019

Posted August 22, 2018
Last modified February 17, 2019

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Nicolas Andruskiewitsch, Universidad Nacional de Cordoba (National University of Cordoba)
On the classification of finite-dimensional Hopf algebras

Abstract: A gentle overview of the status of the classification of finite-dimensional Hopf algebras with emphasis on the relations with Lie theory.

Tuesday, February 26, 2019

Posted November 3, 2018
Last modified February 22, 2019

3:10 pm – 4:00 pm 232 Lockett

Nicolas Andruskiewitsch, Universidad Nacional de Cordoba (National University of Cordoba)
The classification of Hopf algebras with finite Gelfand-Kirillov dimension

The classification of Hopf algebras with finite Gelfand-Kirillov dimension has received attention recently. Nichols algebras play an important role in this question that will be explained in the talk together with an overview of examples and partial results.

Wednesday, February 27, 2019

Posted January 27, 2019
Last modified February 21, 2019

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm – 3:00 pm Lockett 233

Yu-Chan Chang, Louisiana State University
Introduction to handlebody groups

Abstract: Handlebody group is the mapping class group of a 3-dimensional handlebody, it is a subgroup of the mapping class group of the boundary surface of that handlebody. In this introductory talk, I will talk about some properties of handlebody groups and how different they are from the surface mapping groups.

Posted February 22, 2019

5:30 pm Keiser Math Lounge (Lockett 321)

ASA Club Meeting

Ms. Shelley Johnson, a consulting actuary at Foster & Foster, LLC, will be our speaker. She works with the major state retirement systems and will be presenting about her job and other actuarial topics. Pizza will be served.

Thursday, February 28, 2019

Posted October 18, 2018
Last modified February 17, 2019

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Matthew Hedden, Michigan State University
Knot theory and algebraic curves

Abstract: The modern study of knots and links has important roots in the theory of algebraic curves, where links encode subtle features of singularities. This thread was taken in interesting new directions in the 20th century, and the interaction between links in 3-dimensional manifolds and algebraic curves in complex surfaces continues to be a rich and beautiful area. In this talk I will survey the subject, from its seeds in the work of Newton to interesting advances which have occurred in the past decade.

Friday, March 1, 2019

Posted December 27, 2018
Last modified February 22, 2019

3:10 pm – 4:00 pm 232 Lockett

Eric Rowell, Texas A&M
Representations of Mapping Class Groups and Motion Groups

(2+1)TQFTs and their algebraic counterparts (modular categories) provide finite dimensional representations
of mapping class groups, such as the braid group and SL(2,Z). Analogously, one expects to (3+1)TQFTs to
give us representations of motion groups, such as the loop braid group--the motions of the n-component unlink.
I will describe a few questions related to these representations, some of which are motivated by topological quantum
computation, and what is currently known about their answers.

Tuesday, March 5, 2019

Posted December 11, 2018

Algebra and Number Theory Seminar Questions or comments?

Mardi Gras Holiday

Tuesday, March 12, 2019

Posted October 1, 2018
Last modified October 26, 2018

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm 232 Lockett
(Originally scheduled for Tuesday, November 20, 2018)

Luca Candelori, Wayne State University
Transcendence of Periods and Endomorphism Algebras of Jacobian Varieties

In this talk I will describe a new method to bound the number of linear relations with algebraic coefficients between the periods of an algebraic curve. As shown by Shiga and Wolfart, these bounds provide information regarding the dimension of the endomorphism algebra of the corresponding Jacobian variety. I will explain how to employ these new bounds to explore two of the many open questions about endomorphism algebras of Jacobians: which Jacobians have complex multiplication, and which Jacobians are totally decomposable.

Wednesday, March 13, 2019

Posted January 27, 2019
Last modified March 13, 2019

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm – 3:00 pm Lockett 233

Nurdin Takenov, Louisiana State University
3-coloring and other invariants of knots

Abstract: 3 coloring invariant is, perhaps, the simplest knot invariant. Nevertheless, as shown by Przytycki, it can be strengthened and is connected to other knot invariants, like uncrossing number and Jones polynomial. In my talk I will describe these results.

Posted March 7, 2019

3:30 pm – 4:20 pm Lockett 276

Jens Christensen, Colgate University
Mean Value Operators

Abstract: Mean value operators have many uses in mathematics. They can be used to characterize harmonic functions, and several generalization of mean value operators have been used in the theory of PDEs. The operators are a special type of Radon transforms, and they show up in thermo and photo acoustic tomography. In this talk we will study mapping properties of spherical mean value operators. Our main result is that any smooth function (on a non-compact symmetric space of rank one) can be written as the spherical mean value of another smooth function. The work builds on results by Ehrenpreis regarding division in Paley-Wiener space.

Posted October 22, 2018
Last modified March 11, 2019

3:30 pm – 4:30 pm Lockett 233

Caitlin Leverson, Georgia Institute of Technology
Representations, Ruling Polynomials, and the Colored HOMFLY-PT Polynomial

Abstract: Given a pattern braid beta in J1(S1), to any Legendrian knot Lambda in R3 with the standard contact structure, we can associate the Legendrian satellite knot S(Lambda,beta). We will discuss the relationship between counts of augmentations of the Chekanov-Eliashberg differential graded algebra of S(Lambda,beta) and counts of certain representations of the algebra of Lambda. We will then define an m-graded n-colored ruling polynomial from the m-graded ruling polynomial, analogously to how the n-colored HOMFLY-PT polynomial is defined from the HOMFLY-PT polynomial, and extend results of the second author, to show that the 2-graded n-colored ruling polynomial appears as a specialization of the n-colored HOMFLY-PT polynomial. (Joint work with Dan Rutherford.)

Thursday, March 14, 2019

Posted March 11, 2019

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett 233

Alexander Ioffe, Technion
Topics in Variational Analysis

Tuesday, March 19, 2019

Posted December 17, 2018
Last modified January 10, 2022

3:20 pm – 4:10 pm 232 Lockett

Timo Richarz, Technische Universitat Darmstadt
Smoothness of Schubert varieties in affine Grassmannians

The geometry in the reduction of Shimura varieties, respectively moduli spaces of Drinfeld shtuka plays a central role in the Langlands program, and it is desirable to single out cases of smooth reduction. This question reduces to the corresponding Schubert variety which is defined in terms of linear algebra, and thus easier to handle. We consider Schubert varieties which are associated with a reductive group G over a Laurent series local field, and a special vertex in the Bruhat-Tits building. If G splits, a strikingly simple classification is given by a theorem of Evens-Mirković and Malkin-Ostrik-Vybornov. If G does not split, the analogue of their theorem fails: there is a single surprising additional case of “exotic smoothness”. In my talk, I explain how to obtain a complete list of the smooth and rationally smooth Schubert varieties. This is joint work with Thomas J. Haines from Maryland.

Posted February 14, 2019
Last modified March 15, 2019

3:30 pm – 4:30 pm 1034 Digital Media Center

Hongbo Dong, Washington State University
On structured sparsity learning with affine sparsity constraints

Abstract: We introduce a new constraint system, namely affine sparsity constraints (ASC), as a general optimization framework for structured sparse variable selection in statistical learning. Such a system arises when there are nontrivial logical conditions on the sparsity of certain unknown model parameters to be estimated. One classical nontrivial logical condition is the heredity principle in regression models, where interaction terms of predictor variables can be introduced into the model only if the corresponding linear terms already exist in the model. Formally, extending a cardinality constraint, an ASC system is defined by a system of linear inequalities of binary indicators, which represent nonzero patterns of unknown parameters in estimation. We study some fundamental properties of such a system, including set closedness and set convergence of approximations, by using tools in polyhedral theory and variational analysis. We will also study conditions under which optimization with ASC can be reduced to integer programs or mathematical programming with complementarity conditions (MPCC), where algorithms and efficient implementation already exist. Finally, we will focus on the problem of regression with heredity principle, with our previous results, we derive nonconvex penalty formulations that are direct extensions of convex penalties proposed in the literature for this problem.

Wednesday, March 20, 2019

Posted March 15, 2019

3:30 pm – 4:30 pm Lockett 232

Yichuan Zhao, Georgia State University
Empirical likelihood for the bivariate survival function under univariate censoring

Abstract: The bivariate survival function plays an important role in multivariate survival analysis. Using the idea of influence functions, we develop empirical likelihood confidence intervals for the bivariate survival function in the presence of univariate censoring. It is shown that the empirical log-likelihood ratio has an asymptotic standard chi-squared distribution with one degree of freedom. A comprehensive simulation study shows that the proposed method outperforms both the traditional normal approximation method and the adjusted empirical likelihood method in most cases. The Diabetic Retinopathy Data are analyzed for illustration of the proposed procedure. This is joint work with Haitao Huang.

Posted March 13, 2019

5:30 pm Keiser Math Lounge (Lockett 321)

ASA Club Meeting

Cabe Chadick, who is an LSU alumnus and the President & Managing Principal of Lewis & Ellis, Inc Dallas, Texas, will be our speaker.

Pizza will be served.

Thursday, March 21, 2019

Posted January 9, 2019
Last modified March 18, 2019

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Amarjit Budhiraja, UNC Chapel Hill
On Some Calculus of Variations Problems for Rare Event Asymptotics

The theory of large deviations gives decay rates of probabilities of rare events in terms of certain optimal control problems. In general these control problems do not admit simple form solutions and one needs numerical methods in order to obtain useful information. In this talk I will present some large deviation problems where one can use methods of calculus of variations to give explicit solutions to the associated optimal control problems. These solutions then yield explicit asymptotic formulas for probability decay rates in several settings.

Wednesday, March 27, 2019

Posted January 27, 2019
Last modified March 26, 2019

1:30 pm – 3:00 pm Lockett 233

Rima Chatterjee, Louisiana State University
Classification of Legendrian Torus Knots

Abstract: Legendrian Knots have played important role in Contact Geometry. A natural question in Contact Geometry is which knots are Legendrian Simple that is which Legendrian Knots can be classified using their classical invariants. In this talk, I will give a brief overview of the classical invariants of Legendrian Knots and discuss about Legendrian torus knots which is one of the few examples of Legendrian simple knot type.

Posted August 15, 2018
Last modified March 26, 2019

3:30 pm – 4:30 pm Lockett 233

Tye Lidman, North Carolina State University
Splices, Heegaard Floer homology, and Seifert manifolds

Abstract: A natural way to construct three-manifolds is to glue two knot exteriors together. We will study properties of the Heegaard Floer homology of such manifolds. We then use this to characterize homeomorphisms between a special class of three-manifolds. This is joint work with Cagri Karakurt and Eamonn Tweedy.

Posted March 26, 2019

Pasquale Porcelli Lecture Series Special Lecture Series

3:30 pm – 4:30 pm Lockett 232

Arnab Ganguly, LSU
Reading Group Talk: An introduction to RKHS

Abstract: I will present some introductory materials on Reproducing kernel Hilbert spaces and its use in supervised learning.

Thursday, March 28, 2019

Posted September 30, 2018
Last modified February 10, 2019

4:00 pm – 5:00 pm Nicholson Hall 130

Robert Bryant, Duke University Fellow, American Academy of Arts and Sciences (2002), Member, National Academy of Sciences (2007), AMS Fellow (2013), AMS President (2015-2017)
Porcelli Lecture 1 (High-School Level): Mathematical Mysteries of the Ellipse

Abstract: After lines and circles, the simplest curves are the so-called conic sections, hyperbolas, parabolas, and ellipses. Not only are they the next simplest curves, but they have many applications in the physical world and have been studied for more than two thousand years.
However, these curves have many surprising properties that were not discovered until fairly recently.
For example, it has been known for a long time that light emitted from one focus of an ellipse collects at the other focus, and a similar property for the parabola is used in designing headlights. However, this turns out to be a special case of a much more interesting and surprising special property discovered in the 19th century and that has given rise to problems that we still don't know how to solve today.
In this talk, which will use nothing beyond high school algebra (and lots of pictures), I'll explain some of these mysteries and why we study them.

Friday, March 29, 2019

Posted September 30, 2018
Last modified February 10, 2019

Pasquale Porcelli Lecture Series Special Lecture Series

2:30 pm – 3:30 pm Howe-Russell 130

Robert Bryant, Duke University Fellow, American Academy of Arts and Sciences (2002), Member, National Academy of Sciences (2007), AMS Fellow (2013), AMS President (2015-2017)
Porcelli Lecture 2 (Undergraduate Level): Geometry Old and New: From Euclid to String Theory

Abstract: Classical geometry is based on notions of symmetry and congruence, and these ideas, while very old, have deeply influenced our understanding of the physical world. The idea of modeling the world through principles of least action or least energy are tied to symmetry in deep ways. In this talk, I will survey the history of how this relationship was uncovered by mathematicians such as Euler, Gauss, Lie, and Noether and is still developing in our modern understanding of the world, from Einstein's theory of relativity even to contemporary versions of string theory.

Posted September 30, 2018
Last modified February 10, 2019

Pasquale Porcelli Lecture Series Special Lecture Series

4:10 pm – 5:00 pm Howe-Russell 130

Robert Bryant, Duke University Fellow, American Academy of Arts and Sciences (2002), Member, National Academy of Sciences (2007), AMS Fellow (2013), AMS President (2015-2017)
Porcelli Lecture 3 (Graduate Student Level): The Best Possible Shapes of Surfaces

Abstract: Much of classical mathematics involves finding a configuration or shape that provides an optimum solution of a problem. For example, it has long been known (though a rigorous proof took quite a while to find) that the surface of least area enclosing a given volume is a round sphere. There are many other ways to measure surfaces, though, and finding 'the' surface that optimizes a given 'measurement' (subject to some given constraints) remains a challenging problem that has motivated some of the deepest recent work in the mathematics of geometric shapes.

In this talk, I will explain some of the classic ways to measure shapes of surfaces and relate this to classical problems involving surface area (soap films and bubbles) and total curvature as well to as recent progress by myself and others on these important optimization problems.

Tuesday, April 2, 2019

Posted March 6, 2019
Last modified March 15, 2019

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Xiaoliang Wan, Louisiana State University
Coupling the reduced-order model and the generative model for an importance sampling estimator

Abstract: In this work, we develop an importance sampling estimator by coupling the reduced-order model and the generative model in a problem setting of uncertainty quantification. The target is to estimate the probability that the quantity of interest (QoI) in a complex system is beyond a given threshold. To avoid the prohibitive cost of sampling a large scale system, the reduced-order model is usually considered for a trade-off between efficiency and accuracy. However, the Monte Carlo estimator given by the reduced-order model is biased due to the error from dimension reduction. To correct the bias, we still need to sample the fine model. An effective technique to reduce the variance reduction is importance sampling, where we employ the generative model to estimate the distribution of the data from the reduced-order model and use it for the change of measure in the importance sampling estimator. To compensate the approximation errors of the reduced-order model, more data that induce a slightly smaller QoI than the threshold need to be included into the training set. Although the amount of these data can be controlled by a posterior error estimate, redundant data, which may outnumber the effective data, will be kept due to the epistemic uncertainty. To deal with this issue, we introduce a weighted empirical distribution to process the data from the reduced-order model. The generative model is then trained by minimizing the cross entropy between it and the weighted empirical distribution. We also introduce a penalty term into the objective function to deal with the overfitting for more robustness. Numerical results are presented to demonstrate the effectiveness of the proposed methodology.

Wednesday, April 3, 2019

Posted March 18, 2019

10:30 am – 11:30 am 3316E Patrick F. Taylor Hall

Trying to Keep it Real: 25 Years of Trying to Get the Stuff I Learned in Grad School to Work on Mechatronic Systems

See https://www.lsu.edu/eng/ece/seminar/

Posted March 23, 2019
Last modified March 15, 2021

3:30 pm – 4:20 pm Lockett 276

Joachim Hilgert, Paderborn University
Helgason's conjecture revisited

Helgason's conjecture from 1976 said that for generic spectral parameters of a Riemannian symmetric space of non-compact type the corresponding Poisson transform is a bijection between hyperfunction sections of the corresponding principal series (realized on the Furstenberg boundary) and the joint eigenfunctions on the symmetric space. The conjecture was settled in a famous paper by Kashiwara-Kowata-Kimura-Okamoto-Oshima-Tanaka in 1978 using heavy machinery from the so-called algebraic analysis started by Mikio Sato. In the 1980s Oshima sketched an alternative approach using less machinery. The key issue is the construction of boundary values of joint eigenfunctions. In this talk I will explain a construction of boundary values in the spirit of Oshima as worked out in recent joint work with Soenke Hansen and Aprameyan Parthasarathy.

Posted March 21, 2019
Last modified January 7, 2025

3:30 pm – 4:30 pm Lockett 9

Gilles Francfort, Université Paris XIII and New York University
Spring Brake

I wish to demonstrate that minimization is a natural notion when dealing with even simple mechanical systems. The talk will revolve mainly around a simple spring brake combination which will in turn illustrate how the search for minimizers tells us things are never as simple as first thought. All that will be needed for a correct understanding of the material are basic notions of convexity, continuity as well as some familiarity with integration by parts.

This talk will be accessible to undergraduate students.

Refreshments will be served at 3:00PM in the Keisler lounge.

Posted March 20, 2019
Last modified March 21, 2019

3:30 pm – 4:30 pm Lockett 233

Linh Truong, Columbia University
An infinite rank summand of the homology cobordism group

Abstract: We show that the homology cobordism group of integer homology three-spheres contains an infinite rank summand. The proof uses an algebraic modification of the involutive Heegaard Floer package of Hendricks-Manolescu and Hendricks-Manolescu-Zemke. This is inspired by Hom's techniques in the setting of knot concordance. This is joint work with Irving Dai, Jen Hom and Matt Stoffregen.

Friday, April 5, 2019

Posted March 23, 2019

1:00 pm – 12:00 pm Sunday, April 7, 2019 Lockett 240 and 232

Conference on Ordered Structures in Geometry and Analysis

An international conference on Ordered Structures in Geometry and Analysis will be held on the campus of Louisiana State University from Friday April 5, 2019 to April 7, 2019. The conference will be dedicated to Boyd Professor emeritus Jimmie D. Lawson celebrating his 50 years as a researcher, educator, and administrator at LSU. The webpage is: http://www.math.lsu.edu/jimmiefest

Posted March 21, 2019
Last modified January 7, 2025

3:30 pm – 4:30 pm Lockett 9

Gilles Francfort, Université Paris XIII and New York University
The mysterious role of stability in defective solids

Adjudicating the correct model for the behavior of solids in the presence of defects is not straightforward. In this, solid mechanics lags way behind its more popular and at- tractive sibling, fluid mechanics. I propose to describe the ambiguity created by the on- set and growth of material defects in solids. Then, I will put forth a notion of structural stability that helps in securing meaningful evolutions. I will illustrate how such a notion leads us from the good to the bad, and then to the ugly when going from plasticity to fracture, and then damage. The only conclusion to be drawn is that much of the mystery remains.

Refreshments will be served at 3:00PM in the Keisler lounge.

Tuesday, April 9, 2019

Posted February 14, 2019
Last modified March 15, 2019

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Winnifried Wollner, Technische Universität Darmstadt
PDE constrained optimization with pointwise constraints on the derivative of the state

Abstract: In many processes modeled by partial differential equations (PDE) the, pointwise, size of the gradient is a key quantity. Prominent examples for this are damage or plasticity models. In the optimization of such processes pointwise constraints on the gradient are natural. The numerical analysis of these problems is complicated by the fact, that the natural topology coming from the PDE is too weak for handling the bounds on the gradient. Within this talk, we will discuss existence of solutions to such problems as well as their approximability by finite elements with particular emphasis on non-smooth domains.

Wednesday, April 10, 2019

Posted January 27, 2019

1:30 pm – 3:00 pm Lockett 233

Sean Bibby, Louisiana State University
TBA

Posted April 9, 2019

3:30 pm – 4:20 pm Lockett 276

Some Applications of Harmonic Analysis to Toeplitz Operators for Bounded Symmetric Domains

Abstract: In this talk, we will review some recent advances in the theory of Toeplitz operators defined on Bergman spaces of holomorphic functions on complex bounded symmetric domains. These results were made possible by applying the powerful machinery of harmonic analysis and representation theory. In particular, we will see how the problems of finding large commuting families of Toeplitz operators and of calculating the spectra of Toeplitz operators in such families is closely related to the structure of the scalar-type holomorphic discrete series representations of Hermitian Lie groups.

Posted January 25, 2019

3:30 pm – 4:30 pm Lockett 233

Peter Lambert-Cole, Georgia Institute of Technology
TBA

Posted April 9, 2019

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 232

Arnab Ganguly, LSU
An Introduction to RKHS - Part II

Thursday, April 11, 2019

Posted February 12, 2019
Last modified April 8, 2019

3:30 pm – 4:20 pm 232 Lockett
(Originally scheduled for Monday, April 22, 2019)

Peter Jorgensen, Newcastle University
Model categories of quiver representations

This is a report on joint work with Henrik Holm.

Let R be a k-algebra. Given a cotorsion pair (A,B) in Mod(R), Gillespie's Theorem shows how to construct a model category structure on C(Mod R), the category of chain complexes over Mod(R). There is an associated homotopy category H.

If (A,B) is the trivial cotorsion pair (projective modules, everything), then H is the derived category D(Mod R). Several other important triangulated categories can also be obtained from the construction.

Chain complexes over R are the Mod(R)-valued representations of a certain quiver with relations: Linearly oriented A double infinity modulo the composition of any two consecutive arrows. We show that Gillespie's Theorem generalises to arbitrary self-injective quivers with relations, providing us with many new model category structures.

Posted April 10, 2019
Last modified March 2, 2022

3:30 pm Lockett 233

Peter Wolenski, LSU Department of Mathematics Russell B. Long Professor
Fully convex Bolza problems with state constraints and impulses

A Fully Convex Bolza (FCB) problem has the appearance of the classical calculus of variations Bolza problem \[ \min \int_0^T L(x(t),x'(t))\,dt + l(x(0),x(T)) \] where the minimization is over $x()$ belonging to some class of arcs. The distinguishing features of FCB are that the data $L(,)$ and $l(,)$ (i) may take on the value infinity and (ii) are convex functions. Allowance of (i) provides great flexibility incorporating constraints so that most standard control problems come under its purlieu. However, broad generality is restrained by (ii), which although quite special, nonetheless includes the classical linear quadratic regulator and many of its generalizations. Furthermore, (ii) opens up the applicability of the tools of convex analysis. We shall review the Hamilton–Jacobi (HJ) theory for FCB problems when the data has no implicit state constraints and is coercive, in which case the minimizing class of arcs are Absolutely Continuous (AC). When a state constraint $x(t) \in X$ is added to the problem formulation, the dual variable may exhibit an impulse or “jump” when the constraint is active. The two properties of a state constraint and noncoercive data (which induce impulsive behavior) are in fact dual to each other, and the minimizing class becomes those of bounded variation. We shall describe Rockafellar's optimality conditions for these problems and a new technique for approximating them by AC problems that utilizes Goebel's self-dual envelope. The approximating AC problems maintain duality and the existing theory can be applied to them. It is proposed that an HJ theory can be developed for BV problems as an appropriate limit of the approximating AC problems. An explicit example will illustrate this.

Posted April 11, 2019

5:00 pm – 6:00 pm Keisler Lounge, Room 431

Movie Time

The documentary "The Secret Rules Of Modern Living: Algorithms" will be shown. Pizza and beverages will be served.

Friday, April 12, 2019

Posted April 10, 2019
Last modified January 7, 2025

10:30 am – 11:30 am Lockett 113

Peter Jorgensen, Newcastle University
Knots

Abstract: Knots are everyday objects, but they are also studied in mathematics. They were originally envisaged as models for atoms by Lord Kelvin, and have been studied by increasingly sophisticated mathematical methods for more than 100 years. Two knots are considered to be "the same" if one can be manipulated to give the other without breaking the string. The natural question of whether two given knots are the same turns out to be highly non-trivial; indeed, this is the central question of Knot Theory.

The talk is a walk through some aspects of this fascinating area of pure mathematics and will be accessible to undergraduate students.

Refreshments will be served in the Keisler Lounge from 10 to 10:30 am.

Posted April 11, 2019

The Robert W. Courter Seminar Series

3:00 pm – 4:00 pm 1263 Patrick F Taylor Hall

Blaise Bourdin, Department of Mathematics, Louisiana State University
Variational phase-field models of fracture

https://www.lsu.edu/eng/mie/graduate/seminars/index2.php

Saturday, April 13, 2019

Posted March 1, 2019
Last modified March 2, 2019

Algebra and Number Theory Seminar Questions or comments?

until Sunday, April 14, 2019

Southern Regional Number Theory Conference

https://www.math.lsu.edu/nt2019/

If you are planning to attend this conference, please fill out the online application:
https://docs.google.com/forms/d/e/1FAIpQLSfl2XY-js-HS7rwsg8wocbI3K8mQFtJMT-pQZIGphYAlqMhWQ/viewform

Tuesday, April 16, 2019

Posted December 11, 2018

Spring Break

Monday, April 22, 2019

Posted April 10, 2019
Last modified January 7, 2025

3:30 pm – 4:30 pm Lockett 277

Peter Jorgensen, Newcastle University
Quiver representations and homological algebra

The word "quiver" means oriented graph: A graph where each edge has an orientation, i.e. is an arrow from one vertex to another. A representation of a quiver Q associates a vector space to each vertex of Q and a linear map to each arrow of Q. The representations of Q form a so-called abelian category. It is also possible to construct triangulated categories of quiver representations, and abelian and triangulated categories are the basic objects of homological algebra. The talk will consider a simple example and present a number of fundamental properties of abelian and triangulated categories of quiver representations. Refreshments will be served in the Keisler lounge from 3:00 to 3:30pm

Tuesday, April 23, 2019

Posted March 6, 2019
Last modified November 29, 2022

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Hongchao Zhang, Louisiana State University
A Revisit of Gradient Descent Method for Nonlinear Optimization

In this talk, we will discuss some recent advances of the gradient methods developed in nonlinear optimization, including steepest descent methods, Barzilai-Borwein type methods, optimal gradient methods, quasi-Newton methods and conjugate gradient methods. Our focus will be the convergence properties of these methods as well as their practical performances.

Wednesday, April 24, 2019

Posted January 27, 2019
Last modified March 2, 2021

1:30 pm – 3:00 pm Lockett 233

Federico Salmoiraghi, Department of Mathematics, LSU
Sutured Floer Homology and TQFT

In this talk I will describe a result by Juhasz. He introduces a natural notion of cobordism between sutured manifolds, and shows that such a cobordism induces a map on sutured Floer homology. This map is a common generalization of the hat version of the closed 3-manifold cobordism map in Heegaard Floer theory, and the contact gluing map defined by Honda, Kazez, and Matic.

Posted April 16, 2019

4:30 pm – 5:30 pm Lockett 232

Meeting of tenured faculty

Thursday, April 25, 2019

Posted January 17, 2019
Last modified April 22, 2019

3:30 pm – 4:20 pm Lockett 232

Jasson Vindas, Ghent University, Belgium
Complex Tauberian theorems for Laplace transforms

Abstract: Complex Tauberian theorems have been strikingly useful tools in diverse areas of mathematics such as number theory and spectral theory for differential operators. Many results in the area from the last three decades have been motivated by applications in operator theory and semigroups. In this talk we shall discuss some developments in complex Tauberian theory for Laplace transforms. We will focus on two groups of statements, usually labeled as Ingham-Karamata theorems and Wiener-Ikehara theorems. We will present sharp versions of such theorems, including results with minimal boundary requirements on the Laplace transforms, computation of optimal Tauberian constants, and error terms. Several classical applications will be discussed in order to explain the nature of these Tauberian theorems.

Monday, May 6, 2019

Posted April 8, 2019

Algebra and Number Theory Seminar Questions or comments?

9:00 am – 12:00 pm Wednesday, May 8, 2019 205 Prescott Hall

OAL-RAG 2019: Order, Algebra, Logic, and Real Algebraic Geometry

Further info at the conference website: https://www.math.lsu.edu/OAL-RAG2019

Friday, May 10, 2019

Posted May 7, 2019

3:10 pm – 4:00 pm 232 Lockett

Liang Chang, Nankai University
On 3-manifold invariants from Hopf algebras

There are two main approaches for defining quantum invariants of closed 3-manifolds from Hopf algebras. The first one is to use the Heegaard diagram presentation of 3-manifolds. The other one uses the presentation of 3-manifolds by surgery along links. In this talk, we will review these two types of quantum invariants constructed by Kuperberg and Hennings, and report the recent work on their relationship.

Tuesday, May 14, 2019

Posted May 2, 2019
Last modified May 3, 2019

Control and Optimization Seminar Questions or comments?

3:00 pm – 4:00 pm 1263 Patrick F. Taylor Hall

Laurent Burlion, Rutgers University
Advanced Nonlinear Control Methods to Push Aerospace Systems to Their Limits

Abstract: Although often neglected in the design of flight control laws, nonlinearities must be taken into account either to get the best performance or to enlarge the flight envelope of controlled aerospace systems. Indeed, every system has a limited control authority and is subject to some safety constraints which impose limits on certain variables. In this talk, we will first present an overview of our recent applications of nonlinear control design methods to aerospace systems. Then, we will illustrate advanced nonlinear control techniques, including bounded backstepping, anti-windup and extended command governors, that were developed to execute an aircraft vision based landing on an unknown runway. Finally, we will discuss some ongoing research activities being conducted to provide drones with new capabilities, leading to a dramatic improvement in safety.

Monday, August 19, 2019

Posted April 30, 2019
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, August 21, 2019

Posted April 30, 2019
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, August 23, 2019

Posted April 30, 2019
Last modified December 13, 2022

Informal Geometry and Topology Seminar Questions or comments?

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, September 4, 2019

Posted September 11, 2019

1:30 pm – 3:00 pm Lockett 233

Shea Vela-Vick, Louisiana State University
An introduction to low-dimensional topology and contact geometry

Posted August 31, 2019

3:30 pm – 4:30 pm Keisler Lounge, Lockett 321

What We Did This Summer

Students will give short presentations on their summer experiences: internships, summer camps, the IMA bootcamp, etc. Join us to hear about their experiences and learn more about the LSU SIAM Student Chapter.

Monday, September 9, 2019

Posted September 4, 2019

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 233

Wei Li, LSU
Fluorescence ultrasound modulated optical tomography (fUMOT) in the radiated transport regime with angularly averaged measurements

We consider an inverse transport problem in fluorescence ultrasound modulated optical tomography (fUMOT) with angularly averaged illuminations and measurements. We study the uniqueness and stability of the reconstruction of the absorption coefficient and the quantum efficiency of the fluorescent probes. Reconstruction algorithms are proposed and numerical validations are performed. This is joint work with Yang Yang and Yimin Zhong, and it is an extension of our previous work done in 2018, where a diffusion model for this problem was considered.

Wednesday, September 11, 2019

Posted September 11, 2019

1:30 pm – 3:00 pm Lockett 233

Scott Baldridge, Louisiana State University
An introduction to Mirror Symmetry, Calabi-Yau manifolds, and Special Lagrangian Cones

Abstract: In this talk we look at the history of mirror symmetry as it came out of string theory (i.e., a 10-dimensional universe where particles are "strings"). We use that historical account to explain some of the motivation behind studying Calabi-Yau manifolds and special Lagrangian fibrations of these manifolds, which lead to my studying of special Lagrangian cones in my work. The goal is to use this narrative to introduce and discuss common terms (symplectic forms, Lagrangian, fiber bundles and fibrations, etc.) that will be used throughout the graduate student seminar this year. In that sense, this is not going to be an overly technical talk.

Monday, September 16, 2019

Posted September 13, 2019

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 233

Isaac Michael, Louisiana State University
Weighted Birman-Hardy-Rellich type Inequalities with Refinements

In 1961, Birman proved a sequence of inequalities valid for functions in C_0^{n}((0, \infty)) containing the classical (integral) Hardy inequality and the well-known Rellich inequality. Over the years there has been much effort in improving these inequalities with weights and singular logarithmic refinement terms. Using a simple variable transformation in integrals, we prove a generalization of these inequalities involving unrestricted power-type weights and logarithmic refinement terms, on both the exterior interval (R, \infty) and the interior interval (0, R) for any finite R>0. This is based on joint work with Fritz Gesztesy, Lance Littlejohn, and Michael Pang.

Wednesday, September 18, 2019

Posted September 11, 2019

1:30 pm – 3:00 pm Lockett 233

Justin Murray, Louisiana State University
TBD

Monday, September 23, 2019

Posted September 17, 2019
Last modified May 1, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett Hall 237

Farid Bouya, Louisiana State University
Seymour's Second Neighborhood Conjecture from a Different Perspective

Seymour's Second Neighborhood Conjecture states that every orientation of every simple graph has at least one vertex $v$ such that the number of vertices of out-distance 2 from $v$ is at least as large as the number of vertices of out-distance 1 from it. We present an alternative statement of the conjecture in the language of linear algebra.

Tuesday, September 24, 2019

Posted August 27, 2019
Last modified September 5, 2019

3:10 pm – 4:00 pm 285 Lockett

Moises Herradon Cueto, Louisiana State University
The local type of difference equations

D-modules allow us to study differential equations through the lens of algebraic geometry. They are widely studied and have been shown to be full of structure. In contrast, the case of difference equations is lacking some of the most basic constructions. We focus on the following question: D-modules have a clear notion of what it means to restrict to a (formal) neighborhood of a point, namely extension of scalars to a power series ring. However, what does it mean to restrict a difference equation to a neighborhood of a point? I will give an answer which encompasses the intuitive notions of a "zero" and a "pole" of a difference equation, but further it is consistent in two more ways. First of all, we can show that restricting a difference equation to a point and to its complement is enough to recover the difference equation. Secondly, there exists a local Mellin transform analogous to the local Fourier transform. The local Fourier transform describes singularities of a D-module on the affine line in terms of the singularities of its Fourier transform. Similarly, the Mellin transform is an equivalence between D-modules on the punctured affine line and difference modules on the line, and we can relate singularities on both sides via this local Mellin transform. I will also talk about how to apply the same ideas to other kinds of difference equations, such as elliptic equations, which generalize difference and differential equations at once.

Wednesday, September 25, 2019

Posted September 11, 2019

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm – 3:00 pm Lockett 233

Ryan Leigon, Louisiana State University
TBD

Thursday, September 26, 2019

Posted September 5, 2019

College of Science Inclusive Excellence Lecture Series

3:30 pm – 5:00 pm Hill Memorial Library

Suzanne Lenhart, University of Tennessee
One Health: Connecting Humans, Animals and the Environment

"One Health" is a multidisciplinary approach to improving the health of people, animals and the environment. Environmental, wildlife, domestic animal, and human health fall under the One Health concept. Mathematical models of infectious diseases involving animals, environmental features, and humans will be presented. These models can suggest management policies and predict disease spread, and examples including La Crosse virus and Zika virus will be discussed. (Reception after the talk)

Tuesday, October 1, 2019

Posted September 7, 2019
Last modified September 27, 2019

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm 285 Lockett

Solly Parenti, University of Wisconsin, Madison
Unitary CM Fields and the Colmez Conjecture

In 1993, Pierre Colmez conjectured a formula for the Faltings height of a CM abelian variety in terms of logarithmic derivatives of certain L-functions. I will discuss how we can extend the known cases of the conjecture to a class of unitary CM fields using the recently proven average version of the conjecture.

Posted September 26, 2019

Informal Geometry and Topology Seminar Questions or comments?

5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial club meeting

1. Winnie Sloan (is an LSU alumna, a Senior Actuarial Assistant for Travelers in St. Paul, MN, and has assisted many of our students who want advice from a professional actuary) is our speaker via skype. 2. Selecting new officers. Pizza will be served.

Wednesday, October 2, 2019

Posted September 11, 2019

1:30 pm – 3:00 pm Lockett 233

Jiten Ahuja, Louisiana State University
TBD

Monday, October 7, 2019

Posted October 4, 2019
Last modified March 3, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett Hall 237

Zachary Gershkoff, Mathematics Department, LSU
Connectivity in Matroids and Polymatroids

Another way of saying that a matroid is connected is to say that for every pair of elements, there is a U_{1,2}-minor that uses them. We investigate what kind of structure a matroid M has when every two elements of M are in an N-minor for certain N. For 2-polymatroids, we prove a result that's similar to Brylawski and Seymour's result that if M is a connected matroid with a connected minor N, and e is in E(M)−E(N), then M\e or M/e is connected having N as a minor.

Tuesday, October 8, 2019

Posted September 14, 2019
Last modified October 5, 2019

3:10 pm – 4:00 pm 285 Lockett

Chenliang Huang, Indiana University–Purdue University Indianapolis (IUPUI)
The solutions of gl(m|n) Gaudin Bethe ansatz equation, rational pseudodifferential operators, and the gl(m|n) spaces

We consider the gl(m|n) Gaudin Bethe ansatz equation associated to a tensor product of polynomial modules. Given a solution we describe a reproduction procedure which produces a family of new solutions which we call a population of solutions. We also write a rational pseudodifferential operator invariant under the reproduction procedure. We expect that the coefficients of the expansion of this operator are eigenvalues of the higher Gaudin Hamiltonians acting on the corresponding Bethe vector. The kernels of the numerator and denominator of the rational differential operator consist of rational functions and form a super space. Then we show that the population is canonically identified with the set of complete factorizations of the rational pseudodifferential operator, and with the variety of full super flags in the super space of rational functions. We conjecture that the eigenvectors of the Gaudin Hamiltonians are in a bijection with super spaces of rational functions with the prescribed properties which we call the gl(m|n) spaces.

Wednesday, October 9, 2019

Posted September 11, 2019

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm – 3:00 pm Lockett 233

Sudipta Ghosh, Louisiana State University
TBD

Monday, October 14, 2019

Posted October 11, 2019
Last modified March 3, 2021

3:30 pm Lockett Hall 237

Tara Fife, Louisiana State University
Laminar Matroids and their Generalizations

I'll begin by introducing matroids, nested matroids, and laminar matroids. One characterization of laminar matroids is that for all circuits $C_1\cap C_2\not=\emptyset$, either $C_1$ is in the closure of $C_2$ or $C_2$ is in the closure of $C_1$. We use this characterization to define two infinite families of generalized laminar matroids and give structural results of these classes. This is joint work with James Oxley.

Posted October 2, 2019

3:30 pm – 4:30 pm Lockett 233

Phuc Nguyen, Department of Mathematics, Louisiana State University
Weighted and pointwise bounds in measure datum problems with applications

Muckenhoupt-Wheeden type bounds and pointwise bounds by Wolff's potentials are obtained for gradients of solutions to a class of quasilinear elliptic equations with measure data. Such results are obtained globally over sufficiently flat domains in the sense of Reifenberg. The principal operator here is modeled after the $p$-Laplacian, where for the first time a singular case is considered. As an application, sharp existence and removable singularity results are obtained for a class of quasilinear Riccati type equations having a gradient source term with linear or super-linear power growth. This talk is based on joint work with Quoc-Hung Nguyen.

Posted September 4, 2019

3:30 pm – 4:30 pm Lockett 233

Phuc Nguyen, Department of Mathematics, Louisiana State University
TBA

Tuesday, October 15, 2019

Posted October 8, 2019

3:30 pm – 4:30 pm 1034 Digital Media Center

Hongchao Zhang, Louisiana State University
A Nonmonotone Smoothing Newton Algorithm for Weighted Complementarity Problem

Abstract: The weighted complementarity problem, often denoted by WCP, significantly extends the general complementarity problem and can be used for modeling a larger class of problems from science and engineering. In this talk, by introducing a one-parametric class of smoothing functions, we will introduce a smoothing Newton algorithm with nonmonotone line search to solve WCP. We will discuss the global convergence as well as local superlinear or quadratic convergence of this algorithm under assumptions weaker than assuming the nonsingularity of the Jacobian. Some promising numerical results will be also reported.

Posted October 10, 2019

Informal Geometry and Topology Seminar Questions or comments?

5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial club meeting

Abigail Brown, LSU contact for actuary, will come as a guest speaker. She will be discussing interviews, resumes, and other related topics. Pizza will be served.

Wednesday, October 16, 2019

Posted September 11, 2019

1:30 pm – 3:00 pm Lockett 233

Amit Kumar, Louisiana State University
TBD

Monday, October 21, 2019

Posted October 8, 2019

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm tba

Meeting of Full Professors

Wednesday, October 23, 2019

Posted September 11, 2019

1:30 pm – 3:00 pm Lockett 233

Rima Chatterjee, Louisiana State University
TBD

Posted September 11, 2019
Last modified October 22, 2019

3:30 pm – 4:30 pm Lockett 233

Hung Cong Tran, University of Oklahoma
The local-to-global property for Morse quasi-geodesics

Abstract: We show the mapping class group, CAT(0) groups, the fundamental groups of compact 3-manifolds, and certain relatively hyperbolic groups have a local-to-global property for Morse quasi-geodesics. As a consequence, we generalize combination theorems of Gitik for quasiconvex subgroups of hyperbolic groups to the stable subgroups of these groups. In the case of the mapping class group, this gives a combination theorem for convex cocompact subgroups. This is a joint work with Jacob Russell and Davide Spriano.

Thursday, October 24, 2019

Posted October 1, 2019

Algebra and Number Theory Seminar Questions or comments?

5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial club meeting

West Dickens and Alaina Chifici (LSU alumna) from Protective insurance will visit. They will also set up some interviews for Friday October 25 for anyone applying to their internship program. Pizza will be served.

Tuesday, October 29, 2019

Posted August 19, 2019
Last modified October 5, 2019

3:10 pm – 4:00 pm 285 Lockett

Changningphaabi Namoijam, Texas A&M
Transcendence of Hyperderivatives of Logarithms and Quasi-logarithms of Drinfeld Modules

In 2012, Chang and Papanikolas proved the transcendence of certain logarithms and quasi-logarithms of Drinfeld Modules. We extend this result to transcendence of hyperderivatives of these logarithms and quasi-logarithms. To do this, we construct a suitable t-motive and then use Papanikolas' results on transcendence degree of the period matrix of a t-motive and dimension of its Galois group.

Posted September 13, 2019
Last modified October 4, 2021

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Marta Lewicka, University of Pittsburgh
Geometry and Elasticity: the Mathematics of Shape Formation

We discuss some mathematical problems combining geometry and analysis, that arise from the description of elastic objects displaying heterogeneous incompatibilities of strains. These strains may be present in bulk or in thin structures, may be associated with growth, swelling, shrinkage, plasticity, etc. We will describe the effect of such incompatibilities on the singular limits of bidimensional models, in the variational description pertaining to the "non-Euclidean elasticity" and discuss the interaction of nonlinear PDEs, geometry and mechanics of materials in the prediction of patterns and shape formation.

Wednesday, October 30, 2019

Posted September 11, 2019
Last modified October 29, 2019

1:30 pm – 3:00 pm Lockett 233

Nurdin Takenov, Louisiana State University
Braid group and its representation(s)

Abstract: In my presentation I will talk about braid group and its representations. In particular, I will talk about Burau representation and (if there will be enough time) about its generalization.

Posted September 9, 2019
Last modified October 25, 2019

3:30 pm – 4:30 pm Lockett 233

Viet Dung Nguyen, Vietnam Academy of Science and Technology Institute of Mathematics
The higher topological complexity of the complement of fiber type arrangements and related topics

Abstract: In the talk we present our method to compute the higher topological of the complement of fiber type arrangements. The same method will be applied to compute the higher topological complexity for some other spaces.

Thursday, October 31, 2019

Posted October 15, 2019
Last modified January 7, 2025

1:30 pm – 2:30 pm Coates Hall 109

Keith Conrad, University of Connecticut
Heuristics for Statistics in Number Theory

Last month the sum of three cubes was in the news: mathematicians discovered with a computer how to write 42 as a sum of three cubes and then how to write 3 as a sum of three cubes in a new way; it's in fact expected that both 42 and 3 are a sum of three cubes in infinitely many ways. There are many other patterns in number theory that are expected to occur infinitely often: infinitely many twin primes, infinitely many primes of the form $x^2 + 1$, and so on. The basis for these beliefs is a heuristic way of applying probabilistic ideas to number theory, even though there is nothing probabilistic about perfect cubes or prime numbers. The goal of this talk is to show how such heuristics work and, time permitting, to see a situation where such heuristics break down.

Posted September 13, 2019
Last modified October 28, 2019

3:30 pm – 4:20 pm Lockett 232

Selim Esedoglu , University of Michigan
Algorithms for motion by mean curvature of networks.

Many applications in science and engineering call for simulating the evolution of interfaces (curves in the plane, or surfaces in space), including networks of them, under motion by mean curvature and related geometric flows. These dynamics arise as gradient descent for energies that contain the sum of (sometimes weighted and anisotropic) surface areas of the interfaces in the network. The applications include image processing, computer vision, machine learning, and materials science. There are a plethora of algorithms for simulating motion by mean curvature, especially in the challenging multiphase setting. I will review some of the simplest and most elegant: those that attempt to generate the evolution, including any necessary topological changes, by alternating just a few very efficient operations. They include the threshold dynamics algorithm of Merriman, Bence, and Osher, and the Voronoi implicit interface method of Saye and Sethian. Unfortunately, not all of these extremely streamlined, closely related methods converge to their advertised limit. I will discuss how recent developments in our understanding of some of these algorithms have allowed us to fix their lack of convergence.

Friday, November 1, 2019

Posted October 15, 2019
Last modified January 7, 2025

9:30 am – 10:30 am Allen Hall 123

Keith Conrad, University of Connecticut
Applications of Divergence of the Harmonic Series

The harmonic series is the sum of all reciprocals $1 + 1/2 + 1/3 + 1/4 + ...$, and a famous counterintuitive result in calculus is that the harmonic series diverges even though its general term tends to 0. This role for the harmonic series is often the only way students see the harmonic series appear in math classes. However, the divergence of the harmonic series turns out to have applications to topics in math besides calculus and to events in your daily experience. By the end of this talk you will see several reasons that the divergence of the harmonic series should be intuitively reasonable.

This talk will be accessible to undergraduate students.

Monday, November 4, 2019

Posted November 3, 2019

3:30 pm – 4:30 pm Lockett 233

Andrei Tarfulea, Louisiana State University
The Boltzmann equation with slowly decaying initial data

In this talk we look at the Boltzmann equation, a kinetic continuum model for plasma and high-energy gases. We will look at some previous results on well-posedness for the Cauchy problem, before presenting our recent result on local well-posedness (for a much wider range of parameters) with reduced assumptions on the initial data. As an application, our theorem combines with preexisting results to yield a continuation criterion for the larger parameter range. The scope of the talk will be to examine some of the various difficulties and methodologies associated with the Boltzmann collision operator: the physical symmetries, decompositions, and geometric lemmas needed to control (and in some cases extract regularity from) this nonlinear nonlocal interaction.

Tuesday, November 5, 2019

Posted September 9, 2019
Last modified October 13, 2019

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Jose Garay, Louisiana State University
Localized Orthogonal Decomposition Method with Additive Schwarz for the Solution of Multiscale Elliptic Problems

Abstract: The solution of elliptic Partial Differential Equations (PDEs) with multiscale diffusion coefficients using regular Finite Element methods (FEM) typically requires a very fine mesh to resolve the small scales, which might be unfeasible. The use of generalized finite elements such as in the method of Localized Orthogonal Decomposition (LOD) requires a coarser mesh to obtain an approximation of the solution with similar accuracy. We present a solver for multiscale elliptic PDEs based on a variant of the LOD method. The resulting multiscale linear system is solved by using a two-level additive Schwarz preconditioner. We provide an analysis of the condition number of the preconditioned system as well as the numerical results which validate our theoretical results.

Wednesday, November 6, 2019

Posted September 11, 2019

1:30 pm – 3:00 pm Lockett 233

Rob Quarles, Louisiana State University
TBD

Posted August 9, 2019
Last modified October 31, 2019

3:30 pm – 4:20 pm Lockett 232

Dejan Slepcev, Carnegie Mellon University
Variational problems on random structures: analysis and applications to data science

Abstract: Modern data-acquisition techniques produce a wealth of data about the world we live in. Extracting the information from the data leads to machine learning/statistics tasks such as clustering, classification, regression, dimensionality reduction, and others. Many of these tasks seek to minimize a functional, defined on the available random sample, which specifies the desired properties of the object sought.

I will present a mathematical framework suitable for studies of asymptotic properties of such, variational, problems posed on random samples and related random geometries (e.g. proximity graphs). In particular we will discuss the passage from discrete variational problems on random samples to their continuum limits. Furthermore we will discuss how tools of applies analysis help shed light on algorithms of machine learning.

Posted September 16, 2019
Last modified October 1, 2021

3:30 pm – 4:30 pm Lockett 233

Jason Behrstock, CUNY Graduate Center and Lehman College
Hierarchically hyperbolic groups: an introduction

Hierarchical hyperbolicity provides a uniform framework for working with many important examples, including mapping class groups, right angled Artin groups, Teichmüller space, and others. In this talk I'll provide an introduction to studying groups and spaces from this point of view. This talk will include joint work with M. Hagen and A. Sisto.

Thursday, November 7, 2019

Posted October 21, 2019
Last modified November 2, 2019

3:30 pm – 4:20 pm Lockett 232

Ignacio Nahuel Zurrian, Universidad Nacional de Cordoba (National University of Cordoba)
Bispectrality and commuting operators

Abstract: We will discuss the role of bispectrality in the commuting operators phenomenon. We will also consider situations of different nature, e.g. continuous and discrete variables or a matrix/valued setup. Finally, I would like to explore some very recent results as well as the notion of reflecting operators.

Monday, November 11, 2019

Posted October 5, 2019
Last modified October 22, 2019

3:30 pm – 4:30 pm Lockett Room 233

Matthias Maier, Department of Mathematics Texas A&M University
Simulation of Optical Phenomena on 2D Material Devices

In the terahertz frequency range, the effective (complex-valued) surface conductivity of atomically thick 2D materials such as graphene has a positive imaginary part that is considerably larger than the real part. This feature allows for the propagation of slowly decaying electromagnetic waves, called surface plasmon-polaritons (SPPs), that are confined near the material interface with wavelengths much shorter than the wavelength of the free-space radiation. SPPs are a promising ingredient in the design of novel optical devices, promising "subwavelength optics" beyond the diffraction limit. There is a compelling need for controllable numerical schemes which, placed on firm mathematical grounds, can reliably describe SPPs in a variety of geometries. In this talk we present a number of analytical and computational approaches to simulate SPPs on 2D material interfaces and layered heterostructures. Aspects of the numerical treatment such as absorbing perfectly matched layers, local refinement and a-posteriori error control are discussed. We show analytical results for some prototypical geometries and a homogenization theory for layered heterostructures.

Tuesday, November 12, 2019

Posted October 21, 2019
Last modified November 12, 2019

3:30 pm – 4:20 pm Lockett 232

Nathan Glatt-Holtz, Tulane University
A Bayesian Approach to Quantifying Uncertainty in Divergence Free Flows

We treat the statistical regularization of the ill-posed inverse problem of estimating a divergence free flow field u from the partial and noisy observation of a passive scalar θ. Our solution is a Bayesian posterior distribution, that is a probability measure μ which precisely quantifies uncertainties in u once one specifies models for measurement error and a prior knowledge for u. We present some of our recent work which analyzes μ both analytically and numerically. In particular we discuss a posterior contraction (consistency) result as well as some Markov Chain Monte Carlo (MCMC) algorithms which we have developed and refined and rigorously analyzed to effectively sample from μ. This is joint work with Jeff Borggaard, Justin Krometis and Cecilia Mondaini.

Posted November 5, 2019

Informal Geometry and Topology Seminar Questions or comments?

until 5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial club meeting

Senior, Sarah Davidson, will discuss her internship at CNA Insurance in Chicago

Nick Crifasi from AmeriHealth Caritas in Philadelphia will skype. Nick is an ASA in the Society of Actuaries and is an LSU alumnus.

Nick is requesting that seniors graduating in December or May give him their resume. Seniors graduating in December or May please send your resume to Kevin Li at kli27@lsu.edu, and he will send them to Nick.

Wednesday, November 13, 2019

Posted September 11, 2019

1:30 pm – 3:00 pm Lockett 233

Abel Lopez, Louisiana State University
TBD

Thursday, November 14, 2019

Posted September 24, 2019
Last modified November 2, 2019

3:30 pm – 4:20 pm Lockett 232

John Voight, Dartmouth College
Heuristics for units in number rings

Units in number rings are gems of arithmetic, the most famous being the golden ratio and the integer solutions x,y to Pell's equation x^2 - D*y^2 = +/-1 for D > 0. Like gems, they are embedded deeply within. Refined questions about the structure of units remain difficult to answer, for example: how often does it happen that Pell's equation has a solution to the -1 equation? More generally, how often in a number ring is it that all totally positive units are squares? Absent theorems, we may still try to predict the answer to these questions. In this talk, we present heuristics (and some theorems!) for signatures of unit groups inspired by the Cohen-Lenstra heuristics for class groups, but involving an lustrous structure of number rings we call the 2-Selmer signature map. This is joint work with David S. Dummit and Richard Foote and with Ben Breen, Noam Elkies, and Ila Varma.

Monday, November 18, 2019

Posted October 15, 2019
Last modified January 7, 2025

1:30 pm – 2:20 pm Lockett Hall 241

Steven Leth, University of Northern Colorado
Fixed Points of Continuous Functions in the plane

If we crumple up a map of Colorado, then place that crumpled map on top of an identical map, some point on the top map is directly over the same location on the lower map. This might not be true if we use a map of Louisiana or Michigan, which have "disconnected" portions. Also, we must be careful to not tear the map while we are crumpling it. This is an example of a consequence of the famous Brouwer Fixed Point Theorem. We will examine this beautiful mathematical result, and demonstrate how it follows from a simple combinatorial theorem about coloring vertices of triangles. The extent to which the Fixed Point Theorem can be generalized is still unsolved, and we will briefly discuss that as well.

This talk will be accessible to undergraduate students.

Posted November 8, 2019
Last modified November 9, 2019

3:30 pm Lockett 233

F. Alberto Grünbaum, University of California, Berkeley
Quantum walks: a nice playground for old and new mathematics.

I will give an ab-initio talk trying to show how some time honored pieces of analysis can be used to answer questions about recurrence of quantum walks. I will start with a quick review of classical random walks and then show how Schur functions (the same I. Schur of many other deep topics) are useful in the quantum case. Recently these Schur functions have been seen to be useful in getting a topological classification of quantum walks that respect certain symmetries but go beyond the translation invariant case. I will not assume any previous knowledge about quantum walks. This is joint work with Jean Bourgain, Luis Velazquez, Reinhard Werner, Albert Werner and Jon Wilkening.

Tuesday, November 19, 2019

Posted October 15, 2019
Last modified January 7, 2025

Algebra and Number Theory Seminar Questions or comments?

1:30 pm – 2:20 pm Lockett 285

Steven Leth, University of Northern Colorado
An introduction to the use of nonstandard methods

Nonstandard methods utilize the technique of viewing relatively simple structures that we wish to study inside much richer structures with idealized properties. Most famously, we might look at nonstandard models of the real numbers that contain actual "infinitesimal" elements. The existence of the idealized structures gives us access to powerful tools that can often support more intuitive proofs than standard methods allow. We will look at examples of simple nonstandard arguments in several different settings, as well as a few recent results obtained using these methods.

Posted October 11, 2019
Last modified November 15, 2019

3:10 pm – 4:00 pm 285 Lockett

Ignacio Nahuel Zurrian, Universidad Nacional de Cordoba (National University of Cordoba)
Some applications of discrete harmonic analysis

We will discuss some concrete applications of discrete integrable systems through certain representations of Double Affine Hecke Algebras.

Posted September 9, 2019
Last modified October 13, 2019

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm 1034 Digital Media Center

Yakui Huang, Hebei University of Technology
On the Asymptotic Convergence and Acceleration of Gradient Methods

Abstract: We consider the asymptotic behavior of a family of gradient methods, which include the steepest descent and minimal gradient methods as special instances. It is proved that each method in the family will asymptotically zigzag between two directions. Asymptotic convergence results of the objective value, gradient norm, and stepsize are presented as well. To accelerate the family of gradient methods, we further exploit spectral properties of stepsizes to break the zigzagging pattern. In particular, a new stepsize is derived by imposing finite termination on minimizing two dimensional strictly convex quadratic function. It is shown that, for the general quadratic function, the proposed stepsize asymptotically converges to the reciprocal of the largest eigenvalue of the Hessian. Furthermore, based on this spectral property, we propose a periodic gradient method by incorporating the Barzilai-Borwein method. Numerical comparisons with some recent successful gradient methods show that our new method is very promising.

Wednesday, November 20, 2019

Posted September 11, 2019

1:30 pm – 3:00 pm Lockett 233

Emma Lien, Louisiana State University
TBD

Posted August 16, 2019
Last modified March 2, 2021

Joint Harmonic analysis and Applied analysis seminar

3:30 pm – 4:20 pm Lockett 232

Tao Mei, Balyor University
Monotonicity of Markov semigroups and $H^\infty$-calculus

I plan to explain a recent discovery of a monotonicity that is satisfied by a large class of Markov semigroups of operators. For the classical Poisson semigroup $P_t$ generated by the square root of Laplacian. I will explain how this monotonicity helps us in understanding Fourier multipliers associated with "operators", and in the BMO-bounded $H^\infty$-calculus for general "Laplacian" operators.

Thursday, November 21, 2019

Posted September 10, 2019
Last modified March 2, 2021

3:30 pm – 4:20 pm Lockett 232

Leonid V. Berlyand, Department of Mathematics, Pennsylvania State University
PDE/Analysis techniques in deep learning: convergence & stability of neural net classifiers

While algorithms based on deep neural networks (DNNs) have been recently used in a wide range of practical problems (e.g., object, speech, and pattern recognition), there is no rigorous understanding for why and when DNNs may fail. Thus, there is a pressing need for a mathematical understanding of the behavior of DNNs to improve existing algorithms and develop new ones. The power of DNNs lies in their ability to "learn" how to solve problems via training, the iterative minimization of a loss (error) function. We use modern tools from PDE/ODE analysis to address the convergence and stability of DNN training algorithms. First, using entropy-entropy dissipation estimates, we study the convergence of DNNs, and establish a striking feature: the DNN mathematically diverges as the number of gradient descent iterations goes to infinity, but this divergence is very slow (logarithmic), with the loss function vanishing polynomially, leading to "practical convergence." Second (work in progress) we established conditions of the structure and dimensionality of data sets and DNN architecture under which an DNN algorithm is stable, that is, training cannot lead to a significant drop in accuracy. In particular, we demonstrated a connection between stability and distribution of misclassified objects in the training set. This is a joint work with P-E Jabin (U. of Maryland) and A. Safsten ( Ph.D. student at PSU).

Monday, November 25, 2019

Posted September 6, 2019
Last modified November 24, 2019

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 233

Isaac Michael, Louisiana State University
On Weighted Hardy-Type Inequalities

We revisit weighted Hardy-type inequalities employing an elementary ad hoc approach that yields explicit constants. We also discuss the infinite sequence of power weighted Birman--Hardy--Rellich-type inequalities and derive an operator-valued version thereof. This is based on joint work with C. Chuah, F. Gesztesy, L. L. Littlejohn, T. Mei, M. H. Pang

Tuesday, November 26, 2019

Posted November 21, 2019
Last modified November 24, 2019

10:00 am 3316E Patrick F. Taylor Hall

Pavithra Prabhakar, Kansas State University
Robust Verification of Hybrid Systems

Information on ECE Seminar Web Site.

Monday, December 2, 2019

Posted November 24, 2019

3:30 pm – 4:20 pm 232 Lockett

Meeting of all faculty

Tuesday, December 3, 2019

Posted November 25, 2019
Last modified March 2, 2021

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Alexander Shapiro, UC Berkeley
Modular functor from higher Teichmüller theory

Abstract: Quantized higher Teichmüller theory, as described by Fock and Goncharov, assigns an algebra and its representation to a surface and a Lie group. This assignment is equivariant with respect to the action of the mapping class group of the surface, and is conjectured to give an analog of a modular functor, that is it should respect the operation of cutting and gluing of surfaces. In this talk I will outline a proof of the above conjecture, and explain how it is related to representation theory of quantum groups. This talk will be mostly based on joint works with Gus Schrader.

Wednesday, December 4, 2019

Posted December 1, 2019

1:30 pm – 3:00 pm Lockett 233

Charles Livingston, Indiana University
Four-dimensional approaches to some problems in classical knot theory

Posted November 26, 2019
Last modified November 27, 2019

3:30 pm – 4:20 pm 232 Lockett

Yulong Lu, Duke University
Understanding and Accelerating Statistical Sampling via PDEs and Deep Learning

Abstract: A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from probability distributions. Standard Markov chain Monte Carlo methods could be prohibitively expensive due to various complexities of the target distribution, such as multimodality, high dimensionality, large datasets, etc. To improve the sampling efficiency, several new interesting ideas/methods have recently been proposed in the community of machine learning, whereas their theoretical analysis are very little understood. In the first part of the talk, I will show how PDE analysis can be useful to understand some recently proposed sampling algorithms. Specifically, I will focus on the Stein variational gradient descent (SVGD), which is a popular particle sampling algorithm used in the machine learning community. I justify rigorously SVGD as a sampling algorithm through a mean field analysis. Then I will introduce a new birth-death dynamics, which can be used as a universal strategy for accelerating existing sampling algorithms. The acceleration effect of the birth-death dynamics is examined carefully when applied to the classical Langevin diffusion. For both SVGD dynamics and the birth-death dynamics, I will emphasize the (Wasserstein) gradient flow structure and the convergence to the equilibrium of the underlying PDE dynamics. The second part of the talk devotes to learning implicit generative models for sampling. Generative model such as Generative Adversarial Network (GAN) provides an important framework for learning and sampling from complex distributions. Despite the celebrated empirical success, many theoretical questions remain unsolved. A fundamental open question is: how well can deep neural networks express distributions? I will answer this question by proving a universal approximation theorem of deep neural networks for generating distributions.

Thursday, December 5, 2019

Posted September 13, 2019
Last modified November 25, 2019

3:30 pm – 4:20 pm Lockett 232

Eric Rowell, Texas A&M
Mathematical Problems in Topological Quantum Computation

Abstract: Two-dimensional topological states of matter offer a route to quantum computation that would be topologically protected against the nemesis of the quantum circuit model: decoherence. In this talk I will give a mathematicians' perspective on some of the advantages and challenges of this model, focusing on the interplay of condensed matter physics, representation theory, low-dimensional topology and category theory. We will discover some compelling mathematical questions inspired by foundational problems in topological information theory along the way, and I will present a few results and ongoing projects with collaborators.

Monday, December 9, 2019

Posted November 27, 2019
Last modified December 5, 2019

3:30 pm – 4:20 pm Lockett 232

Rui Han, LSU
Spectral gaps in graphene structures

Abstract: In 1976 a celebrated butterfly was plotted by Douglas Hofstadter, describing (as a function of the magnetic flux $\alpha$) the spectrum of a tight-binding model of the motion of electrons on the square lattice under a perpendicular magnetic field (known as Harper's model). Proving the spectrum is a Cantor set for the Harper's model for any irrational flux was dubbed the "Ten Martini Problem" after Kac and Simon. This problem was solved completely about 10 years ago by Avila and Jitomirskaya. After a brief introduction to the Harper's model, I will talk about a model of graphene in magnetic fields, which has an underlying hexagonal lattice structure. I will discuss some recent results, including Cantor spectrum, spectral decomposition, Hausdorff dimension of the spectrum, Dirac points, and Bethe-Sommerfeld conjecture.

Tuesday, December 10, 2019

Posted November 25, 2019
Last modified November 26, 2019

3:30 pm – 4:20 pm 232 Lockett

Krystal Guo, Université de Montreal
Applying algebraic graph theory to quantum computing

Abstract: The interplay between the properties of graphs and the eigenvalues of their adjacency matrices is well-studied. Important graph invariants, such as diameter and chromatic number, can be understood using these eigenvalue techniques. In this talk, we use classical techniques in algebraic graph theory to study quantum walks. A system of interacting quantum qubits can be modelled by a graph. The evolution of the quantum system can be completely encoded as a quantum walk in a graph, which can be seen, in some sense, as a quantum analogue of random walk. This gives rise to a rich connection between algebraic graph theory, linear algebra and quantum computing. In this talk, I will present recent results on the average mixing matrix of a graph; a quantum walk has a transition matrix which is a unitary matrix with complex values and thus will not converge, but we may speak of an average distribution over time, which is modelled by the average mixing matrix.

Thursday, December 12, 2019

Posted December 11, 2019

3:30 pm – 4:30 pm Lockett 232

Meeting of Professorial Faculty

Monday, January 6, 2020

Posted September 23, 2019
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, January 8, 2020

Posted September 23, 2019
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, January 10, 2020

Posted September 23, 2019
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Monday, January 13, 2020

Posted December 19, 2019
Last modified January 8, 2020

3:30 pm – 4:20 pm Lockett 232

Rebecca Winarski, University of Michigan
Polynomials, branched covers, and trees

Abstract: Thurston proved that a branched cover of the plane that satisfies certain finiteness conditions is either equivalent to a polynomial (that is: conjugate via a mapping class) or it has a topological obstruction. We use topological techniques - adapting tools used to study mapping class groups - to produce an algorithm that determines when a branched cover is equivalent to a polynomial, and if it is, determines which polynomial a branched cover is equivalent to. Our approach gives a new, topological solution to Hubbard's twisted rabbit problem, as well as generalizations of this problem. This is joint work with Jim Belk, Justin Lanier, and Dan Margalit.

Wednesday, January 15, 2020

Posted January 11, 2020

3:30 pm – 4:20 pm 232 Lockett Hall

Quoc-Hung Nguyen, ShanghaiTech University
Quantitative estimates for Lagrangian flows associated to non-Lipschitz vector fields

Since the work by DiPerna and Lions (89) the continuity and transport equation under mild regularity assumptions on the vector field have been extensively studied, becoming a florid research field. In this talk, we give an overview of this theory presenting classical results and new quantitative estimates. One important tool in our investigation is a Kakeya type singular operator. We establish the weak type (1,1) bound for this operator and we exploit it to prove well-posedness and stability results for the continuity and transport equation associated to vector fields represented as singular integrals of BV functions. We also discuss the optimality of this result. Finally, we present sharp regularity estimates for solutions of the continuity equation under various assumptions on the velocity fields.

Wednesday, January 22, 2020

Posted January 21, 2020
Last modified March 3, 2021

2:30 pm – 3:20 pm Lockett 235

Sergio Carrillo, Universidad Sergio Arboleda, Bogata, Columbia
Gevrey power series solutions in analytic functions of first order holomorphic PDEs

The goal of this talk is to explain a new Gevrey type—in an analytic function P—for formal power series solutions of some families of singular first order holomorphic PDEs. We will show that under a suitable geometric condition, if P generates the singular locus of the equation, then P is the generic source of divergence of the formal solution. In fact, our result recovers systematically many well-known cases of singularly perturbed holomorphic ODEs. The key estimates we use are based on Nagumo norms and their compatibility with a Weierstrass division theorem. This work is a first step into the study of a Borel-type summability for these series as we shall describe by examples for the case P equal to a monomial.

Friday, January 24, 2020

Posted January 19, 2020
Last modified January 21, 2020

3:30 pm – 4:20 pm 232 Lockett

Kevin Schreve, University of Chicago
Group actions on contractible manifolds and L^2-cohomology

Abstract: The action dimension of a finitely generated group G is the smallest dimension of contractible manifold with proper action by G. I will describe a conjectured homological obstruction to such actions, and how this fits in with a conjecture of Hopf about Euler characteristics of closed, nonpositively curved manifolds. I will then describe some classes of groups where we can show this conjecture holds. This is based on joint work with Grigori Avramidi, Mike Davis, Giang Le, and Boris Okun.

Monday, January 27, 2020

Posted January 20, 2020

3:30 pm – 4:20 pm 232 Lockett

Yu Pan, MIT
Augmentations and exact Lagrangian surfaces.

Abstract: A major theme in symplectic and contact topology is the study of Legendrian knots and the study of exact Lagrangian surfaces that connecting the knots. In the talk, we will talk about some rigidity results of exact Lagrangian surfaces using augmentation, a Floer type invariant of Legendrian knots.

Tuesday, January 28, 2020

Posted January 21, 2020
Last modified January 24, 2020

3:30 pm – 4:20 pm 232 Lockett

Christin Bibby, University of Michigan
Combinatorics and topology of arrangements

Abstract: A hyperplane arrangement is a finite set of hyperplanes in a vector space. The way in which these hyperplanes intersect has a rich combinatorial structure (known as a matroid). A topologist may be more interested in the complement of their union. A motivating example is an ordered configuration space of distinct complex numbers, which is the complement to an arrangement whose underlying combinatorial structure is the lattice of set partitions. In this talk, we will explore some classical questions in the field of hyperplane arrangements, and what changes when more general varieties (or manifolds) play the role of the vector spaces. That is, we consider arrangements of smooth codimension-one subvarieties in a smooth algebraic variety, which intersect like hyperplanes, and examine the interplay between combinatorics, topology, and algebra.

Thursday, January 30, 2020

Posted February 13, 2020

Keiser Math Lounge (Lockett 321)

ASA Club Meeting

Taylor Daigle, who is an actuarial analyst at Pinnacle Actuarial Resources and a 2018 LSU graduate will visit. Pizza will be served.

Friday, January 31, 2020

Posted January 21, 2020
Last modified January 26, 2020

3:30 pm – 4:20 pm 232 Lockett

Martin Friesen, University of Wuppertal
Ergodicity and regularity of affine processes

Abstract: In this talk, we address convergence to equilibrium as well as regularity of transition densities for affine processes on the canonical state space. First, we introduce and review different characterizations of affine processes through their Generator, corresponding Riccati equations, and semi-martingales. Then we prove that each affine process is the unique strong solution to a system of stochastic differential equations. As a particular application of this result, we investigate the convergence of transition probabilities in Wasserstein distances towards their unique invariant measure. Afterward, we study the regularity of transition probabilities (smoothness, Besov, strong Feller property). By combining this regularity with a coupling argument we also deduce exponential ergodicity in total variation. This talk is based on several works joint with: Peng Jin and Barbara Rüdiger.

Monday, February 3, 2020

Posted January 21, 2020
Last modified January 23, 2020

3:30 pm – 4:20 pm 232 Lockett

Li Chen, LSU
On several functional inequalities for Markov semigroups and their applications

Abstract: Markov semigroups lie at the interface of analysis, PDEs, probability and geometry. Markov semigroup techniques, from both analytic and probabilistic viewpoints, have important applications in the study of functional inequalities coming from harmonic analysis, PDEs and geometry. In this talk, we discuss regularization properties of heat semigroups and their applications to the study of Sobolev type inequalities, isoperimetric inequalities and the $L^p$ boundedness of Riesz transforms in different geometric settings. Fractal examples without differential structures will be emphasized. Besides, we also discuss sharp and dimension-free $L^p$ bounds of singular integral operators via the martingale transform method.

Posted January 30, 2020
Last modified February 2, 2020

4:30 pm – 5:20 pm Lockett 233
(Originally scheduled for Thursday, January 30, 2020)

Khai Nguyen, NCSU
The metric entropy for nonlinear PDEs

Inspired by a question posed by Lax in 2002, in recent years it has received an increasing attention the study on the metric entropy (epsilon entropy) for nonlinear PDEs. In this talk, I will present recent results on sharp estimates in terms of epsilon entropy for hyperbolic conservation laws and Hamilton-Jacobi equations. Estimates of this type play a central role in various ares of information theory and statistics as well as of ergodic and learning theory. In the present setting, this concept could provide a measure of the order of "resolution" of a numerical method for the corresponding equations.

Tuesday, February 4, 2020

Posted January 22, 2020
Last modified January 29, 2020

3:00 pm – 3:50 pm Lockett 276

Khai Nguyen, NCSU
Differential Game Models of Optimal Debt Management

Abstract: In this talk, I will present recent results on game theoretical formulation of optimal debt management problems in infinite time horizon with exponential discount, modeled as a noncooperative interaction between a borrower and a pool of risk-neutral lenders. Here, the yearly income of the borrower is governed by a stochastic process and bankruptcy instantly occurs when the debt-to-income ratio reaches a threshold. Since the borrower may go bankrupt in finite time, the risk-neutral lenders will charge a higher interest rate in order to compensate for this possible loss of their investment. Thus, a "solution" must be understood as a Nash equilibrium, where the strategy implemented by the borrower represents the best reply to the strategy adopted by the lenders, and conversely. This leads to highly nonstandard optimization processes.

Posted January 27, 2020
Last modified January 28, 2020

4:10 pm – 5:00 pm Lockett 232

Faculty Meeting

Wednesday, February 5, 2020

Posted February 3, 2020
Last modified October 4, 2021

3:30 pm – 4:20 pm 232 Lockett

Felix Janda, University of Michigan & IAS Princeton
Enumerative geometry: old and new

Ever since people have studied geometry, they have counted geometric objects. For example, Euclid's Elements start with the postulate that there is exactly one line passing through two distinct points in the plane. The kinds of counting problems we are able to pose and to answer has grown significantly since then. Today enumerative geometry is a rich subject with connections to many fields, including combinatorics, physics, representation theory, number theory and integrable systems.

In this talk, I will show how to solve several classical counting questions. I will then move to a more modern problem with roots in string theory which has been the subject of intense study for the last three decades: The computation of the Gromov–Witten invariants of the quintic threefold, an example of a Calabi–Yau manifold.

Thursday, February 6, 2020

Posted January 10, 2020
Last modified February 2, 2020

3:30 pm – 4:20 pm Lockett 232

Christopher Sogge, Johns Hopkins University J. J. Sylvester Professor of Mathematics
The wave equation and Fourier analysis

Abstract: Many problems in harmonic analysis involve the wave equation, and one can use Fourier analysis and Fourier integral operators to solve wave equations. We shall discuss several of these problems, including spherical maximal estimates, local smoothing bounds and Kakeya problems. We shall also go over recent decoupling estimates of Bourgain and Demeter that were inspired by the work of Wolff on regularity estimates for the wave equation.

Friday, February 7, 2020

Posted February 4, 2020

8:30 am – 9:30 am Keisler Lounge, Lockett 321

A Conversation with Prof. Lili Ju, University of South Carolina

Posted August 31, 2019

12:00 pm – 4:00 pm Saturday, February 8, 2020 Digital Media Center Theatre

Scientific Computing Around Louisiana (SCALA 2020)

Monday, February 10, 2020

Posted February 6, 2020

2:00 pm – 3:30 pm Lockett 10

Faculty Meeting

Posted December 2, 2019
Last modified March 2, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett 233

Junshan Lin, Auburn University
Scattering Resonances Through Subwavelength Holes and Their Applications in Imaging and Sensing

The so-called extraordinary optical transmission (EOT) through metallic nanoholes has triggered extensive research in modern plasmonics, due to its significant applications in bio-sensing, imaging, etc. The mechanisms contributing to the EOT phenomenon can be complicated due to the multiscale nature of the underlying structure. In this talk, I will focus on mechanisms induced by scattering resonances. In the first part of the talk, based upon the layer potential technique, asymptotic analysis and the homogenization theory, I will present rigorous mathematical analysis to investigate the scattering resonances for several typical two-dimensional structures, these include Fabry-Perot resonance, Fano resonance, spoof surface plasmon, etc. In the second part of the talk, preliminary mathematical studies for their applications in sensing and super-resolution imaging will be given. I will focus on the resonance frequency sensitivity analysis and how one can achieve super-resolution by using subwavelength structures.

Tuesday, February 11, 2020

Posted October 11, 2019
Last modified January 31, 2020

3:10 pm – 4:00 pm 232 Lockett
(Originally scheduled for Wednesday, November 27, 2019)

Kent Vashaw, Louisiana State University
Noncommutative tensor triangular geometry

We describe a general theory of the prime spectrum of non-braided monoidal triangulated categories. These notions are a noncommutative analogue to Paul Balmer's prime spectra of symmetric tensor-triangulated categories. Noncommutative monoidal triangulated categories appear naturally as stable module categories for non-quasitriangular Hopf algebras and as derived categories of bimodules of noncommutative algebras. In stable module categories of Hopf algebras, the support theory of the category, as described by Benson-Iyengar-Krause, is linked to the Balmer spectrum, which is shown to be the final support datum. We will describe how this connection can be used to compute Balmer spectra in general, and we will compute the Balmer spectra for stable module categories of the small quantum group of a Borel subalgebra at a root of unity, and the stable module categories for smash coproduct Hopf algebras of group algebras with coordinate rings of groups. This is joint work with Daniel Nakano and Milen Yakimov.

Thursday, February 13, 2020

Posted January 22, 2020
Last modified March 3, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Jeffrey Danciger, UT Austin
Affine geometry and the Auslander Conjecture

The Auslander Conjecture is an analogue of Bieberbach's theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichmüller theory will enter the picture.

Tuesday, February 18, 2020

Posted January 15, 2020
Last modified March 2, 2021

3:10 pm – 4:00 pm 232 Lockett

Po-Han Hsu, Louisiana State University
Erdős-Kac theorem and its deviation principles

Posted January 7, 2020

3:30 pm – 4:20 pm Digital Media Center 1034

Giordano Tierra-Chica, University of North Texas
Numerical Schemes for Mixtures of Isotropic and Nematic Flows Taking into Account Anchoring and Stretching Effects

The study of interfacial dynamics between two different components has become the key role to understand the behavior of many interesting systems. Indeed, two-phase flows composed of fluids exhibiting different microscopic structures are an important class of engineering materials. The dynamics of these flows are determined by the coupling among three different length scales: microscopic inside each component, mesoscopic interfacial morphology and macroscopic hydrodynamics. Moreover, in the case of complex fluids composed by the mixture between isotropic (newtonian fluid) and nematic (liquid crystal) flows, its interfaces exhibit novel dynamics due to anchoring effects of the liquid crystal molecules on the interface.

In this talk I will introduce a PDE system to model mixtures composed by isotropic fluids and nematic liquid crystals, taking into account viscous, mixing, nematic, stretching and anchoring effects and reformulating the corresponding stress tensors in order to derive a dissipative energy law. Then, I will present new linear unconditionally energy-stable splitting schemes that allows us to split the computation of the three pairs of unknowns (velocity-pressure, phase field-chemical potential and director vector-equilibrium) in three different steps. The fact of being able to decouple the computations in different linear sub-steps maintaining the discrete energy law is crucial to carry out relevant numerical experiments under a feasible computational cost and assuring the accuracy of the computed results.

Finally, I will present several numerical simulations in order to show the efficiency of the proposed numerical schemes, the influence of the shape of the nematic molecules (stretching effects) in the dynamics and the importance of the interfacial interactions (anchoring effects) in the equilibrium configurations achieved by the system.

(Refreshments at 3:00PM in the Computational Math Area of LDMC)

Wednesday, February 19, 2020

Posted February 7, 2020
Last modified February 17, 2020

3:30 pm – 4:30 pm Lockett 233

Mike Wong, Louisiana State University
Ribbon Homology Cobordisms

Abstract: A cobordism between 3-manifolds is ribbon if it has no 3-handles. Such cobordisms arise naturally from several different topological and geometric contexts. In this talk, we describe a few obstructions to their existence, from Thurston geometries, character varieties, and instanton and Heegaard Floer homologies, and some applications. This is joint work with Aliakbar Daemi, Tye Lidman, and Shea Vela-Vick.

Posted February 7, 2020
Last modified February 16, 2020

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 235

Gestur Olafsson, Mathematics Department, LSU
Toeplitz operators and representation theory I

We will discuss the basic ideas how representation theory can be used in the Theory of Toeplitz operators. We start with a general set up of a group acting on a complex manifold with a quasi-invariant measure such that there are non-trivial holomorphic L^2-functions and discuss how that leads to Toeplitz operators. We then introduce several examples. We then connect this to representation theory and explain how representation theory can be used to obtain commutative C^*-algebras of Toeplitz operators. Finally we describe how those ideas can be used to determine the spectrum of the so obtained C^*-algebra by constructing an isomorphism into a L^2-space which is easier to understand. The talks should be accessible to graduate students. We will at least use two seminar talks for the material.

Most of this material is a joint work with M. Dawson and R. Quiroga.

Tuesday, February 25, 2020

Posted January 14, 2020

Mardi Gras Holiday

Thursday, February 27, 2020

Posted February 24, 2020
Last modified March 3, 2021

Algebra and Number Theory Seminar Questions or comments?

6:00 pm 321 Lockett in the Keisler Lounge

Actuarial club meeting

Matthew Arnold from Blue Cross Blue Shield of Louisiana will be our guest speaker. He is one of their associate actuaries and one of LSU's advising actuaries. His topic will be regarding Medicare Supplement / Medicare Advantage. The meeting will take place at 6pm. As always pizza will be served at the meeting.

Tuesday, March 3, 2020

Posted February 6, 2020
Last modified February 27, 2020

3:10 pm – 12:00 am 232 Lockett

John Doyle, Louisiana Tech University
Dynamical modular curves and uniform boundedness of preperiodic points

In the mid-1990's, Merel proved the strong uniform boundedness conjecture for torsion points on elliptic curves over number fields. Around the same time, work of Nguyen-Saito and Abramovich established the function field analogue by showing that the gonalities of the modular curves X_1(n) tend to infinity. By studying the geometry of dynamical modular curves, one can prove uniform boundedness for preperiodic points for certain interesting families of polynomial maps over function fields. I will discuss this result as well as a consequence for the dynamical uniform boundedness conjecture over number fields, originally posed by Morton and Silverman. This is joint work with Bjorn Poonen.

Posted February 15, 2020

3:30 pm – 4:30 pm Digital Media Center 1034

Li Wang, University of Texas at Arlington
Probabilistic Semi-supervised Learning via Sparse Graph Structure Learning

Abstract: We present a probabilistic semi-supervised learning (SSL) framework based on sparse graph structure learning. Different from existing SSL methods with either a predefined weighted graph heuristically constructed from the input data or a learned graph based on the locally linear embedding assumption, the proposed SSL model is capable of learning a sparse weighted graph from the unlabeled high-dimensional data and a small amount of labeled data, as well as dealing with the noise of the input data. Our representation of the weighted graph is indirectly derived from a unified model of density estimation and pairwise distance preservation in terms of various distance measurements, where latent embeddings are assumed to be random variables following an unknown density function to be learned and pairwise distances are then calculated as the expectations over the density for the model robustness to the data noise. Moreover, the labeled data based on the same distance representations is leveraged to guide the estimated density for better class separation and sparse graph structure learning. A simple inference approach for the embeddings of unlabeled data based on point estimation and kernel representation is presented. Extensive experiments on various data sets show the promising results in the setting of SSL compared with many existing methods, and significant improvements on small amounts of labeled data. div

Wednesday, March 4, 2020

Posted February 7, 2020
Last modified February 16, 2020

3:30 pm – 4:30 pm Lockett 235

Gestur Olafsson, Mathematics Department, LSU
Toeplitz operators and representation theory II

Posted January 30, 2020
Last modified March 3, 2020

3:30 pm – 4:30 pm Lockett 233

Eva Elduque, University of Michigan
Mixed Hodge structures on Alexander modules

Abstract: Given an epimorphism from the fundamental group of a smooth complex algebraic variety U onto the integers Z, one naturally obtains an infinite cyclic cover of the variety. In analogy with knot theory, the homology groups of this infinite cyclic cover, which are endowed with Z-actions by deck transformations, determine the family of Alexander modules associated to the epimorphism. In this talk, we will talk about how to equip the torsion part of the Alexander modules (with respect to the Z-actions) with canonical mixed Hodge structures in the case when the epimorphism is the induced map on fundamental groups of an algebraic map f from U into the punctured complex plane. Furthermore, we will compare the resulting mixed Hodge structure to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of f. The relevant concepts will be introduced during the talk. Joint work with C. Geske, L. Maxim, and B. Wang.

Thursday, March 5, 2020

Posted February 9, 2020
Last modified March 2, 2020

3:30 pm – 4:20 pm Lockett 232

Thang Le, Georgia Tech
Knot invariants and algebraic structures based on knots

Abstract: Knot theory plays an important role in topology and has interesting relations to many remote branches of mathematics and physics, like number theory and non-commutative algebras. In this talk we discuss the an algebra of surfaces defined by knots (skein algebra) which has connections to many important objects including hyperbolic structures of surfaces, cluster algebra, and quantum groups. The talk is elementary, and no prior knowledge of knot theory or quantum groups is required.

Monday, March 9, 2020

Posted December 2, 2019
Last modified March 8, 2020

3:30 pm Lockett 233

Rudi Weikard, University of Alabama at Birmingham
Topics in inverse problems of differential equations

Rudi Weidard's research interests are currently in Inverse Problems. He also investigates differential equations in the complex domain and in abelian functions.

Tuesday, March 10, 2020

Posted March 7, 2020

3:30 pm – 4:20 pm tba

Faculty Meeting

Wednesday, March 11, 2020

Posted November 11, 2019
Last modified March 8, 2020

3:30 pm – 4:30 pm Lockett 233

Zhenkun Li, MIT
Decomposing sutured Instanton Floer homology

Abstract: Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka. In this talk I will explain how to decompose sutured Instanton Floer homology with respect to a properly embedded surfaces inside the sutured manifold, and explain how this decomposition could be used to study the topological complexities of sutured manifolds and taut foliations. This work is partially joint with Sudipta Ghosh.

Posted March 9, 2020

3:30 pm – 4:30 am Lockett 235

Gestur Olafsson, Mathematics Department, LSU
Toeplitz operators and representation theory III

Abstract: We will discuss the basic ideas how representation theory can be used in the Theory of Toeplitz operators. We start with a general set up of a group acting on a complex manifold with a quasi-invariant measure such that there are non-trivial holomorphic L^2-functions and discuss how that leads to Toeplitz operators. We then introduce several examples. We then connect this to representation theory and explain how representation theory can be used to obtain commutative C^*-algebras of Toeplitz operators. Finally we describe how those ideas can be used to determine the spectrum of the so obtained C^*-algebra by constructing an isomorphism into a L^2-space which is easier to understand. The talks should be accessible to graduate students. We will at least use two seminar talks for the material. Most of this material is a joint work with M. Dawson and R. Quiroga.

Thursday, March 12, 2020

Posted March 10, 2020
Last modified March 11, 2020

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 10

Faculty Meeting

Tuesday, March 24, 2020

Posted January 14, 2020

Spring Break

Tuesday, April 7, 2020

Posted March 30, 2020
Last modified April 5, 2020

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm Zoom

Richard Gottesman, Queen's University
Vector-Valued Modular Forms

The collection of vector-valued modular forms form a graded module over the ring of modular forms. I will explain how understanding the structure of this module allows one to show that the component functions of vector-valued modular forms satisfy an ordinary differential equation whose coefficients are modular forms. This enables one to give explicit formulas for vector-valued modular forms in terms of hypergeometric series. In certain cases, one can use such formulas to prove the unbounded denominator conjecture.

Tuesday, April 21, 2020

Posted January 14, 2020
Last modified April 9, 2020

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm Zoom

Alyson Deines, Center for Communications Research La Jolla (CCR-L)
Elliptic Curves of Prime Conductor

The torsion order elliptic curves over $\Q$ with prime conductor have been well studied. In particular, we know that for an elliptic curve $E/Q$ with conductor $p$ a prime, if $p > 37$, then E has either no torsion, or is a Neumann-Setzer curve and has torsion order 2. In this talk we examine similar behavior for elliptic curves of prime conductor defined over totally real number fields.

Tuesday, April 28, 2020

Posted April 20, 2020

3:30 pm – 4:20 pm Cloud

Meeting of Tenured Faculty

Wednesday, June 10, 2020

Posted June 3, 2020
Last modified June 8, 2020

3:30 pm – 4:30 pm zoom link: https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Gestur Olafsson, Mathematics Department, LSU
Toeplitz operators and representation theory III

Wednesday, June 17, 2020

Posted June 15, 2020

3:30 pm – 4:30 pm zoom link: https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Gestur Olafsson, Mathematics Department, LSU
Toeplitz operators and representation theory IV

Wednesday, June 24, 2020

Posted June 15, 2020

3:30 pm – 4:30 pm zoom link: https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Gestur Olafsson, Mathematics Department, LSU
Toeplitz operators and representation theory V

We will discuss the basic ideas how representation theory can be used in the Theory of Toeplitz operators. We start with a general set up of a group acting on a complex manifold with a quasi-invariant measure such that there are non-trivial holomorphic L^2-functions and discuss how that leads to Toeplitz operators. We then introduce several examples. We then connect this to representation theory and explain how representation theory can be used to obtain commutative C^*-algebras of Toeplitz operators. Finally we describe how those ideas can be used to determine the spectrum of the so obtained C^*-algebra by constructing an isomorphism into a L^2-space which is easier to understand. The talks should be accessible to graduate students. We will at least use two seminar talks for the material. Most of this material is a joint work with M. Dawson and R. Quiroga.

Wednesday, July 1, 2020

Posted June 15, 2020

3:30 pm – 4:30 pm zoom link: https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Jens Christensen, Colgate University
Atomic decompositions of Bergman spaces

In the 1980''s Coifman and Rochberg provided atomic decompositions for Bergman spaces on (the unbounded realization of) bounded symmetric domains as well as on the unit ball. Their atoms were point evaluations of the Bergman kernel. Also, their results did not readily transfer to the bounded realization of the domain except in the case of the unit ball. By applying representation/coorbit theory we obtain a large family of new atoms (including the classical ones) for Bergman spaces on bounded symmetric domains. Our approach also allows us to describe the relation between atoms for the bounded and unbounded realizations of the domain thus solving one of the issues raised by Coifman and Rochberg. We finally list a few open questions for domains of rank higher than one. This is joint work with Gestur Olafsson.

Tuesday, July 7, 2020

Posted July 1, 2020

Virtual Short Course for Researchers in Order, Algebra, and Logic

9:00 am – 10:00 am https://us02web.zoom.us/j/9504584395

On the Yosida Representation Theorem: Classical and Point-free Versions (Lecture 5).

The fifth in a series of lectures by James Madden, intended to provide background and foundations leading to an introduction to several unsolved problems on the geometry of Archimedean lattice-ordered groups. Lecture notes for past lectures in this course can be found here: https://www.math.lsu.edu/SeminarOrderAlgebraLogic.

Tuesday, July 14, 2020

Posted July 10, 2020

Virtual Short Course for Researchers in Order, Algebra, and Logic

9:00 am – 10:00 am https://us02web.zoom.us/j/9504584395

Lecture 6: Relative uniform convergence and the Yosida locale

The sixth in a series of lectures by James Madden, intended to provide background and foundations leading to an introduction to several unsolved problems on the geometry of Archimedean lattice-ordered groups. Lecture notes for past lectures in this course can be found here: https://www.math.lsu.edu/SeminarOrderAlgebraLogic.

Wednesday, July 15, 2020

Posted July 6, 2020

3:30 pm – 4:30 pm zoom link: https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Jens Christensen, Colgate University
Atomic decompositions of Bergman spaces II

In the 1980''''s Coifman and Rochberg provided atomic decompositions for Bergman spaces on (the unbounded realization of) bounded symmetric domains as well as on the unit ball. Their atoms were point evaluations of the Bergman kernel. Also, their results did not readily transfer to the bounded realization of the domain except in the case of the unit ball. By applying representation/coorbit theory we obtain a large family of new atoms (including the classical ones) for Bergman spaces on bounded symmetric domains. Our approach also allows us to describe the relation between atoms for the bounded and unbounded realizations of the domain thus solving one of the issues raised by Coifman and Rochberg. We finally list a few open questions for domains of rank higher than one. This is joint work with Gestur Olafsson.

Tuesday, July 21, 2020

Posted July 17, 2020
Last modified March 2, 2021

Virtual Short Course for Researchers in Order, Algebra, and Logic

9:00 am – 10:15 am https://us02web.zoom.us/j/9504584395

Lecture 7: Lindelöf locales and the locale of real numbers

The seventh in a series of lectures by James Madden, intended to provide background and foundations leading to an introduction to several unsolved problems on the geometry of Archimedean lattice-ordered groups. Lecture notes for past lectures in this course can be found here: https://www.math.lsu.edu/SeminarOrderAlgebraLogic.

Tuesday, July 28, 2020

Posted July 24, 2020

Virtual Short Course for Researchers in Order, Algebra, and Logic

9:00 am – 10:15 am https://us02web.zoom.us/j/9504584395

Lecture 8: Computations in the locale of real numbers

The eighth in a series of lectures by James Madden, intended to provide background and foundations leading to an introduction to several unsolved problems on the geometry of Archimedean lattice-ordered groups. Lecture notes for past lectures in this course can be found here: https://www.math.lsu.edu/SeminarOrderAlgebraLogic.

Wednesday, July 29, 2020

Posted July 20, 2020
Last modified July 28, 2020

3:30 pm – 4:30 pm zoom link: https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Matthew Dawson, Centro de Investigacion en Matematicas
Infinite-dimensional groups and virtual root systems

The study of infinite-dimensional Lie groups and Lie algebras is a growing area of mathematics with interesting connections to mathematical physics and harmonic analysis. In this talk we will focus mainly on such groups and Lie algebras that are constructed from finite-dimensional Lie groups and Lie algebras via direct limits. This allows one to construct infinite-dimensional analogues of the classical groups that are nonetheless of countable dimension (so that they are, in some sense, the "smallest" infinite-dimensional Lie groups that can be constructed). They inherit many properties of their finite-dimensional counterparts, but present new phenomena only seen in infinite-dimensional groups. We will finish with a discussion of ongoing joint work with Johanna Hennig on the structure of certain direct limits of semisimple Lie algebras that are known not to possess root-space decompositions in the traditional sense. Nonetheless, we construct a "virtual root-space decomposition" by way of direct integrals, a tool from harmonic analysis.

Tuesday, August 4, 2020

Posted July 31, 2020

Virtual Short Course for Researchers in Order, Algebra, and Logic

9:00 am – 10:15 am https://us02web.zoom.us/j/9504584395

Lecture 9: Computations II. Applications.

The ninth in a series of lectures by James Madden, intended to provide background and foundations leading to an introduction to several unsolved problems on the geometry of Archimedean lattice-ordered groups. Lecture notes for past lectures in this course can be found here: https://www.math.lsu.edu/SeminarOrderAlgebraLogic.

Wednesday, August 5, 2020

Posted July 20, 2020
Last modified March 2, 2021

3:30 pm – 4:30 pm zoom link: https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Matthew Dawson, Centro de Investigacion en Matematicas
Infinite-dimensional groups and virtual root systems

Tuesday, August 11, 2020

Posted August 7, 2020

Virtual Short Course for Researchers in Order, Algebra, and Logic

9:00 am – 10:15 am https://us02web.zoom.us/j/9504584395

Lecture 10: Change of Unit. Examples.

The tenth in a series of lectures by James Madden, intended to provide background and foundations leading to an introduction to several unsolved problems on the geometry of Archimedean lattice-ordered groups. Lecture notes for past lectures in this course can be found here: https://www.math.lsu.edu/SeminarOrderAlgebraLogic.

Wednesday, August 12, 2020

Posted July 20, 2020

3:30 pm – 4:30 pm zoom link: https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Vignon Oussa, Bridgewater State University
HRT conjecture and linear independence of translates on the Heisenberg group.

In this talk, we will establish the relationship between the HRT Conjecture and linear independence of translation systems on the Heisenberg group. We will show that the HRT Conjecture is equivalent to the conjecture that co-central translates of square-integrable functions on the Heisenberg group are linearly independent. This result affirmatively answers a question asked at the HRT workshop in Saint Louis University in 2016

Monday, August 17, 2020

Posted January 31, 2020
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Tuesday, August 18, 2020

Posted August 14, 2020

Virtual Short Course for Researchers in Order, Algebra, and Logic

9:00 am – 10:15 am https://us02web.zoom.us/j/9504584395

Lecture 11: Categories of Representations

The eleventh in a series of lectures by James Madden, intended to provide background and foundations leading to an introduction to several unsolved problems on the geometry of Archimedean lattice-ordered groups. Lecture notes for past lectures in this course can be found here: https://www.math.lsu.edu/SeminarOrderAlgebraLogic.

Wednesday, August 19, 2020

Posted January 31, 2020
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, August 21, 2020

Posted January 31, 2020
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Tuesday, September 1, 2020

Posted August 25, 2021
Last modified September 17, 2021

3:30 pm – 4:30 pm

Kevin Schreve, Louisiana State University
TBD

Wednesday, September 16, 2020

Posted August 22, 2020
Last modified September 14, 2020

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm zoom link: https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Stephen Shipman, Mathematics Department, LSU
Introduction to Fourier analysis for Z^d and applications

The aim of my talks is to develop the Fourier analysis underlying the study of periodic operators; to show how the theory is applied to phenomena of crystal-type structures in solid-state physics; and to indicate the kinds of problems of interest today. The first talk will concentrate on the Fourier analysis for actions of Z^d and its finite-index extensions. The second talk will delve into aspects of the spectrum of periodic operators and their perturbations, including continuous pre-fractal and fractal continuous spectrum; and eigenvalues embedded in the continuum. The third talk will continue with topics of current interest, such as Dirac cones in graphene, multi-layer structures, Berry phase, twisted bi-layer graphene, etc.

Tuesday, September 22, 2020

Posted August 21, 2020
Last modified September 20, 2020

3:10 pm – 4:00 pm Zoom

C. Douglas Haessig, University of Rochester
Hecke polynomials and the Legendre and Kloosterman families

The Legendre family of elliptic curves and the Kloosterman family of exponential sums, while quite different, share many of the same arithmetic properties. In this talk, we will discuss their symmetric power L-functions and their relation to Hecke polynomials of cusp forms. Some of these relations are conjectural, and a few are now proven.

Wednesday, September 23, 2020

Posted August 22, 2020
Last modified September 14, 2020

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm zoom link: https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Stephen Shipman, Mathematics Department, LSU
Introduction to Fourier analysis for Z^d and applications

Tuesday, September 29, 2020

Posted September 3, 2020
Last modified September 15, 2020

3:10 pm – 4:00 pm Zoom

Pablo S. Ocal, Texas A&M University
Hochschild cohomology of general twisted tensor products

The Hochschild cohomology is a tool for studying associative algebras that has a lot of structure: it is a Gerstenhaber algebra. This structure is useful because of its applications in deformation and representation theory, and recently in quantum symmetries. Unfortunately, computing it remains a notoriously difficult task. In this talk we will present techniques that give explicit formulas of the Gerstenhaber algebra structure for general twisted tensor product algebras. This will include an unpretentious introduction to this cohomology and to our objects of interest, as well as the unexpected generality of the techniques. This is joint work with Tekin Karadag, Dustin McPhate, Tolulope Oke, and Sarah Witherspoon.

Wednesday, September 30, 2020

Posted August 22, 2020
Last modified September 14, 2020

3:30 pm – 4:30 pm zoom link: https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Stephen Shipman, Mathematics Department, LSU
Introduction to Fourier analysis for Z^d and applications.

Thursday, October 8, 2020

Posted February 24, 2021

Algebra and Number Theory Seminar Questions or comments?

4:00 pm

Sarah Allred, Louisiana State University
Unavoidable induced subgraphs of large 2-connected graphs

Tuesday, October 13, 2020

Posted September 1, 2020
Last modified October 1, 2021

3:10 pm – 4:00 pm Zoom 987 8361 8703

Walter Bridges, Louisiana State University
Statistics for Partitions and Unimodal Sequences

Under the uniform probability measure on partitions of $n$, what is the size of a typical largest part, as $n →∞$? The study of statistics for partitions is concerned with such questions. This field was revolutionized by Fristedt who in a 1993 transactions paper introduced a useful probabilistic model and a method to transfer results back to the uniform measure. We demonstrate how this machinery can be used to prove an asymptotic formula for certain restricted partitions. The probabilistic approach has some heuristic advantages over a classical circle method/saddle-point method approach.

This work was motivated by the speaker's study of limit shapes for unimodal sequences of integers, 0-1 laws for the shapes of their diagrams. We briefly discuss these results also.

Posted October 8, 2020

4:10 pm – 5:00 pm Zoom

Meeting of the tenured faculty

Wednesday, October 14, 2020

Posted September 17, 2020
Last modified October 8, 2020

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm zoom link: https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Raul Quiroga, Centro de Investigacion en Matematicas (CIMAT)
Moment maps on the unit ball and commuting Toeplitz operators I.

Weighted Bergman spaces on the unit ball are reproducing kernel Hilbert spaces that provide an interesting object to study in functional analysis. These spaces come with the so-called Toeplitz operators, defined as multiplication operators by essentially bounded symbols followed by the orthogonal (Bergman) projection. The C*-algebra generated by all Toeplitz operators is highly non-commutative. However, it was discovered the existence of many large commutative C*-subalgebras contained in the C*-algebra generated by Toeplitz operators. Some of these commutative C*-algebras turned out to be associated with maximal Abelian subgroups (MASG) of the automorphism group of the unit ball. More precisely, the C*-algebra generated by Toeplitz operators with G-invariant symbols is commutative for G a MASG. This is no longer true for an arbitrary connected Abelian group.

We will present a geometric construction that associates to any connected Abelian subgroup H of automorphisms of the unit ball a set of symbols whose Toeplitz operators generate a commutative C*-algebra, regardless of whether H is maximal or not. Such construction is based on the moment map associated with the H-action on the unit ball which uses the symplectic structure involved. The families of symbols so obtained include all the special families of symbols currently found in the literature whose Toeplitz operators generate commutative C*-algebras. Furthermore, our construction provides new families of symbols not previously considered. Also, for all of our special symbols we can obtain spectral integral formulas for the corresponding Toeplitz operators.

Tuesday, October 20, 2020

Posted September 1, 2020
Last modified October 26, 2021

3:10 pm – 4:00 pm Zoom 987 8361 8703

Juliette Bruce, University of California, Berkeley/MSRI
The top weight cohomology of $A_g$

I will discuss recent work calculating the top weight cohomology of the moduli space $A_g$ of principally polarized abelian varieties of dimension $g$ for small values of $g$. The key idea is that this piece of cohomology is encoded combinatorially via the relationship between the boundary complex of a compactification of $A_g$ and the moduli space of tropical abelian varieties. This is joint work with Madeline Brandt, Melody Chan, Margarida Melo, Gwyneth Moreland, and Corey Wolfe.

Wednesday, October 21, 2020

Posted September 17, 2020
Last modified October 8, 2020

3:30 pm – 4:30 pm zoom link: https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Raul Quiroga, Centro de Investigacion en Matematicas (CIMAT)
Moment maps on the unit ball and commuting Toeplitz operators II.

Thursday, October 22, 2020

Posted February 24, 2021

Algebra and Number Theory Seminar Questions or comments?

4:00 pm

Rose McCarty, Princeton University
Coloring visibility graphs

Tuesday, October 27, 2020

Posted October 17, 2020
Last modified October 18, 2020

3:10 pm – 4:00 pm Zoom 987 8361 8703

Jianping Pan, University of California, Davis
Crystal for stable Grothendieck polynomials

The Grothendieck polynomials arise from enumerative geometry, as they can be used to calculate the intersection numbers for the Flag varieties. We introduce a crystal on decreasing factorizations of 321-avoiding elements of the 0-Hecke monoid, whose generating functions are the stable Grothendieck polynomials. This crystal is a K-theoretic generalization of the Morse-Schilling crystal on decreasing factorizations in the symmetric group. We prove that it intertwines with the crystal on set-valued tableaux introduced by Monical, Pechenik, and Scrimshaw (through the residue map). We also define a new insertion algorithm that intertwines with our crystal, with surprising connections to the Hecke insertion algorithm and the uncrowding algorithm for set-valued tableaux.
This talk is based on joint work arXiv:1911.08732 with Jennifer Morse, Wencin Poh, and Anne Schilling.

Wednesday, October 28, 2020

Posted October 8, 2020
Last modified October 26, 2020

3:30 pm – 4:30 pm https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09
(Originally scheduled for Thursday, October 8, 2020)

Nicholas J Christoffersen, LSU
Representations of Cuntz algebras associated to random walks on graphs

We introduce a class of representations of the Cuntz algebra associated to random walks on graphs. The representations are constructed using the dilation theory of row coisometries. We study these representations, their commutant and the intertwining operators. This is a joint work with Dr. Dorin Dutkay at the University of Central Florida.

Monday, November 2, 2020

Posted October 25, 2020
Last modified October 29, 2020

Algebra and Number Theory Seminar Questions or comments?

3:30 pm https://lsu.zoom.us/j/93208607251?pwd=RVRzeE1BSmFnZXEwMEVsdmVicnYxdz09

Khang Huynh, UCLA
A geometric trapping approach to global regularity for 2D Navier-Stokes on manifolds

We use frequency decomposition techniques to give a direct proof of global existence and regularity for the Navier-Stokes equations on two-dimensional Riemannian manifolds without boundary. Our techniques are inspired by an approach of Mattingly and Sinai which was developed in the context of periodic boundary conditions on a flat background, and which is based on a maximum principle for Fourier coefficients. The extension to general manifolds requires several new ideas, connected to the less favorable spectral localization properties in our setting. Our arguments make use of frequency projection operators, multilinear estimates that originated in the study of the non-linear Schrodinger equation, and ideas from microlocal analysis.

This is joint work with Aynur Bulut.

Tuesday, November 3, 2020

Posted October 6, 2020
Last modified October 26, 2021

3:10 pm – 4:00 pm Zoom 987 8361 8703

Manami Roy, Fordham University
An equidistribution theorem for automorphic representations of GSp(4).

There are some well-known classical equidistribution results like Sato-Tate conjecture for elliptic curves and Hecke eigenvalues of classical modular forms. In this talk, we will discuss a similar equidistribution result for a family of cuspidal automorphic representations of GSp(4). We formulate our theorem explicitly in terms of the number of cuspidal automorphic representations in this family. To count the number of these cuspidal automorphic representations, we will explore the connection between Siegel modular forms and automorphic representations of GSp(4). The talk is based on a recent work arXiv:2010.09996 with Ralf Schmidt and Shaoyun Yi.

Thursday, November 5, 2020

Posted February 24, 2021

Algebra and Number Theory Seminar Questions or comments?

4:00 pm

Zach Walsh, Louisiana State University
An Application of Extremal Matroid Theory

Tuesday, November 17, 2020

Posted October 6, 2020
Last modified October 26, 2021

3:10 pm – 4:00 pm Zoom 987 8361 8703

Bella Tobin, Oklahoma State University
Post-critically finite polynomials with everywhere good reduction

Post-critically finite maps are described as dynamical analogs of CM Abelian Varieties. CM abelian varieties defined over the complex numbers are algebraic, and we know they have everywhere good reduction in some finite extension of their base field. This motivates us to ask the question: do PCF maps have good reduction? We will review the basics of good reduction, discuss useful properties of reduction in arithmetic dynamics, and explore the reduction properties of post-critically finite polynomials.

Monday, November 30, 2020

Posted October 28, 2020
Last modified November 29, 2020

Algebra and Number Theory Seminar Questions or comments?

3:30 pm https://lsu.zoom.us/j/92851843655?pwd=dGRGMzIvSmt2UEZwa3g1TmJGVnZTQT09

Edriss Titi, University of Cambridge, Texas A&M University, and Weizmann Institute of Science
Recent Advances Concerning the Navier-Stokes and Euler Equations

In this talk I will discuss some recent progress concerning the Navier-Stokes and Euler equations of incompressible fluid. In particular, issues concerning the lack of uniqueness using the convex integration machinery and their physical relevance. Moreover, I will show the universality of the critical $1/3$ H\"older exponent, conjectured by Onsager for the preservation of energy in Euler equations, by extending the Onsager conjecture for the preservation of generalized entropy in general conservation laws. In addition, I will present a blow-up criterion for the 3D Euler equations based on a class of inviscid regularization for these equations and the effect of physical boundaries on the potential formation of singularity.

Tuesday, December 1, 2020

Posted October 7, 2020
Last modified October 26, 2021

3:10 pm – 4:00 pm Zoom 987 8361 8703

Lea Beneish, McGill University
Weierstrass mock modular forms and vertex operator algebras

Using techniques from the theory of mock modular forms and harmonic Maass forms, especially Weierstrass mock modular forms, we establish several dimension formulas for certain holomorphic, strongly rational vertex operator algebras, complementing previous work by van Ekeren, Moller, and Scheithauer. As an application, we show that certain special values of the completed Weierstrass zeta function are rational. This talk is based on joint work with Michael Mertens.

Thursday, December 3, 2020

Posted February 24, 2021

4:00 pm

Amin Bahmanian, Illinois State University
Laminar Families and Connected Fair Detachments

Monday, January 4, 2021

Posted November 3, 2020
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, January 6, 2021

Posted November 3, 2020
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, January 8, 2021

Posted November 3, 2020
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Monday, January 25, 2021

Posted January 21, 2021
Last modified March 2, 2021

3:30 pm Zoom (https://lsu.zoom.us/j/91681134143)

Li Chen, LSU
L^p Poincaré inequalities on nested fractals

On nested fractals such as Sierpinski gasket and Vicsek sets, neither analogue of curvature nor differential structure exists. In this setting, I will discuss scale invariant L^p Poincaré inequalities on metric balls in the range 1 ≤ p ≤ 2, using an essentially heat kernel based approach. This is joint work with Fabrice Baudoin.

Monday, February 8, 2021

Posted January 21, 2021
Last modified February 7, 2021

3:30 pm Zoom (Link: https://lsu.zoom.us/j/91327987785)

Bjoern Bringmann, UCLA
Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity

In this talk, we discuss the construction and invariance of the Gibbs measure for a three- dimensional wave equation with a Hartree-nonlinearity. In the first part of the talk, we construct the Gibbs measure and examine its properties. We discuss the mutual singularity of the Gibbs measure and the so-called Gaussian free field. In contrast, the Gibbs measure for one or two-dimensional wave equations is absolutely continuous with respect to the Gaussian free field. In the second part of the talk, we discuss the probabilistic well-posedness of the corresponding nonlinear wave equation, which is needed in the proof of invariance. At the moment, this is the only theorem proving the invariance of any singular Gibbs measure under a dispersive equation.

Monday, February 15, 2021

Posted January 24, 2021
Last modified February 14, 2021

3:30 pm Zoom (Link: https://lsu.zoom.us/j/98145526481)

Phillip Isett, UT Austin
A Proof of Onsager's Conjecture for the Incompressible Euler Equations

In an effort to explain how anomalous dissipation of energy occurs in hydrodynamic turbulence, Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations may fail to exhibit conservation of energy if their spatial regularity is below 1/3-Hölder. I will discuss a proof of this conjecture that shows that there are nonzero, (1/3-\epsilon)-Hölder Euler flows in 3D that have compact support in time. The construction is based on a method known as "convex integration," which has its origins in the work of Nash on isometric embeddings with low codimension and low regularity. A version of this method was first developed for the incompressible Euler equations by De Lellis and Székelyhidi to build Hölder-continuous Euler flows that fail to conserve energy, and was later improved by Isett and by Buckmaster-De Lellis-Székelyhidi to obtain further partial results towards Onsager's conjecture. The proof of the full conjecture combines convex integration using the "Mikado flows" introduced by Daneri-Székelyhidi with a new "gluing approximation" technique. The latter technique exploits a special structure in the linearization of the incompressible Euler equations.

Wednesday, February 17, 2021

Posted February 3, 2021
Last modified February 12, 2021

3:30 pm Zoom Link https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Nikolai Vasilevski, CINVESTAV
Toeplitz operators on the Bergman space

The talk is intended for a wide audience, not necessarily consisting of experts in the theory of Toeplitz operators, and is a review of the results on the description of algebras generated by Toeplitz operators, with symbols from various special classes, and acting in standard weighted Bergman spaces on the unit ball. We begin with a somewhat surprising and unpredictable result on the existence of a large class of non-isomorphic commutative C*-algebras generated by Toeplitz operators. As it turned out, their symbols must be invariant under the action of maximal Abelian subgroups of the biholomorphisms of the unit ball. The next surprise was the discovery of a large number of Banach (not C*) algebras, which turned out to be, as a rule, not semisimple. The problem here is to find a compact set of maximal ideals and to describe the radical. Finally we consider in more detail non-commutative C*-algebras generated by Toeplitz operators whose symbols are invariant under the action of a subgroup of some maximal Abelian group of biholomorphisms. As it turned out, different types of the action of the same subgroup lead to completely different properties of the corresponding algebras.

Monday, February 22, 2021

Posted January 24, 2021
Last modified February 15, 2021

3:30 pm Zoom link: https://lsu.zoom.us/j/5494314978

Tuoc Phan, University of Tennessee–Knoxville
Regularity theory in Sobolev spaces for parabolic-elliptic equations with singular degenerate coefficients

We consider a class of second order elliptic and parabolic equations in the upper-half space in which the coefficients can be singular or degenerate on the boundary as of prototype x_d alpha, where alpha is a real number. Two boundary value problems are considered: the zero flux one and the homogeneous Dirichlet one. Corresponding to each of the two problem, generic weighted Sobolev spaces are found to establish the existence, uniqueness, and regularity estimates solutions. As alpha may not be in (-1, 1), our weight x_d alpha may not be in the A_2 Muckenhoupt class of weight as commonly considered in literature. Moreover, the results demonstrate that different weighted Sobolev spaces are required for the two different boundary conditions, a phenomenon that is not seen in the case that the coefficients are uniformly elliptic. The talk is based on joint work with Hongjie Dong (Brown University).

Wednesday, February 24, 2021

Posted February 22, 2021
Last modified February 23, 2021

12:00 pm – 1:00 am Zoom

Bahar Acu, ETH Zürich
Contact Topology and Geometry in High Dimensions

Posted February 19, 2021

3:30 pm Zoom Link https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Nikolai Vasilevski, CINVESTAV
Toeplitz operators on the Bergman space

Thursday, February 25, 2021

Posted February 24, 2021
Last modified February 25, 2021

4:00 pm https://lsu.zoom.us/j/98833974073?pwd=WnhDbDY5d0ljbjBldEVWT1JacE1zQT09

George Drummond, University of Canterbury
Circuit-difference matroids

One characterization of binary matroids is that the symmetric difference of every pair of intersecting circuits is a disjoint union of circuits. We will consider circuit-difference matroids, that is, those matroids in which the symmetric difference of every pair of intersecting circuits is a single circuit. Our main result shows that a connected regular matroid is circuit-difference if and only if it contains no pair of skew circuits. We also characterize the infinitely many excluded series minors for the class.

This was a joint work with Kevin Grace, Tara Fife and James Oxley.

Friday, February 26, 2021

Posted February 25, 2021

3:30 pm – 4:20 pm Zoom

Amita Malik, American Institute of Mathematics
Asymptotic analysis for certain arithmetic objects

Abstract: Counting problems lie at the heart of number theory, be it the study of primes, class numbers or the number of partitions of a positive integer. One of the most difficult underlying questions here pertains to the distribution of the zeros of L-functions. This goes back to the seminal paper on the study of the (Riemann) zeta function by Riemann in 1859. After an overview of the distribution of zeros of these functions, we discuss asymptotic behavior of the partition function with parts concerning a Chebotarev condition. In special cases, we obtain partitions into primes in arithmetic progressions. The error term present here gives an equivalent formulation of the generalized Riemann Hypothesis. Monotonicity of this partition function is established explicitly via an asymptotic formula in connection to a result of Bateman and Erdos.

Monday, March 1, 2021

Posted January 24, 2021
Last modified February 22, 2021

3:30 pm Zoom link: https://lsu.zoom.us/j/5494314978

Jinping Zhuge, University of Chicago
Large-scale regularity for stationary Navier-Stokes equations over non-Lipschitz boundaries

We consider the stationary Navier-Stokes equations over a mesoscopically oscillating John boundary (with a non-slip boundary condition), which is non-Lipschitz and allows (inward) cusps or fractals. With such low regularity on the oscillating boundary, we show a large-scale Lipschitz estimate for the velocity and a large-scale oscillation estimate for the pressure. By introducing the 1st-order and 2nd-order boundary layers, we also show large-scale C^{1,alpha} and C^{2,alpha} estimates (For C^{2,alpha} estimate, we assume the boundary is periodic). The proofs rely on the quantitative excess decay method developed recently in homogenization theory. This is joint work with Christophe Prange and Mitsuo Higaki.

Tuesday, March 2, 2021

Posted March 1, 2021
Last modified October 4, 2021

Algebra and Number Theory Seminar Questions or comments?

12:30 pm – 1:20 pm Zoom

Gene Kopp, University of Bristol
Complex equiangular lines and the Stark conjectures

How many lines can you draw through the origin in $d$-dimensional space with all pairwise angles equal? The complex version of this question in an open problem with applications in quantum information theory. Zauner conjectured based on numerical evidence that a configuration of $d^2$ complex equiangular lines—also called a SIC-POVM (symmetric, informationally complete, positive operator-valued measure)—always exists, but such configurations are known only in finitely many dimensions. We discuss an unexpected connection between Zauner's conjecture and number theory, specifically, class field theory. In known examples, a set of numbers called overlap phases that characterize a SIC-POVM are Galois conjugate to square roots of Stark units—algebraic units in class fields predicted to arise from special values of $L$-functions. We discuss a conjectural construction of SIC-POVMs from special values of $L$-functions and some results toward proving that construction.

Tuesday, March 9, 2021

Posted February 10, 2021
Last modified October 26, 2021

3:10 pm – 4:00 pm Zoom 987 8361 8703

Holly Swisher, Oregon State University
Generalizations of the Andrews-Alder Theorem in Partition Theory

Posted November 30, 2021

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Sam Shepherd, Vanderbilt University
TBA

Wednesday, March 10, 2021

Posted March 4, 2021

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to get password)

Michael Malisoff, LSU Roy P. Daniels Professor
Delay Compensation in Control Systems

Control systems are a class of dynamical systems that contain forcing terms. When control systems are used in biological or engineering applications, the forcing terms are often used to represent different possible forces that can be applied to the systems. Then the feedback control problem consists of finding formulas for the forcing terms, which are functions that can depend on the state of the systems, and which ensure a prescribed qualitative behavior of the dynamical systems, such as global asymptotic convergence towards an equilibrium point. Then the forcing terms are called feedback controls. However, many control systems in biology or engineering are subject to input delays, which preclude the possibility of using current values of the states of the control systems in the expressions for the feedback controls. One approach to solving feedback control problems under input delays involves solving the problems with the delays set equal to zero, and then computing upper bounds on the input delays that the systems can tolerate while still realizing the desired objective. For longer delays, the reduction model approach is often used but can lead to implementation challenges because it leads to distributed terms in the controls. A third approach to delay compensation involves sequential predictors, which can compensate for arbitrarily long input delays using stacks of differential equations instead of distributed terms. This talk reviews recent developments in this area, and is based in part on the speaker's collaborations with Miroslav Krstic, Frederic Mazenc, Fumin Zhang, and students. The talk will be understandable to those familiar with the basic theory of ordinary differential equations. No prerequisite background in systems and control will be needed to understand and appreciate this talk.

Posted March 8, 2021

3:30 pm – 4:20 pm Zoom

Faculty Meeting

Thursday, March 11, 2021

Posted March 10, 2021

4:00 pm https://lsu.zoom.us/j/98833974073?pwd=WnhDbDY5d0ljbjBldEVWT1JacE1zQT09

Ben Moore, University of Waterloo
A density bound for triangle free 4-critical graphs

Carsten Thomassen showed that every girth 5 graph embeddable in the torus or projective plane is 3-colourable. A complementary result of Robin Thomas and Barrett Walls shows that every girth 5 graph embedded in the Klein bottle is 3-colourable. I'll show neither the embeddability condition nor the girth 5 condition is needed in the above theorems by showing that every triangle-free 4-critical graph has average degree slightly larger than 10/3. This is joint work with Evelyne Smith Roberge.

Monday, March 15, 2021

Posted January 26, 2021
Last modified March 2, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Zoom link: https://lsu.zoom.us/j/5494314978

Zhongwei Shen, University of Kentucky
Sharp Convergence Rates for Darcy's Law

In this talk I will describe a recent work on the convergence rates for Darcy's law. We consider the Dirichlet problem for the steady Stokes equations in a periodically perforated and bounded domain. We establish the sharp convergence rate for the solutions as the period converges to zero. This is achieved by constructing two boundary correctors to control the boundary layers created by the incompressibility condition and the discrepancy of the boundary values. One of the correctors deals with the tangential boundary data, while the other handles the normal boundary data.

Tuesday, March 16, 2021

Posted March 15, 2021

3:10 pm – 4:00 pm Zoom 987 8361 8703

Samuel Wilson, LSU
Representations of SL(2, Z/nZ) and Applications to Modular Categories.

In this talk, we describe the irreducible representations of the groups SL(2, Z/nZ) and how they may be constructed as submodules of quadratic modules. We also discuss properties of such representations that are relevant to the study and classification of modular categories.

Wednesday, March 17, 2021

Posted March 10, 2021
Last modified March 11, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to get password)

Peter Wolenski, LSU Department of Mathematics Russell B. Long Professor
Introduction to Convex Analysis via the Elvis Problem

The Elvis problem was introduced into the undergraduate mathematical literature by Timothy Pennings whose dog (named Elvis) enjoyed fetching an object thrown from the shore of Lake Michigan into the water. Elvis was observed to retrieve the object by going in a path that resembled how light would refract in isotropic mediums according to Snell's Law. We retain the problem's "Elvis" nomenclature but greatly generalize the problem by considering anisotropic mediums and use the tools of Convex Analysis to provide a complete description of optimal movement. The velocity sets are closed, bounded convex sets containing the origin in its interior, whereas the original problem used only centered balls. Further generalizations are considered with faster movement allowed on the interface and with more than two mediums.

Posted March 6, 2021
Last modified March 15, 2021

3:30 pm – 4:30 pm https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Pierre Clare, William & Mary
Group C*-algebras, Constructions and representations

The purpose of these two talks is to describe some of the ways in which C*-algebras associated with topological groups allow to use tools from operator algebras and noncommutative geometry to study unitary representations. The first talk will be devoted to describing the unitary dual in the language of C*-algebras. In the second talk, we will focus on induced representations and aspects of the Mackey machine expressed in that language.

Quick review of abstract and concrete C*-algebras. The commutative case (Gelfand transform). Convolution algebras, group C*-algebras. Integration of representations. The abelian case (Fourier transform). Fell topology. The unitary dual as a noncommutative space.

Monday, March 22, 2021

Posted February 3, 2021
Last modified March 22, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Zoom (Link: https://lsu.zoom.us/j/91327987785?pwd=VlAxM0QvSDdPY1JSOHlwamVQVWdJQT09)

Yu Deng, USC
Random tensor and nonlinear dispersive equations

We discuss recent developments in the random data theory for nonlinear dispersive equations. In particular, we introduce the methods of random averaging operators and random tensors, which have been used to solve the full 2D Gibbs measure problem, and prove almost-sure well-posedness results at optimal regularity. This is joint work with Andrea R. Nahmod and Haitian Yue.

Tuesday, March 23, 2021

Posted March 15, 2021
Last modified March 16, 2021

3:10 pm – 4:00 pm Zoom 987 8361 8703

Ling Long, LSU
A Whipple formula revisited

A well-known formula of Whipple relates certain hypergeometric values $_7F_6(1)$ and $_4F_3(1)$. In this paper we revisit this relation from the viewpoint of the underlying hypergeometric data $HD$, to which there are also associated hypergeometric character sums and Galois representations. We explain a special structure behind Whipple's formula when the hypergeometric data $HD$ are primitive and defined over rationals. As a consequence, the values of the corresponding hypergeometric character sums can be explicitly expressed in terms of Fourier coefficients of certain modular forms. We further relate the hypergeometric values $_7F_6(1)$ in Whipple's formula to the periods of modular forms.

This is a joint project with Wen-Ching Winnie Li and Fang-Ting Tu. Most of the talk will be on a general background about how different hypergeometric aspects can be fit together. It should be accessible to graduate students.

Wednesday, March 24, 2021

Posted March 2, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to get password)

Romain Postoyan, CNRS Researcher
A Short Introduction to Event-Triggered Control

Control systems are increasingly implemented on digital platforms, which typically have limited power and computing and communication resources. In this context, the classical implementation of sampled-data control systems may not be suitable. Indeed, while the periodic transmission of data simplifies the analysis (in general) and the implementation of the control law, the induced use of the platform resources may be too demanding. An alternative consists of defining the transmission instants between the plant and the controller based on the actual system needs, and not the elapsed time since the last transmission. This alternative is the basis of event-triggered control. With this paradigm, a transmission occurs whenever a state/output-dependent criterion is violated. The key question is then how to define this triggering rule to ensure the desired control objectives, while guaranteeing the existence of a strictly positive minimum time between any two communications, which is essential in practice. In this presentation, we review basic techniques of the field, with particular attention to nonlinear systems, and compare them on examples. We also explain the interest of introducing auxiliary variables to define the transmission criterion, in which case we talk of dynamic event-triggered control. Finally, we conclude with some open problems.

Posted March 6, 2021
Last modified March 23, 2021

3:30 pm – 4:30 pm https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Irfan Alam, LSU
Generalizing de Finetti's theorem using nonstandard methods

In its classical form, de Finetti's theorem provides a representation of any exchangeable sequence of Bernoulli random variables as a mixture of sequences of iid random variables. Following the work of Hewitt and Savage, such a representation was known for exchangeable random variables taking values in any Polish space. In a recent work, the author has used nonstandard analysis to show that such a representation holds for a sequence of exchangeable random variables taking values in any Hausdorff space as long as their underlying distribution is Radon (in fact, tightness and outer regularity on compact sets are also sufficient). An overview of this work will be presented. The arguments have topological measure theoretic and combinatorial flavors, with nonstandard analysis serving as a bridge between these themes. A main component of this work involves generalizing a result of Paul Ressel that was previously obtained using abstract harmonic analysis.

Monday, March 29, 2021

Posted February 3, 2021
Last modified March 28, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Zoom (Link: https://lsu.zoom.us/j/98145526481)

Victor Lie, Purdue University
The LGC-method

Tuesday, March 30, 2021

Posted March 11, 2021
Last modified March 24, 2021

3:10 pm – 4:00 pm Zoom 987 8361 8703

Yau Wing Li, Massachusetts Institute of Technology
Endoscopy for affine Hecke category

Affine Hecke categories are categorifications of Iwahori-Hecke algebras, which are essential in the classification of irreducible representations of loop group LG with Iwahori-fixed vectors. The affine Hecke category has a monodromic counterpart, which contains sheaves with prescribed monodromy under the left and right actions of the maximal torus. We show that the neutral block of this monoidal category is equivalent to the neutral block of the affine Hecke category (with trivial torus monodromy) for the endoscopic group H. It is consistent with the Langlands functoriality conjecture.

Wednesday, March 31, 2021

Posted March 10, 2021
Last modified March 26, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)

Summer Atkins, University of Florida
Solving Singular Control Problems in Mathematical Biology, Using PASA

We will demonstrate how to use a non-linear polyhedral constrained optimization solver called the Polyhedral Active Set Algorithm (PASA) for solving a general optimal control problem that is linear in the control. In numerically solving for such a problem, oscillatory numerical artifacts can occur if the optimal control possesses a singular subarc. We consider adding a total variation regularization term to the objective functional of the problem to regularize these oscillatory artifacts. We then demonstrate PASA's performance on three singular control problems that give rise to different applications of mathematical biology.

Posted March 17, 2021

3:30 pm – 4:30 pm https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Phuc Nguyen, Department of Mathematics, Louisiana State University
The Hardy-Littlewood maximal function on Choquet spaces

I will present my recent joint work with Keng Hao Ooi in which we obtain the boundedness of the Hardy-Littlewood maximal function on $L^q$ type spaces defined via Choquet integrals associate to Sobolev capacities. The bounds are obtained in full range of exponents which also include a weak type end-point bound.

Monday, April 5, 2021

Posted February 19, 2021
Last modified April 4, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Zoom (Link https://lsu.zoom.us/j/98145526481)

Philippe Sosoe, Cornell University
Optimal integrability threshold for the Gibbs measure associated to the focusing NLS on the torus

In a seminal influential paper, Lebowitz, Rose and Speer (1988) constructed measures on periodic functions inspired by the Gibbs measures of statistical mechanics and based on Brownian motion. These measures are naturally associated to the focusing mass-critical nonlinear Schroedinger equation. They conjectured that these measures are invariant under the nonlinear flow. This was later proved by Bourgain. Lebowitz-Rose-Speer also proposed a critical mass threshold past which the measure no longer exists, given by the mass of the ground state on the real line.

With T. Oh and L. Tolomeo, we prove the optimality of this critical mass threshold. The proof also applies to the two-dimensional radial problem posed on the unit disc. In this case, this answer a question posed by Bourgain and Bulut (2014) on the optimal mass threshold. Furthermore, in the one-dimensional case, we show that the Gibbs measure is normalizable *at* the optimal mass threshold, answering another posed by Lebowitz, Rose, and Speer (1988). This latter fact is somewhat surprising in view of the minimal mass blowup solution for the focusing quintic nonlinear Schroedinger equation on the one-dimensional torus.

Tuesday, April 6, 2021

Posted February 10, 2021
Last modified April 2, 2021

3:10 pm – 4:00 pm Zoom 987 8361 8703

Angelica Babei, Dartmouth College
Period polynomials, their zeros, and Eichler cohomology

The study of period polynomials for classical modular forms has emerged due to their role in Eichler cohomology. In particular, the Eichler-Shimura isomorphism gives a correspondence between cusp eigenforms and their period polynomials. The coefficients of period polynomials also encode critical L-values for the associated modular form and thus contain rich arithmetic information. In this talk, we will examine period polynomials from both angles, including their cohomological interpretation as well as some of their analytic properties. Finally, I will describe joint work with Larry Rolen and Ian Wagner, where we introduce period polynomials for Hilbert modular forms of full level and prove that their zeros lie on the unit circle.

Wednesday, April 7, 2021

Posted February 20, 2021
Last modified March 26, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)

Warren Dixon, University of Florida Department of MAE Fellow of ASME and IEEE
Assured Autonomy: Uncertainty, Optimality, and Data Intermittency

Autonomous systems can provide advantages such as access, expendability, and scaled force projection in adversarial environments. However, such environments are inherently complex in the sense they are uncertain and data exchanges for sensing and communications can be compromised or denied. This presentation provides a deep dive into some feedback control perspectives related to uncertainty, optimality, and data intermittency that provide foundations for assured autonomous operations. New results will be described for guaranteed deep learning methods that can be employed in real-time with no data. These efforts include methods for (deep) reinforcement learning based approaches to yield approximate optimal policies in the presence of uncertainty. The presentation will conclude with examples of intermittent feedback that explore the data exchange limits for guaranteed operation, including purposeful intermittency to enable new capabilities. Specific examples include intermittency due to occlusions in image-based feedback and intermittency resulting from various network control problems.

Posted March 31, 2021
Last modified April 5, 2021

3:30 pm – 4:30 pm https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Pierre Clare, William & Mary
Group C*-algebras II

The purpose of these two talks is to describe some of the ways in which C*-algebras associated with topological groups allow to use tools from operator algebras and noncommutative geometry to study unitary representations. In the this talk, we will focus on induced representations and aspects of the Mackey machine expressed in that language.
Hilbert modules, crossed products and the Mackey Machine.
Induced representations a la Mackey. Hilbert modules. Induced representations a la Rieffel. Crossed products C*-algebras. Imprimitivity

Thursday, April 8, 2021

Posted April 21, 2021

4:00 pm

Zachary Gershkoff, Mathematics Department, LSU
Elastic elements in 3-connected matroids

Monday, April 12, 2021

Posted April 9, 2021
Last modified November 5, 2021

3:30 pm Zoom (Link: https://lsu.zoom.us/j/91327987785?pwd=VlAxM0QvSDdPY1JSOHlwamVQVWdJQT09)

Rui Han, LSU
A Polynomial Roth Theorem for Corners in the Finite Field Setting

The investigation of polynomial extensions of the Roth's theorem was started by Bourgain and Chang, and has seen a lot of recent advancements. The most striking of these are a series of results of Peluse and Prendiville which prove quantitative versions of the polynomial Roth and Szemerédi theorems in the integer setting. There is yet no corresponding result for corners, the two dimensional setting for polynomial Roth's Theorem, where one considers progressions of the form (x, y), (x+t, y), (x, y+t^2) in [1 ,..., N]^2, for example.
We will talk about a recent result on the corners version of the result of Bourgain and Chang, showing an effective bound for a three term polynomial Roth's theorem in the finite field setting. This is based on joint work with Michael Lacey and Fan Yang.

Tuesday, April 13, 2021

Posted April 21, 2021

Control and Optimization Seminar Questions or comments?

4:00 pm

Josephine Reynes, Texas State University
Applications of Hypergraphic Matrix-minors via Contributors

Wednesday, April 14, 2021

Posted March 22, 2021
Last modified March 26, 2021

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)

Jean-Michel Coron, Universite Pierre et Marie Curie, France Member of Institut Universitaire de France
Boundary Stabilization of 1-D Hyperbolic Systems

Hyperbolic systems in one space dimension appear in various real life applications, such as navigable rivers and irrigation channels, heat exchangers, plug flow chemical reactors, gas pipe lines, chromatography, and traffic flow. This talk will focus on the stabilization of these systems by means of boundary controls. Stabilizing feedback laws will be constructed. This includes explicit feedback laws which have been implemented for the regulation of the rivers La Sambre and La Meuse. The talk will also deal with the more complicated case where there are source terms.

Posted April 7, 2021
Last modified May 1, 2021

3:30 pm – 4:30 pm https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Egor Maximenko, National Polytechnic Institute, Mexico
Radial Toeplitz operators on the Fock space and square-root-slowly oscillating sequences

In this talk, based on a joint article with Kevin Esmeral (https://doi.org/10.1007/s11785-016-0557-0), we describe the C*-algebra generated by radial Toeplitz operators with bounded symbols acting on the Fock space. We prove that this C*-algebra is isometrically isomorphic to the C*-algebra of bounded sequences uniformly continuous with respect to the square-root-metric $\rho(j,k)=|\sqrt(j)-\sqrt(k)|$. More precisely, we show that the spectral sequences (i.e., the sequences of the eigenvalues) of radial Toeplitz operators form a dense subset of the latter C*-algebra of sequences. The main idea is to approximate the spectral sequences by convolutions and apply an appropriate version of Wiener's density theorem.

Monday, April 19, 2021

Posted February 14, 2021
Last modified April 18, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Zoom (Link: https://lsu.zoom.us/j/99328865552?pwd=TThEaXF0cjQzVFprYk1ENGc2UmxGdz09)

Marcelo Disconzi, Department of Mathematics, Vanderbilt University
General-relativistic viscous fluids

The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical relativity simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and comprehensive theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem, discuss the mathematics behind it, and report on a new approach to relativistic viscous fluids that addresses these issues.

Tuesday, April 20, 2021

Posted March 18, 2021
Last modified April 16, 2021

3:10 pm – 4:00 pm Zoom 987 8361 8703

Gene Kopp, University of Bristol
Gauss composition with level structure, polyharmonic Maass forms, and Hecke L-series

The Gauss composition law famously describes the class group of a quadratic number field by an operation on binary quadratic forms up to matrix transformation. Using a stricter notion of equivalence, we describe ray class groups of quadratic fields in terms of quadratic forms. We apply this description to the problem of representing primes by binary quadratic forms with congruence conditions on the variables. We also use this description to write special values of Hecke L-series for real quadratic fields as twisted traces of cycle integrals of polyharmonic Maass forms. Here, "polyharmonic" means "vanishing under a power of the Laplacian." This is ongoing joint work with Olivia Beckwith.

Wednesday, April 21, 2021

Posted April 18, 2021

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Gerardo Ramos-Vazquez
Homogeneous polyanalytic kernels in the Bergman space

The aim of this talk is to compute the reproducing kernels (RK) of the Bergman spaces of polyanalytic functions over the unit ball and the Siegel domain. First, we show a mean-value property for polyanalytic functions on the unit ball using the reproducing property of Jacobi polynomials. The RK of the Bergman space of such functions in the unit ball is a simple consequence. Secondly, we build a unitary "jump" operator from the Bergman space over the unit ball to the Bergman space over the Siegel domain. With the help of this operator, we compute the RK of the Bergman space over the Siegel domain from the previous calculations.

Tuesday, April 27, 2021

Posted March 22, 2021
Last modified April 16, 2021

3:10 pm – 4:00 pm Zoom 987 8361 8703

Marc Besson, University of North Carolina at Chapel Hill
T-fixed subschemes of affine Schubert varieties and Frenkel-Kac theorems

I will discuss line bundles of level one on twisted affine Schubert varieties. Following work of Zhu, we describe the restriction map from global sections of a level one line bundle to the $T^{\sigma}$-fixed subscheme. Our technique uses global methods and we study this map using the associated map for untwisted affine Schubert varieties. As a corollary we are able to describe the smooth locus of many twisted affine Schubert varieties, proving most cases of a conjecture of Haines and Richarz.

Wednesday, April 28, 2021

Posted March 5, 2021
Last modified January 10, 2022

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)

Vincent Andrieu, CNRS
An Overview of Asymptotic Observer Design Methods

Dynamic observers are estimation algorithms allowing us to reconstruct missing data from a model of a dynamic system and information obtained from the measurements. In this presentation, we present the main methods allowing the synthesis of an asymptotic observer. Starting from necessary conditions inspired by Luenberger's work, we show the importance of contraction properties. Then, we give different existing methods. Finally, we give an overview of open issues in the field.

Posted April 26, 2021
Last modified July 25, 2021

3:30 pm – 4:30 pm https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Vishwa Dewage, Louisiana State University
C*-algebra generated by Toeplitz operators with quasi-radial symbols

The n-dimensional Fock space is defined to be the space of holomorphic functions that are square integrable with respect to the Gaussian measure.
Using representation theory, we diagonalize the Toeplitz operators on Fock space with essentially bounded quasi-radial symbols. Then we show that the commutative C*-algebra generated by these Toeplitz operators is isometrically isomorphic to a space of bounded functions that are uniformly continuous with respect to the square root metric.
This is a joint work with my advisor, Prof. Olafsson.

Posted April 21, 2021

4:00 pm https://lsu.zoom.us/j/98833974073?pwd=WnhDbDY5d0ljbjBldEVWT1JacE1zQT09

Charles Semple, University of Canterbury, New Zealand
Recovering non-treelike evolution from small trees

Phylogenetic (evolutionary) trees and, more generally, phylogenetic networks are used in computational biology to represent the ancestral history of a collection of present-day taxa. The latter allows for the representation of non-treelike (reticulate) evolution such as hybridisation and recombination. A well-known result in mathematical phylogenetics says that every phylogenetic tree is recoverable from (determined by) its set of induced subtrees on three leaves. This result typically underlies those algorithms for reconstructing and analysing phylogenetic trees that take, as input, a collection of smaller phylogenetic trees on overlapping leaf sets and output a parent tree that `best'' represents the input. These algorithms are collectively known as supertree methods. They are practical and widely used in tree reconstruction. As an initial step towards developing analogous algorithms for reconstructing phylogenetic networks, to what extent is a phylogenetic network recoverable from its set of induced subtrees? In this talk, we investigate this question, and discuss a surprising and unexpected result for the class of normal (phylogenetic) networks.

Tuesday, May 4, 2021

Posted April 30, 2021
Last modified July 25, 2021

Control and Optimization Seminar Questions or comments?

9:30 am – 10:30 am https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Christian Jakel, University of Sao Paulo
Free massless fields and interacting massive fields in 1 + 1 de Sitter space

We report on the current status of our program physics without assumptions. The basic idea is to analyze the physics determined by the space-time itself. In particular, we describe massless and massive scalar particles on the two-dimensional de Sitter space dS. The quantum theory arises, without any further assumption, from the representation theory of the isometry group SO_0(1,2) of dS. Tomita-Takesaki modular theory provides a group theoretic localization of the observables on dS. In the massless case, it gives rise to an infinite number of one-parameter groups (the modular groups) which implement the geometric action of the conformal transformations on the observables. Their generators (the modular Hamiltonians) satisfy the Virasoro algebra commutation relations. In the massive case, modular theory can be used add polynomial interactions. This is a joint work with Urs Achim Wiedemann and Jens Mund.

Wednesday, May 5, 2021

Posted March 18, 2021
Last modified January 10, 2022

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)

Lars Gruene, University of Bayreuth, Germany
On Turnpike Properties and Sensitivities and their Use in Model Predictive Control

Model predictive control (MPC) is one of the most popular modern control techniques. It generates a feedback-like control input from the iterated solution of open-loop optimal control problems. In recent years, there was a lot of progress in answering the question when MPC yields approximately optimal solutions. In this talk we will highlight the role of the turnpike property for this analysis. Moreover, we will show that for PDE-governed control problems the turnpike property can be seen as a particular instance of a more general sensitivity property. This can be used in order to obtain efficient discretization schemes for the numerical solution of the optimal control problems in the MPC algorithm.

Posted April 7, 2021
Last modified December 6, 2021

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Friday, May 21, 2021 https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Egor Maximenko, National Polytechnic Institute, Mexico
Radial operators on polyanalytic weighted Bergman spaces

In this talk, based on a recent paper with Roberto Moisés Barrera-Castelán and Gerardo Ramos-Vazquez, we describe the von Neumann algebra $\mathcal{R}_n$ of radial operators acting on the $n-$ analytic weighted Bergman space $\mathcal{A}_n^2$ on the unit disk. First, extending the results of Ramazanov (1999, 2002), we explain that disk polynomials (studied by Koornwinder in 1975 and Wunsche in 2005) form an orthonormal basis of $\mathcal{A}_n^2$. Using this basis, we provide the Fourier decomposition of $\mathcal{A}_n^2$ into the orthogonal sum of the subspaces associated with different frequencies. This leads to the decomposition of the von Neumann algebra $\mathcal{R}_n$ into the direct sum of some matrix algebras. In other words, all radial operators are represented as matrix sequences. In particular, we represent in this form the Toeplitz operators with bounded radial symbols, acting in $\mathcal{A}_n^2$. Moreover, using ideas by Englis (1996), we show that the set of all Toeplitz operators with bounded generating symbols is not weakly dense in the algebra of all bounded linear operators acting in $\mathcal{A}_n^2)$

Friday, May 7, 2021

Posted April 1, 2021
Last modified April 26, 2021

10:00 am https://lsu.zoom.us/j/94269991036 (Contact Prof. Malisoff to request password)

Hiroshi Ito, Kyushu Institute of Technology
Constructions of Lyapunov Functions for Input-to-State Stability and Control of SIR Model

To predict the spread of infectious diseases, mathematical models have been playing an essential role. The most popular model, called the SIR model, describes the behavior of the relationship between populations of susceptible, infected and recovered individuals. The model exhibits bifurcation resulting in the emergence of the endemic equilibrium when the disease transmission rate is large, or the net flow of susceptible individuals entering the region is large. In many cases, societies cannot make the inflow small enough to directly eradicate a disease of high transmission rate. Investigating and confirming stability and robustness properties of both disease-free and endemic equilibria are important and useful for the prediction and control of infectious diseases. This presentation first provides a brief induction to the stability analysis, and then limitations of standard tools and results in mathematical epidemiology are explained from the standpoint of a control theorist. The presentation focuses on the theory of construction and the use of Lyapunov functions for the specific nonlinear dynamical system. Major attention is paid to strictness of Lyapunov functions specialized to disease models. A new result allows one to establish robustness of the SIR model with respect to the inflow perturbation in terms of input-to-state stability. The usefulness to be demonstrated in this presentation includes designing feedback control laws for infectious diseases with mass vaccination.

Wednesday, May 12, 2021

Posted March 18, 2021
Last modified April 17, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)

George Avalos, University of Nebraska
Mathematical Analysis of Interactive Fluid and Multilayered Structure PDE Dynamics

We discuss our recent work on a certain multilayered structure-fluid interaction (FSI) which arises in the modeling of vascular blood flow. The coupled PDE system under consideration mathematically accounts for the fact that mammalian veins and arteries are typically composed of various layers of tissues. Each layer will generally manifest its own intrinsic material properties, and will be separated from the other layers by thin elastic laminae. Consequently, the resulting modeling FSI system will manifest an additional PDE, which evolves on the boundary interface, to account for the thin elastic layer. (This is in contrast to the FSI PDEs which appear in the literature, wherein elastic dynamics are largely absent on the boundary interface.) As such, the PDE system will constitute a coupling of 3D fluid-2D wave-3D elastic dynamics. For this multilayered FSI system, we will in particular present results on well-posedness and stability. This is joint work with Pelin Guven Geredeli and Boris Muha.

Wednesday, May 19, 2021

Posted March 15, 2021
Last modified May 17, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)

Francesco Bullo, University of California, Santa Barbara IEEE, IFAC, and SIAM Fellow
Non-Euclidean Contraction Theory and Network Systems

In this talk we discuss recent work on contraction theory and its application to network systems. First, we introduce weak semi-inner products as an analysis tool for non-Euclidean norms and establish equivalent characterizations of contraction and incremental stability. We also review robustness and network stability in this new setting. Second, we discuss the notion of weakly and semi-contracting systems. For weakly contracting systems we prove a dichotomy for asymptotic behavior of their trajectories and show asymptotic stability for certain non-Euclidean norms. For semi-contracting systems we study convergence to invariant subspaces and applications to networks of diffusively-coupled oscillators. This is joint work with Pedro Cisneros-Velarde, Alexander Davydov, and Saber Jafarpour.

Thursday, May 20, 2021

Posted May 26, 2021

Control and Optimization Seminar Questions or comments?

4:00 pm

Cameron Crenshaw, Louisiana State University
On the Cogirth of Binary Matroids

Wednesday, May 26, 2021

Posted May 19, 2021

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)

Francesco Bullo, University of California, Santa Barbara IEEE, IFAC, and SIAM Fellow
Non-Euclidean Contraction Theory and Network Systems

This is a continuation of last week’s Control and Optimization Seminar by the same speaker.

Tuesday, June 1, 2021

Posted May 24, 2021
Last modified May 28, 2021

3:30 pm – 4:30 pm https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09

Siddhartha Sahi, Rutgers University
Some properties of the Macdonald kernel and associated integral transforms

Abstract: Jack polynomials are an important family of symmetric polynomials that depend on a parameter $\alpha$. For certain values of $\alpha$ they specialize to radial parts of spherical functions on symmetric cones; in particular the values $\alpha=2/d,\ d=1,2,4$ correspond to positive definite Hermitian matrices over $\R,\C,\H$, respectively. I.G. Macdonald has introduced a certain kernel function $e(x,y)$, which is defined as a multivariate power series involving Jack polynomials in two sets of variables $ x,y\in R^n$. In this paper we establish three key properties of the Macdonald kernel and associated integral transforms. As anticipated by Macdonald, these results allow one to develop a reasonable theory of Fourier and Laplace transforms, and hypergeometric functions, for arbitrary $\alpha>0$; thereby generalizing classic results of Bochner, Herz, and many others, for symmetric cones. This is joint work with Gestur Olafsson. $\\$ The talk will start at 3:30-4:30 PM Central time ( 4:30- 5:30 PM Eastern time)

Monday, August 16, 2021

Posted April 26, 2021
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, August 18, 2021

Posted April 26, 2021
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics.

Friday, August 20, 2021

Posted April 26, 2021
Last modified December 13, 2022

1:00 pm – 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics.

Wednesday, September 1, 2021

Posted September 6, 2021

Informal Geometry and Topology Seminar Questions or comments?

Wednesday, September 8, 2021

Posted September 8, 2021

1:30 pm – 3:00 pm Lockett 233

Rob Quarles, Louisiana State University
A generating set of knots

Abstract: In this (informal) talk we will explore a normalization of the (Conway-normalized) Alexander polynomial that contains some interesting properties. In particular we will construct a generating set of knots that will give us the Alexander polynomials of any given n-crossing knot, using no knots with more than n crossings. We will then explore the connection between this set of knots and a strong, simple knot invariant given by Bar-Natan and van der Veen.

Posted September 6, 2021
Last modified September 7, 2021

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm Lockett 233

Kevin Schreve, Louisiana State University
Homological growth of groups

Lück's approximation theorem says that the L^2-Betti numbers of a residually finite group measure the rational homological growth of residual sequences of finite index normal subgroups. One can then ask about mod p homology growth or growth of torsion in integral homology. I will calculate these for right-angled Artin groups, and mention some consequences.

Wednesday, September 15, 2021

Posted September 8, 2021

1:30 pm – 3:00 pm Lockett 233

Roland van der Veen, Bernoulli Institute, University of Groningen
A tale of tangles and tensors

Abstract: In this informal talk I will emphasize the analogies between the algebraic structure found in tangles and that of the tensor powers of some algebra H. In both cases one has to deal with a lot of legs, indices and strands. We build bigger tangles by gluing strands of smaller ones just like we contract indices of tensors to make new ones. Then there are other operations on tangles such as doubling a strand or reversing it and this extra structure translates to the algebra H being a Hopf algebra so if you didn't know about Hopf algebras yet, tangles will teach you! Many meaningful topological notions such as genus and ribonness can be formulated in terms of tangles and their operations so given a suitable Hopf algebra and the above dictionary we should be able to shed some light on those. Time permitting some of this will be demonstrated using Mathematica. This is joint work with Dror Bar-Natan and I will discuss (part of) sections 4 and 7 of our recent preprint: https://arxiv.org/abs/2109.02057

Posted August 25, 2021
Last modified September 8, 2021

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 233

Roland van der Veen, Bernoulli Institute, University of Groningen
Generating functions and quantum knot invariants

Abstract: Calculations of quantum knot invariants often get complicated quickly. Be it skein relations or representations or quantum groups there always seems to be a huge number of unruly terms even for moderately simple knots. The goal of this talk is to show how generating functions can improve the situation, with a focus on the case of the sl_2 invariant (colored Jones polynomial). The main idea is to place the entire multiplication table of the relevant algebra in a generating function. Instead multiplying terms directly we will compose the generating functions in a way that is reminiscent of Feynman diagram calculus. The result is a strong yet computable knot invariant that shares many properties with the Alexander polynomial. This is joint work with Dror Bar-Natan and I will discuss (part of) sections 2,6 and 8 of our recent preprint: https://arxiv.org/abs/2109.02057

Friday, September 17, 2021

Posted September 16, 2021

Math Physics Reading seminar

2:00 pm – 3:00 pm 233 Lockett Hall

Rui Han, LSU
Math Physics Reading seminar

This is a new weekly reading seminar on Mathematical Physics. The first two lectures (starting Sep 17) of this series are on the basics of Hilbert space and spectral theory. We will try to make this series as self-contained as possible. All are welcome!

Wednesday, September 22, 2021

Posted September 8, 2021
Last modified October 13, 2021

1:30 pm – 3:00 pm Lockett 233

Amit Kumar, Louisiana State University
TBD

Posted September 17, 2021
Last modified September 21, 2021

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm – 3:00 pm Lockett 233

Sudipta Ghosh, Louisiana State University
Connected sum formulas in knot Floer homology

Knot Floer homology is an invariant of knot which was first introduced in the context of Heegaard Floer homology and later extended other Floer theories. In this talk, we discuss a new approach to the connected sum formula using direct limits. Our methods apply to versions of knot Floer homology arising in the context of Heegaard, instanton and monopole Floer homology. This is joint work with Ian Zemke.

Posted September 6, 2021

Control and Optimization Seminar Questions or comments?

3:30 pm

Angela Wu, Louisiana State University
Obstructing Lagrangian concordance for closures of 3-braids

Two knots are said to be concordant if they jointly form the boundary of a cylinder in four-dimensional Euclidean space. In the symplectic setting, we say they are Lagrangian concordant if the knots are Legendrian and the cylinder is Lagrangian. In this talk I'll show that no Legendrian knot which is both concordant to and from the unstabilized Legendrian unknot can be the closure of an index 3 braid except the unknot itself.

Friday, September 24, 2021

Posted September 21, 2021

9:30 am – 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)

Michael Malisoff, LSU Roy P. Daniels Professor
Event-Triggered Control Using a Positive Systems Approach

Control systems are a class of dynamical systems that contain forcing terms. When control systems are used in engineering applications, the forcing terms can represent forces that can be applied to the systems. Then the feedback control problem consists of finding formulas for the forcing terms, which are functions that can depend on the state of the systems, and which ensure a prescribed qualitative behavior of the dynamical systems, such as global asymptotic convergence towards an equilibrium point. Then the forcing terms are called feedback controls. Traditional feedback control methods call for continuously changing the feedback control values, or changing their values at a sequence of times that are independent of the state of the control systems. This can lead to unnecessarily frequent changes in control values, which can be undesirable in engineering applications. This motivated the development of event-triggered control, whose objective is to find formulas for feedback controls whose values are only changed when it is essential to change them in order to achieve a prescribed system behavior. This talk summarizes the speaker's recent research on event-triggered control theory and applications in marine robotics, which is collaborative with Corina Barbalata, Zhong-Ping Jiang, and Frederic Mazenc. The talk will be understandable to those familiar with the basic theory of ordinary differential equations. No prerequisite background in systems and control will be needed to understand and appreciate this talk.

Posted September 19, 2021

Math Physics Reading seminar

2:00 pm – 3:00 pm 233 Lockett Hall

Math Physics Reading seminar

Wednesday, September 29, 2021

Posted September 6, 2021
Last modified October 1, 2021

Informal Geometry and Topology Seminar Questions or comments?

9:30 am Lockett 233

Michael Farber, Queen Mary University of London
Ample simplicial complexes

I will first describe a remarkable simplicial complex X which can be uniquely characterized by its universality and homogeneity. It contains an isomorphic copy of any simplicial complex with countably many vertexes as an induced subcomplex. A random simplicial complex on countably many vertexes is isomorphic to X with probability 1. The main focus of the talk will be on r-ample simplicial complexes which are finite approximations to X and possess many striking properties. The r-ample complexes can potentially be used for designing stable and resilient networks. The talk is based on joint work with C. Even-Zohar, L. Mead and L. Strauss.

Posted September 8, 2021
Last modified September 29, 2021

1:30 pm – 3:00 pm Lockett 233

Nilangshu Bhattacharyya, Louisiana State University
Construction of Khovanov (Co)chain complex

Abstract: The talk will be based on Bar-Natan's construction of the Khovanov (Co)chain complex of link/knot. We would discuss that the graded Euler Characteristic of the (Co)Chain Complex is the same as the Jones Polynomial of oriented knot.

Friday, October 1, 2021

Posted September 28, 2021

Math Physics Reading seminar

2:00 pm – 3:00 pm 233 Lockett Hall

Math Physics Reading seminar

This is a new weekly reading seminar on Mathematical Physics. The first three lectures (starting Sep 17) of this series are on the basics of Hilbert space and spectral theory. We will try to make this series as self-contained as possible. All are welcome!

Monday, October 4, 2021

Posted September 28, 2021

3:30 pm Zoom

Meeting of Tenured Faculty

Tuesday, October 5, 2021

Posted September 28, 2021

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm Zoom

Meeting of Full Professors

Wednesday, October 6, 2021

Posted September 9, 2021
Last modified October 6, 2021

1:30 pm – 3:00 pm Lockett 233

Justin Murray, Louisiana State University
Colored Ruling Polynomials and Colored Kauffman Polynomials

Abstract: In this talk, I will give definitions of m-graded n-colored ruling polynomials and discuss some relations to DGA representations, and other colored knot polynomials. Along the way I’ll probably define (smooth) BMW algebras and a Legendrian BMW algebra.

Posted September 20, 2021
Last modified October 4, 2021

3:30 pm Lockett 233

Christin Bibby, Louisiana State University
Homology representations of compactified configurations on graphs applied to tropical moduli spaces

The homology of a compactified configuration space of a graph is equipped with commuting actions of a symmetric group and the outer automorphism group of a free group. We construct an efficient free resolution for these homology representations. Using the Peter-Weyl Theorem for symmetric groups, we consider irreducible representations individually, vastly simplifying the calculation of these homology representations from the free resolution. As our main application, we obtain computer calculations of the top weight rational cohomology of the moduli space of genus 2 curves with n marked points, equivalently the rational homology of tropical moduli space, as a representation of the symmetric group acting by permuting point labels for all n≤10. We further give new multiplicity calculations for specific irreducible representations of the symmetric group appearing in cohomology for n≤17. Our approach produces information about these homology groups in a range well beyond what was feasible with previous techniques. This is joint work with Melody Chan, Nir Gadish, and Claudia He Yun.

Posted September 21, 2021
Last modified October 4, 2021

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Zoom link: https://lsu.zoom.us/j/94413235134?pwd=YUNxUFh3TWJRc1NFUWc2aTAzbkYyUT09

Franz Luef, Norwegian University of Science and Technology
Wiener’s Tauberian Theorem in Quantum Harmonic Analysis

Abstract: We present variants of Wiener’s Tauberian Theorems for operators as well as of the Wiener-Pitt theorem, which are based on operator convolutions introduced by R.F. Werner in his seminal work on quantum harmonic analysis on phase space. These results have applications in time-frequency analysis and for quantization schemes. This talk is based on joint work with Eirik Skrettingland.

Friday, October 8, 2021

Posted September 28, 2021
Last modified October 26, 2021

9:30 am – 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)

Magnus Egerstedt, University of California, Irvine Stacey Nicholas Dean of Engineering, IEEE Fellow, IFAC Fellow
Constraint-Based Control Design for Long Duration Autonomy

When robots are to be deployed over long time scales, optimality should take a backseat to “survivability”, i.e., it is more important that the robots do not break or completely deplete their energy sources than that they perform certain tasks as effectively as possible. For example, in the context of multi-agent robotics, we have a fairly good understanding of how to design coordinated control strategies for making teams of mobile robots achieve geometric objectives, such as assembling shapes or covering areas. But, what happens when these geometric objectives no longer matter all that much? In this talk, we consider this question of long duration autonomy for teams of robots that are deployed in an environment over a sustained period of time and that can be recruited to perform a number of different tasks in a distributed, safe, and provably correct manner. This development will involve the composition of multiple barrier certificates for encoding tasks and safety constraints through the development of non-smooth barrier functions, as well as a detour into ecology as a way of understanding how persistent environmental monitoring can be achieved by studying animals with low-energy life-styles, such as the three-toed sloth. Biography of Magnus Egerstedt.

Monday, October 11, 2021

Posted August 23, 2021
Last modified October 6, 2021

3:30 pm – 4:30 pm Zoom link: https://lsu.zoom.us/j/5494314978

Jun-cheng Wei, University of British Columbia Canada Research Chair (CRC Tier I) in Nonlinear Partial Differential Equations
Stability of Sobolev Inequalities and related topics

Suppose $u\in \dot{H}^1(\mathbb{R}^n)$. In 1984, Struwe proved that if $||\Delta u+u^{\frac{2n}{n-2}}||_{H^{-1}}:=\Gamma(u)\to 0$ then $\delta(u)\to 0$, where $\delta(u)$ denotes the $\dot{H}^1(\mathbb{R}^n)$-distance of $u$ from the manifold of sums of Talenti bubbles. In 2020, Figalli and Glaudo obtained the first quantitative version of Struwe's decomposition in lower dimensions, namely $\delta(u)\lesssim \Gamma(u)$ when $3\leq n\leq 5$. In this talk, I will present an optimal nonlinear estimate: $\delta (u)\leq C\Gamma(u)|\log \Gamma(u)|^{\frac{1}{2}}$ if $n=6$ and $\delta (u)\leq C |\Gamma(u)|^{\frac{n+2}{2(n-2)}}$ if $n\geq 7.$ Related stability questions for isoperimetric inequality and harmonic map inequality will be discussed. (Joint work with B. Deng and L. Sun.)

Wednesday, October 13, 2021

Posted October 8, 2021
Last modified October 10, 2021

3:30 pm – 4:30 pm https://lsu.zoom.us/j/94413235134

Allan Merino, University of Ottawa
Howe duality and characters (Part I)

Abstract: For every irreducible reductive dual pair (G, G’) in Sp(W), Roger Howe proved the existence of an isomorphism between the spaces R(G) and R(G’), where R(G) is the set of infinitesimal equivalence classes of irreducible admissible representations of $\tilde{G}$ (preimage of G in the metaplectic group) which can be realized as a quotient of the metaplectic representation. All the representations appearing in the correspondence have a distribution character, and characters are analytic objects completely identifying the irreducible representations. In particular, one natural question is to understand the transfer of characters in the theta correspondence (or Howe’s duality). The goal of my first talk is to define carefully the notions I mentioned previously: Metaplectic representation, character of an infinite dimensional representation and Howe’s duality theorem with some well-known results and applications. In the last minutes of my talk, I will explain how this transfer of characters work when G is compact, and give an explicit way to compute the character of the corresponding representation $ \pi’$ by using the Howe oscillator semigroup.

Posted September 7, 2021
Last modified October 4, 2021

3:30 pm Lockett 233

Matt Clay, University of Arkansas
Chain flaring and L^2–torsion of free-by-cyclic groups

We introduce a condition on the monodromy of a free-by-cyclic group, G_φ, called the chain flare condition, that implies that the L^2–torsion, ρ^(2)(G_φ), is non-zero. We conjecture that this condition holds whenever the monodromy is exponentially growing.

Thursday, October 14, 2021

Posted September 28, 2021
Last modified October 4, 2021

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:20 pm 232 Lockett

Mikhail Khovanov, Columbia University
Evaluating foams

Explicit constructions of link homology groups are based on foams, which can be thought of as cobordisms in 3D between planar graphs. We will explain a particular example of foams and their evaluations that relates to both the 4-color theorem and to the link homology that categorifies the quantum SL(3) link invariant (the Kuperberg bracket).

Friday, October 15, 2021

Posted October 5, 2021
Last modified October 25, 2021

9:30 am – 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request passcode)

Alberto Bressan, Penn State Eberly Family Chair Professor
Optimal Control of Propagation Fronts and Moving Sets

We consider a controlled reaction-diffusion equation, modeling the spreading of an invasive population. Our goal is to derive a simpler model, describing the controlled evolution of a contaminated set. The first part of the talk will focus on the optimal control of 1-dimensional traveling wave profiles. Using Stokes' formula, explicit solutions are obtained, which in some cases require measure-valued optimal controls. In turn, this leads to a family of optimization problems for a moving set, related to the original parabolic problem via a sharp interface limit. In connection with moving sets, in the second part of the talk I will present some results on controllability, existence of optimal strategies, and necessary conditions. Examples of explicit solutions and several open questions will be also discussed. This is a joint research with Maria Teresa Chiri and Najmeh Salehi.

Monday, October 18, 2021

Posted October 5, 2021

3:30 pm Zoom

Mihaela Ignatova, Temple University
Electroconvection in Fluids

We describe results on an electroconvection model in fluids. The model consists of two dimensional Navier-Stokes equations, driven by electrical and body forces, coupled to an advection and fractional diffusion equation for the surface charge density, driven by voltage applied at the boundary. We prove global regularity of solutions and show that the long-time behavior is described by a finite dimensional attractor. In the absence of body forces, the attractor reduces to a singleton, i.e., there is a unique, globally stable stationary solution.

Wednesday, October 20, 2021

Posted October 10, 2021

3:30 pm – 4:30 pm https://lsu.zoom.us/j/94413235134

Allan Merino, University of Ottawa
Howe duality and characters (Part II)

In 2000, T. Przebinda introduced the Cauchy-Harish-Chandra integral and conjectured that the transfer of characters should be obtained via this map. This conjecture is known to be true if G is compact and was proven by Przebinda for unitary representations in the stable range case. In general, it has been established that the Cauchy-Harish-Chandra integral sends the $\tilde{G}$-invariant eigendistributions on $\tilde{G}$ into the $\tilde{G’}$-invariant eigendistributions on $\tilde{G’} $as long as $rk(G) \leq rk(G’)$. After recalling carefully the construction of the Cauchy-Harish-Chandra integral and stating Przebinda’s conjecture, I am going to explain, by using results of A. Paul, how to prove this conjecture for the pair (G,G’) = (U(p, q), U(r, s)), with p+q = r+s, starting with a discrete series representation of $\tilde{G}$. At the end of my talk, I will discuss some auxiliary results I got in my paper and an ongoing project on transfer of characters for (G, G’), with $rk(G) \leq rk(G’)$, starting from a discrete series representation. At the end of my talk, I am going to discuss an ongoing project on the proof of the previous conjecture for an arbitrary dual pair (G, G’) starting with a discrete series representation of \tilde{G}.

Posted September 8, 2021
Last modified October 18, 2021

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Nikita Nikolaev, University of Sheffield
Abelianisation of Filtered Local Systems on Surfaces

I will describe an approach to analysing local systems on surfaces which is a functorial correspondence between local systems of rank n with C*-local systems an n-fold covering surface. Such an approach, called abelianisation, emerged in the last decade in the work of Gaiotto, Moore, Neitzke on spectral networks that arise in the context of supersymmetric gauge theories. It can be seen as a generalisation of the abelianisation of Higgs bundles (a.k.a., the spectral correspondence, a key step in the analysis of Hitchin integrable systems) to flat bundles. I will explain my point of view on the mathematical theory behind abelianisation (which involves the deformation theory of the direct image functor) and give an outlook of what kind of things I hope to prove in the near future.

Friday, October 22, 2021

Posted September 21, 2021
Last modified October 11, 2021

9:30 am – 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request passcode)

Ilya Kolmanovsky, University of Michigan IEEE Fellow, AACC Eckman Awardee
Reference Governors for Control of Systems with Constraints

As systems are downsized and performance requirements become more stringent, there is an increasing need for methods that are able to enforce state and control constraints as a part of the control design. The constraints can represent actuator range and rate limits, safety and comfort limits, and obstacle avoidance requirements. Reference governors are add-on supervisory algorithms that monitor and, if necessary, modify commands that are passed to the nominal controller/closed-loop system to ensure that pointwise-in-time state and control constraints are not violated. Approaches to the construction of reference governors will be described along with the supporting theory. Recent extensions of reference governors, such as a controller state and reference governor (CSRG) that in addition to modifying references can reset the controller states, and opportunities for the application of reference governors to ensure feasibility of model predictive controllers, will be discussed. The learning reference governor, which integrates learning into the reference governor operation, to handle constraints in uncertain systems, will also be touched upon. The potential for the practical applications of reference governors will be illustrated with several examples.

Monday, October 25, 2021

Posted October 18, 2021

3:30 pm – 4:30 pm Zoom

Frederic Marazzato, Louisiana State University
Variational Discrete Element Methods

Discrete Element Methods (DEM) have been introduced in [Hoover et al, 1974] to compute granular materials. Their application to compute elastic materials has remained an open question for a long time [Jebahi et al, 2015]. A first step in that direction was achieved in [Monasse et al, 2012], however the method suffered from several limitations. In [Marazzato et al, 2020], a discretization method for dynamic elasto-plasticity was proposed based on DEM by making a link with hybrid finite volume methods. Only cell dofs are used and a reconstruction is devised to obtain P^1 non-conforming polynomials in each cell and thus constant strains and stresses in each cell. An adaptation of the method consisting in adding cellwise constant rotational dofs made possible the computation of Cosserat materials [Marazzato, 2021]. Taking advantage of the capacity of DEM to deal with discontinuous displacement fields, another adaptation of the method made possible the computation of fracture in two-dimensional settings. Numerical examples for both static and dynamic computations in two and three dimensions will demonstrate the robustness of the proposed methodology.

Wednesday, October 27, 2021

Posted October 24, 2021

3:30 pm – 4:30 pm Zoom https://lsu.zoom.us/j/94413235134

Cody Stockdale, Clemson University
Weighted theory of Toeplitz operators on the Bergman space

Abstract: We discuss the weighted compactness and boundedness properties of Toeplitz operators, $T_u$, on the Bergman space with respect to B\'ekoll\`e-Bonami type weights. We give sufficient conditions on $u$ that imply the compactness of $T_u$ on $L^p_{\sigma}$ for $p \in (1,\infty)$ and all weights $\sigma \in B_p$, and from $L^1_{\sigma}$ to $L_{\sigma}^{1,\infty}$ for all $\sigma \in B_1$. Additionally, using a new extrapolation result, we characterize the compact Toeplitz operators on the weighted Bergman space $\mathcal{A}^p_\sigma$ for all $\sigma$ belonging to a nontrivial subclass of $B_p$. Concerning boundedness, we show that $T_u$ extends boundedly on $L^p_{\sigma}$ for $p \in (1,\infty)$ and weights $\sigma$ in a $u$-adapted class of weights containing $B_p$. Finally, we establish an analogous weighted endpoint weak-type $(1,1)$ bound for weights beyond $B_1$. This is joint work with Nathan Wagner (Washington University in St. Louis).

Thursday, October 28, 2021

Posted September 20, 2021
Last modified October 27, 2021

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Orsola Capovilla-Searle, University of California, Davis
Infinitely many Lagrangian Tori in Milnor fibers constructed via Lagrangian Fillings of Legendrian links

One approach to studying symplectic manifolds with contact boundary is to consider Lagrangian submanifolds with Legendrian boundary; in particular, one can study exact Lagrangian fillings of Legendrian links. There are still many open questions on the spaces of exact Lagrangian fillings of Legendrian links in the standard contact 3-sphere, and one can use Floer theoretic invariants to study such fillings. We show that a family of oriented Legendrian links has infinitely many distinct exact orientable Lagrangian fillings up to Hamiltonian isotopy. Within this family, we provide some of the first examples of a Legendrian link that admits infinitely many planar exact Lagrangian fillings. Weinstein domains are examples of symplectic manifolds with contact boundary that have a handle decomposition compatible with the symplectic structure of the manifold. Weinstein handlebody diagrams are given by projections of Legendrian submanifolds. We provide Weinstein handlebody diagrams of the 4-dimensional Milnor fibers of T_{p,q,r} singularities, which we then use to construct infinitely many Lagrangian tori and spheres in these spaces.

Friday, October 29, 2021

Posted August 25, 2021
Last modified October 26, 2021

9:30 am – 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request passcode)

Kyriakos Vamvoudakis, Georgia Institute of Technology
Learning-Based Actuator Placement and Receding Horizon Control for Security against Actuation Attacks

Cyber-physical systems (CPS) comprise interacting digital, analog, physical, and human components engineered for function through integrated physics and logic. Incorporating intelligence in CPS, however, makes their physical components more exposed to adversaries that can potentially cause failure or malfunction through actuation attacks. As a result, augmenting CPS with resilient control and design methods is of grave significance, especially if an actuation attack is stealthy. Towards this end, in the first part of the talk, I will present a receding horizon controller, which can deal with undetectable actuation attacks by solving a game in a moving horizon fashion. In fact, this controller can guarantee stability of the equilibrium point of the CPS, even if the attackers have an information advantage. The case where the attackers are not aware of the decision-making mechanism of one another is also considered, by exploiting the theory of bounded rationality. In the second part of the talk, and for CPS that have partially unknown dynamics, I will present an online actuator placement algorithm, which chooses the actuators of the CPS that maximize an attack security metric. It can be proved that the maximizing set of actuators is found in finite time, despite the CPS having uncertain dynamics. Biography of Kyriakos Vamvoudakis.

Monday, November 1, 2021

Posted October 8, 2021
Last modified October 18, 2021

3:30 pm – 4:30 pm Zoom: https://lsu.zoom.us/j/5494314978

Stefan Steinerberger, University of Washington
Laplacian Eigenfunctions: Hot Spots and Anti Hot Spots

The Hot Spots conjecture (first posed by Rauch in the 1970s) is a particularly fun open problem: vaguely put, if you let the heat equation act for a long period of time in an insulated room then, for generic initial data, the hottest and the coldest spot are both on the boundary of the room. I will discuss the origin behind the problem and survey some of the existing results. However, as first shown by Burdzy and Werner around 20 years ago, the Hot Spots conjecture fails in certain selected domains (very curious domains, I will show many pictures). However, it cannot fail too much: for all domains in all dimensions, there is a universal inverse result and the hottest spot inside the domain is at most 60 times as hot as the hottest spot on the boundary.

Wednesday, November 3, 2021

Posted November 4, 2021

3:30 pm – 4:30 pm https://lsu.zoom.us/j/94413235134

Cody Stockdale, Clemson University
Weighted theory of Toeplitz operators on the Bergman space II

Posted September 9, 2021
Last modified October 28, 2021

3:30 pm Lockett 233

Yvon Verberne, Georgia Tech
Automorphisms of the fine curve graph

The fine curve graph of a surface was introduced by Bowden, Hensel and Webb. It is defined as the simplicial complex where vertices are essential simple closed curves in the surface and the edges are pairs of disjoint curves. We show that the group of automorphisms of the fine curve graph is isomorphic to the group of homeomorphisms of the surface, which shows that the fine curve graph is a combinatorial tool for studying the group of homeomorphisms of a surface. This work is joint with Adele Long, Dan Margalit, Anna Pham, and Claudia Yao.

Posted November 2, 2021

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm https://lsu.zoom.us/j/94413235134

Cody Stockdale, Clemson University
Weighted theory of Toeplitz operators on the Bergman space II

Friday, November 5, 2021

Posted September 27, 2021
Last modified November 3, 2021

9:30 am – 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request passcode)

Silviu-Iulian Niculescu, Laboratoire des Signaux et Systèmes (L2S)
Delays in Interconnected Dynamical Systems: A Qualitative Analysis

It is well-known that interconnections of two or more dynamical systems lead to an increasing complexity of the overall systems’ behavior, due to the effects induced by the emerging dynamics (which may include feedback loops) in significant interactions (involving sensing and communication) with environmental changes. One of the major problems appearing in such interconnection schemes is related to the propagation, transport, and communication of delays acting through, and inside, the interconnections. The aim of this talk is to briefly present user-friendly methods and techniques (based in part on frequency-domain approaches) for the analysis and control of dynamical systems in the presence of delays. The presentation is as simple as possible, focusing on the main intuitive (and algebraic and geometric) ideas to develop theoretical results, and their potential use in practical applications. Single and multiple delays will be considered. The talk ends with illustrative examples.

Monday, November 8, 2021

Posted September 5, 2021
Last modified November 3, 2021

Mathematical Physics and Representation Theory Seminar

3:30 pm – 4:30 pm Zoom: https://lsu.zoom.us/j/93759214365

Christopher Henderson, University of Arizona
Pushed, pulled, and pushmi-pullyu fronts for the Burgers-FKPP equation: stability and long-time asymptotics

A minimal model for flame propagation in a fluid is the Burgers-FKPP equation. This reaction-advection-diffusion model involves a parameter beta measuring the strength of the induced drift, and a major question is how the fluid dynamics affect the long-time behavior of solutions. By studying special `traveling wave' solutions of this equation, consisting of a fixed profile that moves at a constant positive speed, it has long been known that there are two regimes: (1) when beta is less than 2, fronts are `pulled' by their behavior at infinity, and (2) when beta is greater than 2, fronts are `pushed' by the behavior at the front. In essence, regime (1) involves studying a linear problem (albeit on a noncompact set), while regime (2) involves truly nonlinear analysis, although essentially only on a compact set. However, the phase-plane analysis used to establish this is unable to say anything about the long-time behavior of generic solutions to the Burgers-FKPP equation. In particular, the stability of these traveling waves was unknown. This talk will discuss a recent work with An and Ryzhik in which we establish the precise long-time dynamics of the traveling waves, including showing their stability. Surprisingly, the proof is extremely intricate. A particularly complex case, which will be the main focus of the talk, is beta = 2, when the noncompactness of the pulled case is present with the nonlinearity of the pushed case. The analysis of this case involves techniques not usually seen applied to such problems, such as relative entropy arguments.

Posted October 4, 2021
Last modified November 5, 2021

3:30 pm – 4:20 pm Zoom: https://lsu.zoom.us/j/7376728101

Colleen Delaney, Indiana University Bloomington
Zesting and Witten-Reshetikhin-Turaev invariants

I’ll discuss the ribbon zesting construction on pre-modular categories from a diagrammatic point of view and show that Witten-Reshetikhin-Turaev invariants of framed knots and links decouple under zesting. As an application, I will explain how the Mignard-Schauenburg ``modular isotopes” can be understood through zesting. This talk is based on joint work with Cesar Galindo, Julia Plavnik, Eric Rowell, and Qing Zhang as well as Sung Kim.

Tuesday, November 9, 2021

Posted October 31, 2021

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm Zoom 987 8361 8703

Neelam Saikia, University of Virginia
Frobenius Trace Distributions for Gaussian Hypergeometric Functions

Informal Geometry and Topology Seminar Questions or comments?

Wednesday, November 10, 2021

Posted September 9, 2021

1:30 pm – 3:00 pm Lockett 233

Jackson Knox, Louisiana State University
TBD

Posted November 3, 2021
Last modified November 5, 2021

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233

Assaf Bar-Natan, University of Toronto
Grand Arcs and Infinite-Type Surfaces

A surface S is called infinite-type if it has an infinite pair-of-pants decomposition (and a really funny name). Some examples are the flute surface (plane minus the natural numbers), the Cantor tree (sphere minus a Cantor set), Jacob's Ladder (infinite tori glued in a bi-directional line), or even the Loch Ness Monster (infinite tori glued in a line but only in one direction). The mapping class group, or, the group of homeomorphisms of a surface up to homotopy is a mysterious object for finite-type surfaces, and even more mysterious for infinite-type. One way to study this group is to find a good graph upon which it acts. We will do exactly that in this talk by introducing the grand arc graph. This is based on joint work with Y. Verberne. This talk should be accessible to anyone familiar with the classification of finite-type surfaces.

Posted September 18, 2021
Last modified November 29, 2021

3:30 pm Lockett 233

Assaf Bar-Natan, University of Toronto
Geodesics in the Thurston Metric on Teichmüller Space

For a given surface S, Teichmüller space is the space of all hyperbolic metrics on S up to isotopy homotopic to the identity. In the 70s, Thurston defined his eponymous metric by considering lipschitz constants between maps from one hyperbolic structure to another. The Thurston metric is asymmetric, but that's okay! Geodesics work as you'd expect, but there are forward and backwards geodesics, and they are also sometimes unique! In this talk, I will describe the structure of geodesics in the Thurston metric, and explain where non-uniqueness of geodesics comes from, and how we can fight it! This talk will include a brief introduction to Teichmüller spaces.

Posted November 4, 2021

3:30 pm – 4:30 pm Zoom link: https://lsu.zoom.us/j/94413235134

Gerardo Vazquez, National Polytechnic Institute, Mexico
Translation-invariant operators in reproducing kernel Hilbert spaces

Abstract.: Let $G$ be a locally compact abelian group with a Haar measure, and $Y$ be a measure space. Suppose that H is a reproducing kernel Hilbert space of functions on $G\times Y$, such that $H$ is naturally embedded into $L^2(G\times Y)$ and is invariant under the translations associated with the elements of $G$. Under some additional technical assumptions, we study the W*-algebra $\mathcal{V}$ of translation-invariant bounded linear operators acting on $H$. We obtain an explicit and constructive description of $\mathcal{V}$ in terms of the Fourier transform of the reproducing kernel. The talk is based on a joint work with Crispin Herrera Yañez and Egor Maximenko. We use many ideas of Nikolai Vasilevski and his colleagues.

Posted November 8, 2021

Control and Optimization Seminar Questions or comments?

4:00 pm Zoom Link: https://lsu.zoom.us/j/98833974073?pwd=WnhDbDY5d0ljbjBldEVWT1JacE1zQT09

Kevin Grace, Vanderbilt University
Dyadic Matroids with Spanning Cliques

The Matroid Minors Project of Geelen, Gerards, and Whittle describes the structure of minor-closed classes of matroids representable over a fixed finite field. To use these results to study specific classes, it turns out to be important to study the matroids in the class containing spanning cliques. A spanning clique of a matroid M is a complete-graphic restriction of M with the same rank as M. In this talk, we will describe the structure of dyadic matroids with spanning cliques. The dyadic matroids are those matroids that can be represented by a real matrix each of whose nonzero subdeterminants is a power of 2, up to a sign. A subclass of the dyadic matroids is the signed-graphic matroids. In the class of signed-graphic matroids, the entries of the matrix are determined by a signed graph. Our result is that dyadic matroids with spanning cliques are signed-graphic matroids and a few exceptional cases. The main results in this talk will come from joint work with Ben Clark, James Oxley, and Stefan van Zwam.

Friday, November 12, 2021

Posted August 18, 2021
Last modified October 31, 2021

9:30 am – 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)

Kirsten Morris, University of Waterloo IEEE Fellow, SIAM Fellow
Optimal Controller and Actuator Design for Partial Differential Equations

Control can be very effective in altering dynamics. One issue for partial differential equations is that performance depends not only on the controller, but also on its location and spatial design. Existence of a concurrent optimal controller and spatial distribution has been established for several classes of partial differential equations and objectives. Some of these results will be discussed and illustrated with examples.

Monday, November 15, 2021

Posted September 22, 2021
Last modified November 12, 2021

Mathematical Physics and Representation Theory Seminar

9:30 am – 10:30 am Zoom: https://lsu.zoom.us/j/93122784507

Thomas Alazard, École Normale Supérieure Paris-Saclay, CNRS
Entropies of free surface flows in fluid dynamics

I will discuss recent works with Didier Bresch, Nicolas Meunier, and Didier Smets on the dynamics of a free surface carried by an incompressible flow obeying Darcy's law. This talk focuses on monotonicity properties of different kinds: maximum principles, Lyapunov functions, and entropies. The analysis is based on exact identities which in turn allow us to study the Cauchy problem.

Posted October 3, 2021
Last modified November 5, 2021

2:30 pm – 3:20 pm Lockett 233

Gurbir Dhillon, Yale University
Kazhdan--Lusztig theory for affine Lie algebras at critical level

Formulas for simple characters have a long and rich history in representation theory, and our main result is one more such formula, originally conjectured by Feigin--Frenkel. However, in the majority of the talk, we will provide a general survey of such results for non-specialists. After recalling Weyl's character formula for highest weight modules for simple algebraic groups, we will discuss the Kazhdan--Lusztig character formula for highest weight modules for simple Lie algebras. In particular, we will convey some of the striking ideas involved in its proof via localization, due to Beilinson--Bernstein and Brylinski-Kashiwara, which birthed the subject of geometric representation theory. Moving beyond simple Lie algebras and groups, we will recall that associated to each simple Lie algebra is a one parameter family of infinite dimensional Lie algebras, the affine Lie algebras, which appear repeatedly in algebraic geometry and mathematical physics. By work of Kashiwara--Tanisaki, the highest weight characters at all points in the family save one were understood by the mid 1990s. At this remaining point, the critical level, the representation theory of affine Lie algebras undergoes a phase transition, and the remarkable phenomena present at this point have deep connections to the geometric Langlands program. An analog of the Kazhdan--Lusztig conjecture for affine Lie algebras at critical level was proposed by Feigin--Frenkel in the early 1990s. We have proven this conjecture in forthcoming work joint with David Yang, using localization theory at critical level as developed by Beilinson--Drinfeld and Frenkel--Gaitsgory. The main emphasis throughout will be on basic ideas and simple examples, and we will not presume familiarity with any of these subjects beyond the finite dimensional representations of SL2.

Tuesday, November 16, 2021

Posted October 16, 2021

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm Lockett 232

Edna Jones, Rutgers, The State University of New Jersey
A strong asymptotic local-global principle for integral Kleinian sphere packings

We will discuss a strong asymptotic local-global principle for certain integral Kleinian sphere packings. Examples of Kleinian sphere packings include Apollonian circle packings and Soddy sphere packings. Sometimes each sphere in a Kleinian sphere packing has a bend (1/radius) that is an integer. When all the bends are integral, which integers appear as bends? For certain Kleinian sphere packings, we expect that every sufficiently large integer locally represented as a bend of the packing is a bend of the packing. We will discuss ongoing work towards proving this for certain Kleinian sphere packings. This work uses orientation-preserving isometries of (n+1)-dimensional hyperbolic space, quadratic polynomials, the circle method, spectral theory, and expander graphs.

Wednesday, November 17, 2021

Posted September 9, 2021
Last modified November 5, 2021

3:30 pm Lockett 233

Daniel Platt, Imperial College London
G2-instantons on resolutions of G2-orbifolds

In dimensions 3 and 4, useful invariants of smooth manifolds can be defined by counting certain principal bundle connections, namely the Casson invariant and Donaldson theory. There is a big research programme trying to define analogues in dimension 7 for manifolds with holonomy G2. However, in this dimension, there are some problems that don’t appear in lower dimensions, and not many examples are known. In this talk, I will explain a new construction for G2-instantons. This is intimately related to gauge theory in four dimensions and the Fueter equation in three dimensions. In the beginning I will briefly explain holonomy and the holonomy group G2, no previous knowledge of G2 required!

Posted November 4, 2021

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Zoom link: https://lsu.zoom.us/j/94413235134

Egor Maximenko, National Polytechnic Institute, Mexico
Examples of reproducing kernel Hilbert spaces with translation-invariant operators

This is a continuation of the talk given by Gerardo Ramos Vazquez. It is based on our joint paper with Crispin Herrera Yañez. Here we apply our scheme to a series of examples: vertical and angular operators in the analytic Bergman space on the upper half-plane, vertical and angular operators in the harmonic Bergman space on the upper half-plane, vertical operators in the poly-analytic and true-poly-analytic Bergman spaces on the upper half-plane, vertical operators in the wavelet spaces associated to the positive affine group, radial operators in analytic and harmonic Bergman spaces on the unit disk, vertical operators in the RKHS associated to the Gauss-Weierstrass kernel on $\mathbb{C}^n$. In most of the examples, the Toeplitz operators with group-invariant symbols were studied before, but we deal with the whole W*-algebra of group-invariant operators.

Friday, November 19, 2021

Posted September 20, 2021
Last modified November 12, 2021

9:30 am – 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request passcode)

Sonia Martinez, University of California, San Diego IEEE Fellow
Data-Driven Dynamic Ambiguity Sets: Precision Tradeoffs under Noisy Measurements

Stochastic and robust optimization constitute natural frameworks to solve decision-making and control problems subject to uncertainty. However, these fall short in addressing real-world scenarios for which models of the uncertainty are not available. Data-driven approaches can be of help to approximate such models, but typically require large amounts of data in order to produce performance-guaranteed results. Motivated by settings where the collection of data is costly and fast decisions need to be made online, we present recent work on the construction of dynamic ambiguity sets for uncertainties that evolves according to a dynamical law. In particular, we characterize the tradeoffs between the amount of progressively assimilated data and its future adequacy, due to its gradual precision loss in its predicted values.

Monday, November 22, 2021

Posted October 1, 2021
Last modified November 21, 2021

Mathematical Physics and Representation Theory Seminar

3:30 pm – 4:30 pm Lockett 232

Fan Yang, LSU
Improving estimates for discrete averages

In this talk I will discuss some recent results on discrete l^p improving estimates for averages along the prime numbers and polynomials. We will show how the Hardy-Littlewood Circle method can be used to prove the first sharp results for square integers and prime numbers, and how the general polynomial average is connected to the Vinogradov's mean value theorem. This talk is based on joint works with Rui Han, Vjekoslav Kovac (University of Zagreb), Ben Krause (KCL), Michael Lacey (Gatech) and Jose Madrid (UCLA).

Posted September 28, 2021
Last modified November 14, 2021

3:30 pm – 4:20 pm Lockett 233

Mee Seong Im, United States Naval Academy
Iterated wreath products and foams, with applications

I will explain a new perspective of foams with connections to the representation theory of iterated wreath products. If I have time, I will discuss the connections of foams to field extensions, Sylvester sums, and matrix factorizations. This is joint work with Mikhail Khovanov, with Appendix joint with Lev Rozansky.

Monday, November 29, 2021

Posted October 26, 2021

3:30 pm – 4:30 pm Zoom Webinar

Debdeep Bhattacharya, Mathematics Department, Louisiana State University
Long-time behavior of low regularity data in the 2d modified Zakharov-Kuznetsov equation

Wednesday, December 1, 2021

Posted October 1, 2021
Last modified November 29, 2021

3:30 pm Lockett 233

Dahye Cho, Stony Brook University
Symplectic Criteria on Stratified Uniruledness of Affine Varieties and Applications

We explain about Hamiltonian Floer cohomology of certain open symplectic manifolds including affine varieties, that is Morse cohomology of the space of loops on a symplectic manifold. Using the long exact sequences of symplectic cohomology, we develop criteria for affine varieties to admit uniruled subvarieties of certain dimensions. If time permits, we provide applications of the criteria in birational geometry of log pairs in the direction of the Minimal Model Program.

Posted November 16, 2021
Last modified November 23, 2021

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Zoom https://lsu.zoom.us/j/94413235134
(Originally scheduled for Wednesday, November 24, 2021, 3:30 pm)

Vignon Oussa, Bridgewater State University
Phase retrieval for nilpotent groups

This talk presents new results on phase retrieval for group representations. Precisely, we show that the (unitary) irreducible representations of nilpotent groups (finite and infinite) allow phase retrieval. This is joint work with Hartmut Fuehr.

Friday, December 3, 2021

Posted September 8, 2021
Last modified October 11, 2021

9:30 am – 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request passcode)

Jorge Cortes, University of California, San Diego IEEE Fellow, SIAM Fellow
Resource-Aware Control and Coordination of Cyberphysical Systems

Trading computation and decision making for less communication, sensing, or actuator effort offers great promise for the autonomous operation of both individual and interconnected cyberphysical systems. Resource-aware control seeks to prescribe, in a principled way, when to use the available resources efficiently while still guaranteeing a desired quality of service in performing the intended task. This talk describes advances of this paradigm along three interconnected thrusts: the design of triggering criteria that balance the trade-offs among performance, efficiency, and implementability; the synthesis of distributed triggers in network systems that can be evaluated by individual agents; and the benefits of flexibly interpreting what constitutes a resource. Throughout the presentation, we illustrate our discussion with applications to stabilization under information constraints, opportunistic actuation of safety-critical systems, and information exchanges in the coordination of multi-agent systems.

Monday, December 6, 2021

Posted November 10, 2021
Last modified December 5, 2021

Control and Optimization Seminar Questions or comments?

3:30 pm https://lsu.zoom.us/j/8706058864

Burak Hatinoglu, UC Santa Cruz
Spectral Properties of Periodic Elastic Beam Lattices

This talk will be on the spectral properties of elastic beam Hamiltonian defined on periodic hexagonal lattices. These continua are constructed out of Euler-Bernoulli beams, each governed by a scalar valued fourth-order Schrödinger operator equipped with a real periodic symmetric potential. Unlike the second-order Schrödinger operator commonly applied in quantum graph literature, here the self-adjoint vertex conditions encode geometry of the graph by their dependence on angles at which edges are met. I will firstly consider this Hamiltonian on a special equal-angle lattice, known as graphene or honeycomb lattice. I will also discuss spectral properties for the same operator on lattices in the geometric neighborhood of graphene. This talk is based on a recent joint work with Mahmood Ettehad (University of Minnesota), https://arxiv.org/pdf/2110.05466.pdf.

Friday, December 10, 2021

Posted September 27, 2021
Last modified October 11, 2021

9:30 am – 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request passcode)

Yacine Chitour, Laboratoire des Signaux et Systèmes (L2S)
Worst Exponential Decay Rate for Degenerate Gradient Flows Subject to Persistency of Excitation

In this talk, I will present results for the estimation of the worst rate of exponential decay of degenerate gradient flows $\dot x = −Sx$, issued from adaptive control theory. Under persistent excitation assumptions on the positive semi-definite matrix $S$, upper bounds for this rate of decay consistent with previously known lower bounds are provided and analogous stability results for more general classes of persistently excited signals. The strategy of proof consists in relating the worst decay rate to optimal control questions and studying in detail their solutions. As a byproduct of our analysis, estimates for the worst $L_2$-gain of the time-varying linear control systems $\dot x = −cc^{\scriptscriptstyle T}x$ are obtained, where the signal $c$ is persistently excited. This is a joint work with Paolo Mason and Dario Prandi.

Monday, January 10, 2022

Posted January 6, 2022

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Topology

Wednesday, January 12, 2022

Posted January 6, 2022

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Algebra

Friday, January 14, 2022

Posted January 6, 2022

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Analysis

Thursday, January 20, 2022

Posted January 7, 2022
Last modified January 20, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:20 pm Zoom

Fan Yang, LSU
Localization for quasi-periodic quantum systems

Abstract: I will introduce models for quantum-mechanical particles where the Hamiltonian has random disorder (Anderson model) or is quasi-periodic. These models arise in condensed matter physics and are expected to exhibit insulator-like behavior (Anderson localization), when the disorders are large enough. These phenomena are proved using analytic methods, ranging from spectral theory and Fourier analysis to Diophantine approximations. I will discuss new analytical developments for studying the Maryland model (unbounded aperiodic potential) and quantum walks in magnetic and electric fields. I will give an outlook of various problems that one could study using our methods.

Friday, January 21, 2022

Posted January 13, 2022
Last modified January 17, 2022

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Joel Rosenfeld, University of South Florida
Dynamic Mode Decompositions for Control Affine Systems

We will review the machine learning technique of dynamic mode decomposition (or DMD) for continuous time systems and show how this may be extended to produce models for the state of an unknown control-affine systems using trajectory data. Trajectory data in this setting comes as a pair of control signals and the corresponding control trajectory, and the DMD method for control-affine systems enables the prediction of the action of the system in response to a previously unobserved control signal. This will require a discussion of reproducing kernel Hilbert spaces (or RKHSs), vector valued RKHSs, control Liouville operators, and multiplication operators.

Posted January 10, 2022
Last modified January 12, 2022

3:30 pm – 4:20 pm Zoom

Zhiyu Wang, Georgia Tech
Polynomial $\chi$-binding functions for graph classes

A graph class is called polynomially $\chi$-bounded if there is a function $f$ such that $\chi(G) \leq f(\omega(G))$ for every graph $G$ in this class, where $\chi(G)$ and $\omega(G)$ denote the chromatic number and clique number of $G$ respectively. A $t$-broom is a graph obtained from $K_{1,t+1}$ by subdividing an edge once. A fork is a graph obtained from $K_{1,4}$ by subdividing two edges. We show two conjectures: (1) we show that for graphs $G$ without induced $t$-brooms, $\chi(G) = o(\omega(G)^{t+1})$, answering a question of Schiermeyer and Randerath. For $t=2$, we strengthen the bound on $\chi(G)$ to $7.5\omega(G)^2$, confirming a conjecture of Sivaraman. (2) We show that any {triangle, fork}-free graph $G$ satisfies $\chi(G)\leq \omega(G)+1$, confirming a conjecture of Randerath.

Monday, January 24, 2022

Posted January 21, 2022

Algebra and Number Theory Seminar Questions or comments?

12:00 pm – 12:50 pm Zoom

Benjamin Fehrman, University of Oxford
Rare events in interacting particle systems and stochastic PDE

Abstract: Interacting particle systems arise in diverse contexts, including to model magnetism in statistical mechanics, opinion and disease dynamics in society, competition between species, and neural networks in machine learning. For large populations evolving over a long period of time, the random fluctuations in these systems average out and their evolution can be described deterministically. However, the particle process will exhibit large deviations away from its mean. These events though rare can have substantial effects---such as a large concentration of energy or the appearance of a vacuum---and they are therefore important to understand and simulate. The purpose of this talk is to introduce a continuum model that replicates the far-from-equilibrium behavior in interacting particle systems. While such approximations have long been used to model out-of-equilibrium behavior in fluctuating hydrodynamics, their use has lacked a rigorous mathematical justification due to the supercriticality and degeneracy of the associated stochastic equations. We will first introduce a general probabilistic framework for describing fluctuations in random systems. Beginning with the simple random walk, which is a random process generated by flipping a coin, we will describe the law of large numbers, the central limit theorem, and a large deviations principle. We will then explain how these ideas are applied to interacting particle systems, and how such considerations provide a formal link to certain stochastic PDE. We have developed a robust existence and uniqueness theory for such equations, and shown that along appropriate scaling limits the solutions correctly describe the random fluctuations and rare events in particle systems. These results make rigorous the longstanding formal connection above, and provide new techniques to understand and model particle processes.

Tuesday, January 25, 2022

Posted January 19, 2022

3:10 pm – 4:00 pm Zoom 987 8361 8703

Isabella Negrini, McGill University
A Shimura-Shintani correspondence for rigid analytic cocycles

In their paper Singular moduli for real quadratic fields: a rigid analytic approach, Darmon and Vonk introduced rigid meromorphic cocycles, i.e. elements of $H^1(SL_2(\mathbb Z[1/p]), M^x)$ where $M^x$ is the multiplicative group of rigid meromorphic functions on the p-adic upper-half plane. Their values at RM points belong to narrow ring class fields of real quadratic fiends and behave analogously to CM values of modular functions on $SL_2(\mathbb Z)\backslash H$. In this talk I will present some progress towards developing a Shimura-Shintani correspondence in this setting.

Posted January 11, 2022
Last modified January 12, 2022

3:30 pm – 4:20 pm Zoom

Daniel Massatt, University of Chicago
Electronic Structure of Incommensurate 2D Heterostructures with Mechanical Relaxation

Since their discovery by Geim, 2D heterostructures have become a hotbed of research due to their novel structure. Stacking varying materials on top of each other allows for a vast range of possible materials and corresponding properties. However, this stacking typically leads to an aperiodic, or incommensurate, material due to lattice mismatch or rotational misalignment. This incommensuration increases the potential for tunability of electronic and mechanical properties, leading for example to the famous discovery of unconventional superconductivity of twisted bilayer graphene at the magic angle.

Experiment is vastly more expensive than numerical simulation, so much work is needed on building analysis and algorithms for understanding and computing efficiently these incommensurate materials. In this work, we discuss configuration and momentum space methodologies to build algorithms to compute observables of incommensurate heterostructures. We exploit the ergodicity of the misalignment, and for appropriate materials (such as those with conic or parabolic bands) we use carefully selected perturbative expansions in momentum space with a thorough error analysis.

Wednesday, January 26, 2022

Posted January 12, 2022
Last modified January 25, 2022

11:30 am – 12:20 pm Zoom

Guangqu Zheng, University of Edinburgh
Wiener chaos, Gaussian analysis and Stochastic partial differential equations

Abstract: This talk goes around the concept of Wiener chaos, which was first introduced by N. Wiener (1938) and later modified by K. Ito (1951, 56). It has been recurrently brought up in recent years, as it arises naturally in the study of stochastic partial differential equations, parameter estimation, nodal statistics of a Gaussian random fields and stochastic geometry, to name a few. Notably, Nualart-Peccati’s fourth moment theorem (2004) and Nourdin-Peccati’s Malliavin-Stein approach (2008) further push Wiener chaos to the center of Gaussian analysis, and it has turned out to be very effective in obtaining quantitative limit theorems in practice. In this talk, we will focus on the central limit theorem for the stochastic wave equation driven by Gaussian noise. We will present how the Wiener chaos enters the picture, and then highlight the key ideas and sketch main steps for obtaining relevant limit theorems. If time permits, we will talk about how this line of research (ideas, techniques) may lead to some other interesting results, for example: (i) extending random field solution theory for nonlinear SPDEs driven by colored noise, (ii) obtaining Gaussian fluctuations for (renormalized) singular stochastic dispersive/parabolic PDEs.

Posted December 13, 2021
Last modified January 19, 2022

3:30 pm Lockett 233

Gage Martin, Boston College
Annular links, double branched covers, and annular Khovanov homology

Given a link in the thickened annulus, you can construct an associated link in a closed 3-manifold through a double branched cover construction. In this talk we will see that perspective on annular links can be applied to show annular Khovanov homology detects certain braid closures. Unfortunately, this perspective does not capture all information about annular links. We will see a shortcoming of this perspective inspired by the wrapping conjecture of Hoste-Przytycki. This is partially joint work with Fraser Binns.

Thursday, January 27, 2022

Posted January 25, 2022

3:30 pm – 4:20 pm Zoom

Ana Balibanu, Harvard University
Poisson transversals in representation theory

Abstract: Geometric representation theory studies groups and algebras by realizing their representations geometrically, through actions on associated algebraic varieties. Symplectic and Poisson structures appear naturally in this setting, and give key insights into the geometry of the spaces that carry them. In turn, these spaces provide foundational examples for new research directions in Poisson geometry. The purpose of this talk is to illustrate this interplay in the framework of transversal structures. We will begin by introducing the notion of Poisson transversality, and by giving examples of several well-known representation-theoretic algebraic varieties that arise as Poisson transversals. Motivated by multiplicative analogues of these varieties, we will then define a general class of transversal slices for quasi-Poisson structures. This construction is based on the algebraic data that comes from an associated complex semisimple group, and can be used to produce canonical compactifications of these spaces which have interpretations in the setting of mathematical physics.

Friday, January 28, 2022

Posted January 26, 2022

Mathematical Physics and Representation Theory Seminar

3:30 pm – 4:20 pm Zoom

Michael Lindsey, Courant Institute, NYU
A sampling of Monte Carlo methods

Abstract: In this talk I discuss recent work in several different areas involving Monte Carlo sampling. In the first part of the talk, I consider generic sampling problems, especially in low to moderate dimension, for which I introduce an ensemble Markov chain Monte Carlo (MCMC) method that overcomes the difficulty of slow transitions between isolated modes. In the second part, I consider the problems of computing ground states and excited states of quantum many-body systems, which are eigenpairs of exponentially high-dimensional Hermitian operators. I present a new optimization method within the framework of variational Monte Carlo (VMC). The VMC framework approaches these problems by stochastic optimization over a parametric class of wavefunctions. Of particular interest are recently introduced neural-network-based parametrizations for which this approach yields state-of-the-art results. In the last part, I consider a lattice model of quantum critical metals that captures a plausible mechanism for high-temperature superconductivity. This model can be studied numerically by Monte Carlo methods, but previous approaches cannot reach the large-volume limit needed to reveal critical scaling properties due to cubic computational cost in the lattice volume. I present recent work toward a linear-scaling approach.

Monday, January 31, 2022

Posted September 29, 2021
Last modified January 30, 2022

3:30 pm – 4:20 pm Zoom: https://lsu.zoom.us/j/98489192227, Lockett 233

Iva Halacheva, Northeastern University
Welded tangles and the Kashiwara-Vergne group

Welded or w-tangles are a higher dimensional analogue of classical tangles, which admit a yet further generalization to welded foams, or w-trivalent graphs, a class of knotted tubes in 4-dimensional space. Welded foams can be presented algebraically as a circuit algebra. Together with Dancso and Robertson we show that their automorphisms can be realized in Lie theory as the Kashiwara-Vergne group, which plays a key role in the setting of the Baker-Campbell-Hausdorff series. In the process, we use a result of Bar-Natan and Dancso which identifies homomorphic expansions for welded foams, a class of powerful knot invariants, with solutions to the Kashiwara-Vergne equations.

Tuesday, February 1, 2022

Posted January 25, 2022

3:30 pm – 4:20 pm Zoom

Spencer Leslie, Duke University
Periods, L-values, and stabilization

Abstract: The study of period integrals of automorphic forms originates in deep questions about cohomology of locally symmetric spaces. A particularly powerful tool for studying periods is a relative trace formula, which often allows one to relate these integrals to other arithmetic objects like L-functions. In this talk, I review some of this story, discuss this modern approach to relating period integrals to L-functions, and introduce an important case of active research: unitary Friedberg-Jacquet periods. These periods are conjecturally related to central values of certain L-functions and are thus connected to deep conjectures on the cohomology of the associated locally symmetric spaces. To prove these conjectural relationships, a promising approach is to use a relative trace formula. However, new problems (known as instability) arise in this setting that must be overcome if one is to prove this relation. I will discuss my work on a theory of endoscopy and a stable relative trace formula to overcome these problems. This gives a refinement of the relative trace formula amenable to proving this conjecture.

Wednesday, February 2, 2022

Posted February 1, 2022

3:30 pm – 4:20 pm Zoom

Meeting of the Professorial Faculty

Thursday, February 3, 2022

Posted January 31, 2022
Last modified February 1, 2022

3:30 pm – 4:20 pm Zoom

Mee Seong Im, United States Naval Academy
One-dimensional topological theories with zero-dimensional defects and finite state automata

Abstract: I will explain a surprising relation between topological theories for one-dimensional manifolds with decorations and values in the Boolean semiring and finite-state automata and their generalizations. This is joint work with Mikhail Khovanov.

Monday, February 7, 2022

Posted January 6, 2022

3:30 pm – 4:30 pm Zoom

Marta Lewicka, University of Pittsburgh
Geodesics and isometric immersions in kirigami

Kirigami is the art of cutting paper to make it articulated and deployable, allowing for it to be shaped into complex two and three-dimensional geometries. We are concerned with two questions: (i) What is the shortest path between points at which forces are applied? (ii) What is the nature of the ultimate shape of the sheet when it is strongly stretched? Mathematically, these questions are related to the nature and form of geodesics in the Euclidean plane with linear obstructions (cuts), and the nature and form of isometric immersions of the sheet with cuts when it can be folded on itself. We provide a constructive proof that the geodesic connecting any two points in the plane is piecewise polygonal. We then prove that the full family of polygonal geodesics can be simultaneously rectified into a straight line via a piecewise affine planar isometric immersion.

Wednesday, February 9, 2022

Posted December 10, 2021
Last modified February 11, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Shelly Harvey, Rice University
Knotting and linking in 4-dimensions

Knots are circles embedded into Euclidean space. Links are knots with multiple components. The classification of links is essential for understanding the fundamental objects in low-dimensional topology: 3- and 4-dimensional manifolds since every 3- and 4-manifold can be represented by a weighted link. When studying 3-manifolds, one considers isotopy as the relevant equivalence relation whereas when studying 4-manifolds, the relevant condition becomes knot and link concordance. In some sense, the nicest class of links are the ones called boundary links; like a knot, they bound disjointly embedded orientable surfaces in Euclidean space, called a multi-Seifert surface. The strategy to understand link concordance, starting with Levine in the 60s, was to first understand link concordance for boundary links and then to try to relate other links to boundary links. However, this point of view was foiled in the 90's when Tim Cochran and Kent Orr showed that there were links (with all known obstructions vanishing, i.e., Milnor's invariants) that were not concordant to any boundary link. In this work, Chris Davis, Jung Hwan Park, and I consider weaker equivalence relations on links filtering the notion of concordance, called n-solvable equivalence. We will show that most links are 0- and 0.5-solvably equivalent but that for larger n, that there are links not n-solvably equivalent to any boundary link (thus cannot be concordant to a boundary link). This is joint work with C. Davis and J. H. Park.

Friday, February 11, 2022

Posted February 3, 2022

9:30 am – 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)

Michele Palladino, University of L’Aquila
Optimal Control of the Moreau’s Sweeping Process

We present recent and new results on the optimal control of Moreau’s sweeping process (SP). We will present a novel approach for proving a version of the Pontryagin Maximum Principle in a general setting. Such an approach exploits a kind of small-time local controllability property which the SP dynamics naturally satisfies in a neighborhood of the moving constraint. Open problems and further research directions will be extensively discussed.

Posted February 8, 2022

3:30 pm – 4:20 pm Zoom

Yuwen Li, The Pennsylvania State University
Preconditioning in H(curl) and H(div)

Abstract: Preconditioning is widely used for efficiently solving large-scale systems of linear equations. In the first part of my talk, I will present a novel application of preconditioning and derive a posteriori error estimates of finite element methods in H(curl) and H(div) using preconditioning theory. In the second part, I will show new user-friendly preconditioners for solving discrete H(curl) and H(div) systems on triangulated surfaces. Part of this talk is based on joint work with Ludmil Zikatanov.

Monday, February 14, 2022

Posted January 14, 2022
Last modified February 8, 2022

3:30 pm – 4:30 pm Zoom

Petronela Radu, University of Nebraska, Mathematics Department
Nonlocal operators to the boundary and beyond

The emergence of nonlocal theories as promising models in different areas of science (continuum mechanics, biology, image processing) has led the mathematical community to conduct varied investigations of systems of integro-differential equations. In this talk I will present some results we obtained at the operator level (including a new formulation of nonlocal Calculus with corresponding Helmholtz-Hodge type decompositions) as well as for systems of integral equations with weakly singular kernels (conservation laws, diffusion equations), flux-type boundary conditions with applications at both, theoretical, and applied levels.

Tuesday, February 15, 2022

Posted February 14, 2022

1:30 pm – 2:20 pm Zoom

Mikhail Khovanov, Columbia University
Universal construction and its uses in link homology and beyond.

Abstract: Universal construction starts with an evaluation of closed n-dimensional manifolds and extends that to a weak TQFT (topological quantum field theory) for n-dimensional cobordisms. We explain its role in a combinatorial approach to SL(N) link homology and review other applications, including in construction of new rigid tensor categories.

Wednesday, February 16, 2022

Posted December 17, 2021
Last modified February 9, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Fraser Binns, Boston College
Links with Knot Floer homology of Low Rank

Knot Floer homology is a powerful link invariant due to Ozsváth–Szabó and J. Rasmussen. In this talk I will discuss a rank bound in knot Floer homology for fibered links coming from Baldwin–Vela-Vick–Vértesi's BRAID invariant and explain how it can be used to classify links with knot Floer homology of low rank. This talk is based on joint work with Subhankar Dey.

Friday, February 18, 2022

Posted January 13, 2022

9:30 am – 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)

Emmanuel Trelat, Sorbonne Universite, Paris, France
On the Turnpike Property

The turnpike property was discovered in the 50's by Nobel prize winner Samuelson in economics. It stipulates that the optimal trajectory of an optimal control problem in large time remains essentially close to a steady state, itself being the optimal solution of an associated static optimal control problem. We have established the turnpike property for general nonlinear finite and infinite dimensional optimal control problems, showing that the optimal trajectory is, except at the beginning and the end of the time interval, exponentially close to some (optimal) stationary state, and that this property also holds for the optimal control and for the adjoint vector coming from the Pontryagin maximum principle. We prove that the exponential turnpike property is due to a hyperbolicity phenomenon which is intrinsic to the symplectic feature of the extremal equations. We infer a simple and efficient numerical method to compute optimal trajectories in that framework, in particular an appropriate variant of the shooting method. The turnpike property turns out to be ubiquitous and the turnpike set may be more general than a single steady-state, like for instance a periodic trajectory. We also show the shape turnpike property for PDE models in which a subdomain evolves in time according to some optimization criterion. These works are in collaboration with Gontran Lance, Can Zhang, and Enrique Zuazua.

Monday, February 21, 2022

Posted February 14, 2022

1:00 pm – 2:00 pm Zoom

Li Chen, LSU
Dirichlet fractional Gaussian fields on the Sierpinski gasket

In this talk, we discuss the Dirichlet fractional Gaussian fields on the Sierpinski gasket. We show that they are limits of fractional discrete Gaussian fields defined on the sequence of canonical approximating graphs. This is a joint work with Fabrice Baudoin (UConn).

Posted February 16, 2022

4:30 pm – 5:30 pm James E. Keisler Lounge (321 Lockett) and 240 Lockett

Math Club

Refreshments in the Lounge beginning at 4:30pm, and movie in 240 Lockett

Posted February 10, 2022

5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial Science information meeting

Pizza will be served. A drawing for The Infinite Actuary Exam P or Exam FM prep course. A discussion of the LSU program and actuarial profession. Appointment of officers to the Actuarial Club. Discussion about inviting professional actuaries. Visit by the Director, Preliminary Courses, The Infinite Actuary.

Tuesday, February 22, 2022

Posted February 21, 2022

3:30 pm – 4:20 pm Zoom

Meeting of the Professorial Faculty

Wednesday, February 23, 2022

Posted February 1, 2022
Last modified March 3, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Zsuzsanna Dancso, University of Sydney
Welded Tangles and the Kashiwara–Vergne Groups

I'll explain a general method of “translating” between a certain type of problem in quantum topology, and solving equations in graded spaces in (quantum) algebra. I'll go through old and new applications of this principle: Drinfel'd associators and parenthesised braids, Grothendieck–Teichmüller groups, welded tangles and the Kashiwara–Vergne equations, and a topological description of the Kashiwara–Vergne groups. The “recent” portion of the talk is based on joint work with Iva Halacheva and Marcy Robertson (arXiv: 2106.02373), with Dror Bar-Natan (arXiv: 1405.1955), and work-in-progress with Marcy Robertson and Tamara Hogan.

Friday, February 25, 2022

Posted February 8, 2022
Last modified February 21, 2022

9:30 am – 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)

Cameron Nowzari, George Mason University
Implementable Event-Triggered Controllers for Networked Cyber-Physical Systems

Rapid development of technology is quickly leading us to an increasingly networked and wireless world. With massive wireless networks on the horizon, the efficient coordination of such large networks becomes an important consideration. To efficiently use the available resources, it is desirable to limit wireless communication to only the instances when the individual subsystems actually need attention. Unfortunately, classical time-triggered control systems are based on performing sensing, actuation, and even communication actions periodically in time rather than when it is necessary. This motivates the need to transcend this prevailing paradigm in exchange for event-triggered control (ETC); where individual subsystems must decide for themselves when to take different actions based on local information. The concept of ETC has been proposed as early as the 1960's but now we are starting to see practical applications. Since then, the idea of ETC has been surging in popularity to now essentially stand alone in the area of systems and control. This then begs the question: why is ETC not yet more mainstream and why has industry still not adopted it in most actual control systems? In this talk we look at this question and argue that the majority of ETC algorithms being proposed today are too theoretical to be useful. We then show how we are addressing this problem by developing a standard set of tools and methodologies for co-designing efficient event-triggered communication and control algorithms for networked systems that can actually be used by practitioners; with quantifiable benefits, performance guarantees, and robustness properties. This talk identifies numerous shortcomings between theoretical concepts and what is actually needed in practice for the theory to be useful, and discusses how we might close this gap. Finally, this talk will cover specific challenges we encountered in applying the state of-the-art event-triggered control algorithms to a wireless clock synchronization problem, and how we overcame them.

Friday, March 4, 2022

Posted February 3, 2022
Last modified February 24, 2022

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Pauline Bernard, MINES ParisTech
Observer Design for Continuous-Time Dynamical Systems

We review the main techniques of state observer design for continuous-time dynamical systems. Starting from necessary conditions for the existence of such asymptotic observers, we classify the available methods depending on the detectability/observability assumptions they require. We show how each class of observer relies on transforming the system dynamics into a particular normal form which allows the design of an observer, and how each observability condition guarantees the invertibility of its associated transformation and the convergence of the observer. A particular focus will be given to the promising theory of KKL or nonlinear Luenberger observers.

Monday, March 7, 2022

Posted January 31, 2022
Last modified March 6, 2022

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:20 pm Lockett 233, https://lsu.zoom.us/j/91730960984

Peter Koroteev, UC Berkeley
DAHA Representations and Branes

I will describe our recent geometric representation theory construction for the double affine Hecke algebra (DAHA) of rank one. The spherical subalgebra of DAHA can be understood as flat one-parameter deformation (geometric quantization) of the SL(2, C) character variety X of a one-punctured torus. This variety for rank one DAHA is described by an affine cubic surface which is an elliptic fibration of Kodaira type I_0^*. Our main result provides an equivalence between the Fukaya category of X and the category of finite-dimensional modules of DAHA. Upon this correspondence, compact Lagrangian submanifolds of X are related to finite-dimensional representations of DAHA. This is a work in progress with S. Gukov, S. Nawata, D. Pei, and I. Saberi.

Posted January 16, 2022
Last modified March 4, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 am Zoom: https://lsu.zoom.us/j/5494314978

Chenjie Fan, Academy of Mathematics and Systems Science of the Chinese Academy of Sciences
On stochastic NLS: wellposedness and long time behavior

We present our study on stochastic NLS. The aim is to understand how a noise can impact a dispersive system. We will start with local theory, talk about global wellposedness, and report our recent work on long time behavior. Joint work with Weijun Xu and Zehua Zhao.

Tuesday, March 8, 2022

Posted March 2, 2022
Last modified March 6, 2022

3:10 pm – 4:00 pm Lockett 232 and Zoom 987 8361 8703

Krishnaswami Alladi, University of Florida
On the local distribution of the number of small prime factors — a variation of the classical theme

The study of the local distribution of the number of prime factors has an illustrious history going back to a 1917 paper of Hardy–Ramanujan. The celebrated Erdős–Kac theorem of 1939 on the global distribution of the number of prime factors created the subject of Probabilistic Number Theory. The study of the global distribution of $\nu_y(n)$, the number of (distinct) prime factors of $n$ which are less than $y$, plays a crucial role in the proof of the Erdős–Kac theorem. Although much is known about the “local distribution” of $\nu(n)$, the number of prime factors of $n$, namely the asymptotics of the function $N_k(x)=\sum_{n\le x, \nu(n)=k}1$, little attention has been paid to the local distribution of $\nu_y(n)$. In discussing the asymptotic behavior of $N_k(x,y)=\sum_{n\le x, \nu_y(n)=k}1$, we noticed a very interesting variation of the classical theme that seems to have escaped attention. To explain this phenomenon, we will obtain uniform asymptotic estimates for $N_k(x,y)$ by a variety of analytic techniques such as those of Selberg, and of Buchstab–De Bruijn (involving difference-differential equations). All this will be described and explained against the background of classical work. The talk will be accessible to non-experts and graduate students. This is joint work with my recent PhD student Todd Molnar.

Wednesday, March 9, 2022

Posted February 24, 2022

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233

Sam Shepherd, Vanderbilt University
Cubulating groups

I will explain what it means to cubulate a group, and discuss some properties of cubulated groups. I will then describe a strategy for cubulating groups using wallspaces.

Posted December 10, 2021
Last modified February 24, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Sam Shepherd, Vanderbilt University
Commensurability of lattices in right-angled buildings

Given compact length spaces $X_1$ and $X_2$ with a common universal cover, it is natural to ask whether $X_1$ and $X_2$ have a common finite cover. In particular, are there properties of $X_1$ and $X_2$, or of their fundamental groups, that guarantee the existence of a common finite cover? We will discuss several examples, as well as my new result which concerns the case where the common universal cover is a right-angled building. Examples of right-angled buildings include products of trees and Davis complexes of right-angled Coxeter groups. My new result will be stated in terms of (weak) commensurability of lattices in the automorphism group of the building.

Friday, March 11, 2022

Posted January 29, 2022
Last modified February 1, 2022

9:30 am – 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)

Luc Jaulin, ENSTA-Bretagne
Interval Contractors to Solve Dynamical Geometrical Equations with Application to Underwater Robotics

In Euclidean space, the separation between distinct points corresponds to their distance and is purely spatial and positive. In space-time, the separation between events takes into account not only spatial separation between the events, but also their temporal separation. We will consider problems involving geometrical constraints in space-time in an underwater robotics context. The motion of the robots will be described by differential equations, and the clocks attached to each robot are not synchronized. An interval contractor based technique is used to solve the distributed state estimation problem. The method is illustrated on the localization of a group of underwater robots with unsynchronized clocks. In this problem, the travel time of the sound that gives us the distances between robots cannot be neglected.

Saturday, March 12, 2022

Posted January 24, 2022

conference information ; registration form

until Sunday, March 13, 2022 Lockett Hall and Zoom (TBA)

Southern Regional Number Theory Conference

Monday, March 21, 2022

Posted March 2, 2022
Last modified March 7, 2022

1:00 pm – 2:00 pm Zoom

George Yin, University of Connecticut
Stochastic Kolmogorov Systems: Some Recent Progress

We present some of our recent work on stochastic Kolmogorov systems. The motivation stems from dealing with important issues of ecological and biological systems. Focusing on environmental noise, we will address such fundamental questions: what are the minimal conditions for long-term persistence of a population, or long-term coexistence of interacting species. [The talk reports some of our joint work with D.H. Nguyen, N.T. Dieu, N.H. Du, and N.N Nguyen.]

Posted January 17, 2022
Last modified February 10, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm

Jonas Lührmann, Texas A&M University
Asymptotic stability of the sine-Gordon kink under odd perturbations

The sine-Gordon model is a classical nonlinear scalar field theory that was discovered in the 1860s in the context of the study of surfaces with constant negative curvature. Its equation of motion features soliton solutions called kinks and breathers, which play an important role for the long-time dynamics. I will begin the talk with an introduction to classical 1D scalar field theories and the asymptotic stability problem for kinks. After surveying recent progress on the problem, I will present a joint work with W. Schlag on the asymptotic stability of the sine-Gordon kink under odd perturbations. Our proof is perturbative and does not rely on the complete integrability of the sine-Gordon model. Key aspects are a super-symmetric factorization property of the linearized operator and a remarkable non-resonance property of a variable coefficient quadratic nonlinearity.

Tuesday, March 22, 2022

Posted February 14, 2022
Last modified March 6, 2022

3:10 pm – 4:00 pm Zoom 987 8361 8703

Yatin Patel, Wayne State University
Minimal Integral Models for Principal Series Weil Characters

We prove a conjecture of Udo Riese about the minimal ring of definition for principal series Weil characters of $\mbox{SL}(2,p)$, for $p$ an odd prime. More precisely, we show that the $(p+1)$-dimensional Weil characters can be realized over the ring of integers of $\mathbb Q(\epsilon p)$ where $\epsilon= (-1)^{(p-1)/2}$, and we provide explicit integral models over these quadratic rings. We do so by studying the Galois action on the integral models of Weil characters recently discovered by Yilong Wang.

Wednesday, March 23, 2022

Posted January 14, 2022
Last modified February 2, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Sudipta Ghosh, Louisiana State University
Connected sums and directed systems in knot Floer homologies

Knot Floer homology is an invariant of knots which was first introduced in the context of Heegaard Floer homology and later extended to other Floer theories. In this talk, we discuss a new approach to the connected sum formula using direct limits. Our methods apply to versions of knot Floer homology arising in the context of Heegaard, instanton and monopole Floer homology. The same argument we use to prove the connected sum formula also generalizes Kronheimer-Mrowka's oriented skein exact triangle from the hat version of instanton knot homology to the minus version of instanton knot homology. This is joint work with Ian Zemke.

Friday, March 25, 2022

Posted January 28, 2022
Last modified March 9, 2022

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Anton Selivanov, University of Sheffield, UK
Time-Delay Implementation of Derivative-Dependent Control

Time delays in input or output channels often lead to instability and, therefore, are usually avoided. However, there are systems where delays have a stabilizing effect. This happens because time-delays allow one to approximate output derivatives and use them in the feedback law. In this talk, I will consider an LTI system that can be stabilized using only output derivatives. The derivatives are approximated by finite differences, leading to time-delayed feedback. I will present a method for designing and analyzing such feedback under continuous-time and sampled measurements. It will be shown that, if the derivative-dependent control exponentially stabilizes the system, then its time-delayed approximation stabilizes the system with the same decay rate provided the time delay is small enough.

Monday, March 28, 2022

Posted January 17, 2022
Last modified March 27, 2022

3:30 pm Zoom

Stan Palasek, UCLA
Quantitative regularity theory for the Navier-Stokes equations in critical spaces

An important question in the theory of the incompressible Navier-Stokes equations is whether boundedness of the velocity in various norms implies regularity of the solution. Critical norms are conjectured to be (roughly) the threshold between positive and negative answers to this question. Of particular interest are 3D solutions in the critical endpoint space $L_t^\infty L_x^3$ for which Escauriaza-Seregin-Sverak famously proved global regularity. Recently Tao improved upon this result by proving quantitative bounds on the solution and conditions on a hypothetical blowup. In this talk we discuss the quantitative approach to regularity including some sharper results in the axisymmetric case, as well as extensions to other critical spaces and to higher dimensions.

Wednesday, March 30, 2022

Posted March 6, 2022
Last modified March 30, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Nurdin Takenov, Louisiana State University
On a relation between ADO and Links-Gould invariants

Akutsu-Deguchi-Ohtsuki (ADO) and Links-Gould are two link invariants. Both of them are connected to Alexander polynomial and can be considered its generalizations. In the talk I will define them, describe some of their properties and state a conjecture about a relation between them. Then I will sketch the proof of the conjecture for some classes of links and some thoughts about perspectives of a full proof of a conjecture.

Friday, April 1, 2022

Posted January 13, 2022
Last modified February 21, 2022

9:30 am – 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)

Pierdomenico Pepe, University of L'Aquila
Sampled-Data Event-Based Stabilization of Retarded Nonlinear Systems

We present an event-based controller for the stabilization of nonlinear retarded systems. The main features of the controller we provide are that (i) only sampled-data measures of the Euclidean internal variable are needed, thus avoiding continuous-time monitoring of the state in infinite dimensional spaces, ii) the event function is only evaluated at sampling instants, and involves a finite number of most recent measures, and iii) discontinuous feedbacks and non- uniform sampling are allowed. The controller guarantees semi-global practical asymptotic stability to an arbitrarily small final target ball around the origin, by suitably fast sampling.

Monday, April 4, 2022

Posted February 14, 2022
Last modified April 1, 2022

Mathematical Physics and Representation Theory Seminar

1:00 pm – 2:00 pm Zoom

Erkan Nane, Auburn University
Moments of fractional stochastic heat equations in a bounded domain

We consider the fractional stochastic heat type equation with nonnegative bounded initial condition, and with noise term that behaves in space like the Riesz kernel and is possibly correlated in time, in the unit open ball centered at the origin in $\mathbb{R}^d$. When the noise term is white in time, we establish a change in the growth of the solution of these equations depending on the noise level. On the other hand when the noise term behaves in time like the fractional Brownian motion with index $H\in (1/2,1)$, we also derive explicit bounds leading to a well-known intermittency property. These results are our recent joint work with Mohammud Foondun and Ngartelbaye (Serge) Guerngar.

Posted February 8, 2022
Last modified March 16, 2022

2:30 pm – 3:20 pm Lockett 233

Akos Nagy, UC Santa Barbara
BPS monopoles with arbitrary symmetry breaking

Magnetic monopole solutions of Maxwell's equations have been known since Dirac's famous paper in 1931. In the mid-1970s, Bogomolny and, independently, Prasad and Sommerfeld, gave nonabelian generalizations to these solutions in Yang-Mills theory, which are now called Bogomolny-Prasad-Sommerfeld (BPS) monopoles. These are gauge theoretic field configurations over 3-dimensional backgrounds. In this talk I will introduce BPS monopoles both from the mathematical and physical points of view and recall some of the most important results about them, with an emphasis on BPS monopoles over the euclidean 3-space. In particular, I will introduce the concept of symmetry breaking for these fields. While a lot is known about monopoles with maximal symmetry breaking, the general case has been much less understood. After the general introduction, I will present my recent results on the construction of monopoles with arbitrary, nonmaximal symmetry breaking. This is achieved by understanding the analytic behavior of harmonic spinors associated to Dirac operators twisted by monopoles. This is a joint work with Benoit Charbonneau.

Posted January 18, 2022
Last modified March 31, 2022

3:30 pm – 4:30 pm Zoom: https://lsu.zoom.us/j/5494314978

Mariana Smit Vega Garcia, Western Washington University
Almost minimizers for obstacle problems

In the applied sciences one is often confronted with free boundaries, which arise when the solution to a problem consists of a pair: a function u (often satisfying a partial differential equation), and a set where this function has a specific behavior. Two central issues in the study of free boundary problems are: (1) What is the optimal regularity of the solution u? (2) How smooth is the free boundary? The study of the classical obstacle problem - one of the most renowned free boundary problems - began in the ’60s with the pioneering works of G. Stampacchia, H. Lewy, and J. L. Lions. During the past decades, it has led to beautiful developments, and its study still presents very interesting and challenging questions. In contrast to the classical obstacle problem, which arises from a minimization problem (as many other PDEs do), minimizing problems with noise leads to the notion of almost minimizers. In this talk, I will introduce obstacle-type problems and overview recent developments in almost minimizers for the thin obstacle problem, illustrating techniques that can be used to tackle questions (1) and (2) in various settings.

Tuesday, April 5, 2022

Posted March 28, 2022
Last modified March 30, 2022

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm Lockett Hall 232

Frank Sottile, Texas A&M
Critical Points of Discrete Periodic Operators via Toric Varieties

It is believed that the dispersion relation of a Schrodinger operator with a periodic potential has non-degenerate critical points. In work with Kuchment and Do, we considered this for discrete operators on a periodic graph G, for then the dispersion relation is an algebraic hypersurface. A consequence is a dichotomy; either almost all parameters have all critical points non-degenerate or almost all parameters give degenerate critical points, and we showed how tools from computational algebraic geometry may be used to study the dispersion relation. \[ \hspace{1em} \] With Matthew Faust, we use ideas from combinatorial algebraic geometry to give an upper bound for the number of critical points at generic parameters, and also a criterion for when that bound is obtained. The dispersion relation has a natural compactification in a toric variety, and the criterion concerns the smoothness of the dispersion relation at toric infinity.

Wednesday, April 6, 2022

Posted March 25, 2022
Last modified March 31, 2022

1:30 pm Lockett 233

Dan Rutherford, Ball State University
Introduction to Legendrian contact homology for surfaces

Legendrian contact homology is an algebraic invariant of Legendrian knots and surfaces that arises from the Morse theory of the symplectic action functional. My goal in this talk will be to make this construction accessible to a general mathematical audience. I will begin with a brief introduction to homology via the simplicial homology of a space and then explain a beautiful connection between homology and calculus known as Morse theory. Next, I will introduce Legendrian surfaces in R^5 and explain how to view them via their front projections which are singular surfaces in R^3. After explaining the original Morse/Floer theory definition of Legendrian contact homology, I will conclude the talk by presenting a recent simplicial reformulation of the invariant that is joint work with Mike Sullivan.

Posted January 19, 2022
Last modified March 31, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Dan Rutherford, Ball State University
Normal rulings, augmentations, and the colored Kauffman polynomial

Normal rulings are certain decompositions of front diagrams of Legendrian links in $R^3$ that were discovered independently by Chekanov-Pushkar and Fuchs in the context of generating families and augmentations of the Legendrian DG-algebra respectively. They can be used to define combinatorial invariants of Legendrian links called ruling polynomials. In this talk, I will survey some results connecting normal rulings with augmentations and with 2-variable topological knot polynomials (HOMFLY-PT and Kauffman). In particular, I will discuss joint work with C. Leverson and J. Murray relating counts of higher rank augmentations to the n- colored HOMFLY-PT and Kauffman polynomials.

Friday, April 8, 2022

Posted January 31, 2022
Last modified April 6, 2022

9:30 am – 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)

Franco Rampazzo, Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova
Goh and Legendre-Clebsch Conditions for Non-Smooth Optimal Control Problems

Various generalizations of the original Maximum Principle (Pontryagin et al., 1956) have been produced in different theoretical frameworks in the literature, starting from the pioneering works of F. Clarke in the 1970s up to recent papers. For an end-point constrained optimal control problem with control affine dynamics, I will present ideas (from a work in progress with F. Angrisani) in the direction of adding higher order necessary conditions to the Maximum Principle. In particular, one can generalize the classical Goh condition and the Legendre-Clebsch condition (which include Lie brackets) to the case where the data are nonsmooth. In fact, the recently introduced notion of Quasi Differential Quotient (Palladino and R., 2020) allows one to treat two simultaneous kinds of non-smoothness, namely the one concerning the adjoint inclusion and the one connected with the set-valued Lie brackets (R. and Sussmann 2001), within the same framework.

Monday, April 11, 2022

Posted February 14, 2022
Last modified April 8, 2022

Mathematical Physics and Representation Theory Seminar

1:00 pm – 2:00 pm Zoom

Le Chen, Auburn University
Exact solvability and moment asymptotics of SPDEs with time-independent noise

In this talk, I will report a joint work with Raluca Balan and Xia Chen and a following-up work with Nicholas Eisenberg. In this line of research, we first study the stochastic wave equation in dimensions $d\leq 3$, driven by a Gaussian noise $\dot{W}$ which does not depend on time. We assume that the spatial noise is either white, or the covariance functional of the noise satisfies a scaling property similar to the Riesz kernel. The solution is interpreted in the Skorohod sense using Malliavin calculus. We obtain the exact asymptotic behaviour of the $p$-th moment of the solution when either the time or $p$ goes to infinity. For the critical case, namely, when $d=3$ and the spatial noise is white, we obtain the exact transition time for the second moment to be finite. The main obstacle for this work is the lack of the Feynman-Kac representation for the moment, which has been overcome by a careful analysis of the Wiener chaos expansion. Our methods turn out to be very general and can be applied to a broad class of SPDEs, which include stochastic heat and wave equations as two special cases.

Posted January 30, 2022
Last modified April 3, 2022

2:30 pm – 3:20 pm Lockett 233

Tudor Padurariu, Columbia University
Categorical Hall algebras in Donaldson-Thomas theory

Kontsevich-Soibelman defined the cohomological Hall algebra (CoHA) of a quiver with potential. By a result of Davison-Meinhardt, CoHAs are deformations of the universal enveloping algebra of the BPS Lie algebra of the quiver with potential. One can also define categorical and K-theoretic Hall algebras of a quiver with potential. Examples of such Hall algebras are (positive parts of) quantum affine algebras. I will introduce the categorical and K-theoretic replacements of the BPS spaces and explain how to prove analogues of the Davison-Meinhardt theorem in these contexts. These results have applications in Donaldson-Thomas theory and in the study of Hall algebras of surfaces.

Posted January 20, 2022
Last modified February 8, 2022

3:30 pm – 4:30 pm Zoom

Davit Harutyunyan, University of California Santa Barbara
TBA

Posted March 30, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett Hall 232

Davit Harutyunyan, EPFL
On the extreme rays of the cone of 3 by 3 quasiconvex quadratic forms

The extreme rays of the convex cone of 3 by 3 quasiconvex quadratic forms play an important role in applied mathematics and in particular in the theory of composite materials. In this work, we provide a characterization of 3 by 3 quasiconvex quadratic forms, the determinant of the acoustic tensor of which is an extremal polynomial, and conjecture/discuss about other cases. While the problem arises in Applied Mathematics (The Theory of Composites), it is also related to the problem of "Sums of Squares" in Convex Geometry and Real Algebraic Geometry. We combine methods from classical Linear Algebra, Convex Geometry and Real Algebraic Geometry in the proofs. This is joint work with Narek Hovsepyan.

Tuesday, April 12, 2022

Posted February 16, 2022
Last modified March 18, 2022

3:10 pm – 4:00 pm Zoom 987 8361 8703

Christina Giannitsi, Georgia Institute of Technology
Improving and Maximal Inequalities for Primes in Progressions

Wednesday, April 13, 2022

Posted March 25, 2022
Last modified March 28, 2022

3:30 pm Lockett 233

Rachael Boyd, University of Cambridge
A Deligne complex for Artin monoids

This talk is based on joint work with Charney and Morris-Wright (https://arxiv.org/abs/2007.12156). I will motivate the study of Artin monoids before outlining our construction of the monoid Deligne complex, which generalises the notion of Deligne complexes for Artin groups. I will discuss geometric properties of this complex, including the fact that the monoid Deligne complex is always contractible, with a locally isometric embedding into the Deligne complex of the corresponding Artin group.

Posted April 5, 2022
Last modified April 7, 2022

3:30 pm – 4:30 pm zoom - https://lsu.zoom.us/j/94413235134

Wavelet Spaces as Reproducing Kernel Hilbert Spaces

In this talk, I will explore wavelet spaces arising from time-frequency analysis and wavelet analysis. These spaces have an intriguing reproducing kernel Hilbert space structure. Additionally, the spaces can be investigated from an abstract harmonic analysis perspective through representation theory. I will demonstrate a non-trivial distinctness result for wavelet spaces that heavily utilize the representation-theoretic viewpoint. Finally, if time permits, I will relate the reproducing kernel Hilbert space structure of these spaces to the HRT-conjecture in time-frequency analysis.

Thursday, April 14, 2022

Posted February 12, 2022
Last modified April 7, 2022

3:30 pm – 4:20 pm Lockett 232

Andrey Smirnov, UNC-Chapel Hill
3-dimensional mirror symmetry and elliptic cohomology

Theoretical physicists predict the existence of a large class of symplectic varieties that appear in pairs (X, X'). The enumerative invariants of the varieties X and X' are expected to be closely related. In recent years it has been understood that equivariant elliptic cohomology provides a natural language to mathematically define and study this phenomenon. My talk is an elementary introduction to equivariant elliptic cohomology and the theory of the elliptic stable envelopes. I will define 3d mirror symmetry in this language and consider some simple explicit examples. If time permits, we discuss applications to enumerative geometry, quantum cohomology, and K-theory. The talk is aimed at a broad audience, no prior knowledge of equivariant cohomology theories is assumed.

Monday, April 18, 2022

Posted February 14, 2022

Mathematical Physics and Representation Theory Seminar

1:00 pm – 2:00 pm Zoom

Fabrice Baudoin, University of Connecticut
Asymptotic windings of the block determinants of a unitary Brownian motion and related diffusions

We study several matrix diffusion processes constructed from a unitary Brownian motion. In particular, we use the Stiefel fibration to lift the Brownian motion of the complex Grassmannian to the complex Stiefel manifold and deduce a skew-product decomposition of the Stiefel Brownian motion. As an application, we prove asymptotic laws for the determinants of the block entries of the unitary Brownian motion. This is a joint work with Jing Wang (Purdue University)

Posted February 8, 2022
Last modified April 16, 2022

2:30 pm – 3:20 pm Lockett 233

Vasily Krylov, MIT
Symplectic duality and equivariant Hikita-Nakajima conjecture for ADHM spaces

We will discuss the general notion of symplectic duality between symplectic resolutions of singularities and give examples. Equivariant Hikita-Nakajima conjecture is a general conjecture about the relation between the geometry of symplectically dual varieties. We will consider the example of the Hilbert scheme of points on the affine plane and briefly discuss the proof of the equivariant Hikita-Nakajima conjecture in this particular case. We will also briefly discuss the generalization of this proof to the case of ADHM spaces (moduli spaces of instantons on R^4). Time permitting we will say about the possible approach towards the proof of Hikita-Nakajima conjecture for other symplectically dual pairs (such as Higgs and Coulomb branches of quiver gauge theories). The talk is based on the joint work with Pavel Shlykov arXiv:2202.09934.

Posted February 18, 2022
Last modified April 17, 2022

3:30 pm – 4:30 pm Zoom: https://lsu.zoom.us/j/5494314978

Pablo Raul Stinga, Iowa State University
Regularity for C^{1,a} interface transmission problems

We present existence, uniqueness, and optimal regularity of solutions to transmission problems for harmonic functions with C^{1,a} interfaces. The main tool we develop for the regularity estimates is a new geometric stability argument based on the mean value property. This is joint work with Luis A. Caffarelli (UT Austin) and our graduate student María Soria-Carro (UT Austin).

Wednesday, April 20, 2022

Posted January 26, 2022
Last modified April 14, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Locket 233

Sümeyra Sakallı , University of Arkansas
Complex Ball Quotients and New Symplectic 4-Manifolds with Nonnegative Signatures

We first construct a complex surface with positive signature, which is a ball quotient. We obtain it as an abelian Galois cover of CP^2 branched over the Hesse arrangement. Then we analyze its fibration structure, and by using it we build new symplectic and also non-symplectic exotic 4-manifolds with positive signatures. In the second part of the talk, we discuss Cartwright-Steger surfaces, which are also ball quotients. Next, we present our constructions of new symplectic and non-symplectic exotic 4-manifolds with non-negative signatures that have the smallest Euler characteristics in the so-called ‘arctic region’ on the geography chart. More precisely, we prove that there exist infinite families of irreducible symplectic and infinite families of irreducible non-symplectic, exotic 4-manifolds that have the smallest Euler characteristics among the all known simply connected 4-manifolds with nonnegative signatures and with more than one smooth structures. This is a joint work with A. Akhmedov and S.-K. Yeung.

Friday, April 22, 2022

Posted February 6, 2022
Last modified February 18, 2022

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Xiaobo Tan, Michigan State University IEEE Fellow, NSF CAREER Awardee
Modeling and Control of Hysteresis Using Minimal Representations

Hysteresis remains a key nonlinearity in magnetic and smart material actuators that challenges their control performance. High-fidelity modeling and effective compensation of hysteresis, yet with low computational complexity, are of immense interest. In this talk I will share some recent advances in this direction via several examples. First, I will present the optimal reduction problem for a Prandtl-Ishlinskii (PI) operator, one of the most popular hysteresis models, where an optimal approximation of the original operator with fewer constituent elements (play operators) is obtained via efficient dynamic programming. Second, I will discuss adaptive estimation of play radii, instead of their weights, as an alternative means for accurate modeling of hysteresis with a PI operator of low complexity. Finally, I will report a dynamic inversion approach to hysteresis compensation that requires minimal, qualitative conditions on the system model. Throughout the talk I will use experimental results from smart materials to illustrate the methods.

Monday, April 25, 2022

Posted March 2, 2022
Last modified April 19, 2022

1:00 pm – 2:00 pm Zoom

Maria Gordina, University of Connecticut
Limit laws for a hypoelliptic diffusions

In this talk we will consider several classical problems for hypoelliptic diffusions: the small ball problem (SBP), Chung's laws of iterated logarithm (LIL) , and finding the Onsager-Machlup functional. Namely we will look at hypoelliptic Brownian motion on the Heisenberg group and a Kolmogorov diffusion for the SBP and LIL, and the Onsager-Machlup functional for hypoelliptic Brownian motion in the Heisenberg group. One of these processes is not Gaussian, but it has a space-time scaling property. Kolmogorov diffusion does not have this property, but it is Gaussian, so one should use a different approach. The Onsager-Machlup functional is used to describe the dynamics of a continuous stochastic process, and it is closely related to the SBP and LIL. Unlike in the Riemannian case we do not rely on the tools from differential geometry such as comparison theorems or curvature bounds as these are not easily available in the sub-Riemannian setting. The talk is based on the joint work with Marco Carfagnini.

Posted April 25, 2022

2:00 pm – 2:50 pm

Meeting of Tenured Faculty

Wednesday, April 27, 2022

Posted April 5, 2022

3:30 pm – 4:30 pm zoom

TBA

Posted March 10, 2022
Last modified April 22, 2022

3:30 pm Lockett 233

Alan Logan, University of St Andrews
The Surface Group Conjectures

The Surface Group Conjectures are statements about recognising surface groups among one-relator groups. In this talk, I will motivate these conjectures and add a new conjecture to this family. I will then explain the proofs of all these conjectures in the case of both two-generator one-relator groups and one-relator groups with torsion. Based on joint work with Giles Gardam and Dawid Kielak.

Posted April 23, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett, 232

Rui Han, LSU
Matthew McCoy, Louisiana State University
Dylan Spedale
Fan Yang, LSU
Lp improving estimates for averages in R^d, F_q^d and Z^d

We will survey the L^p improving estimates for spherical averages in the Euclidean space R^d, and talk about some recent sharp results for spherical averages in the finite field F_q^d and polynomial and prime number averages in the integer setting.

Friday, April 29, 2022

Posted January 27, 2022
Last modified February 15, 2022

9:30 am – 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)

Andrea Serrani, Ohio State University
Adaptive Feedforward Compensation of Harmonic Disturbances for Convergent Nonlinear Systems

Rejecting periodic disturbances occurring in dynamical systems is a fundamental problem in control theory, with numerous technological applications such as control of vibrating structures, active noise control, and control of rotating mechanisms. From a theoretical standpoint, any design philosophy aimed at solving this problem reposes upon a specific variant of the internal model principle, which states that regulation can be achieved only if the controller embeds a copy of the exogenous system generating the periodic disturbance. In the classic internal model control (IMC), the plant is augmented with a replica of the exosystem, and the design is completed by a unit which provides stability of the closed loop. In a somewhat alternative design methodology, referred to as adaptive feedforward compensation (AFC), a stabilizing controller for the plant is computed first and then an observer of the exosystem is designed to provide asymptotic cancelation of the disturbance at the plant input. In particular, the parameters of the feedforward control are computed adaptively by means of pseudo-gradient optimization, using the regulated error as a regressor. Contrary to IMC, which has been the focus of extensive investigation, application of AFC methods to nonlinear systems has remained so far elusive. This talk aims at presenting results that set the stage for a theory of AFC for nonlinear systems by providing a nonlinear equivalent of the condition for the solvability of the problem in the linear setting, and by re-interpreting classical linear schemes in a fully nonlinear setting. To this end, the problem is approached by combining methods from output regulation theory with techniques for semi-global stabilization.

Monday, May 2, 2022

Posted February 6, 2022
Last modified April 25, 2022

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:20 pm Lockett 233

Eugene Rabinovich, University of Notre Dame
Classical Bulk-Boundary Correspondences via Factorization Algebras

A factorization algebra is a cosheaf-like local-to-global object which is meant to model the structure present in the observables of classical and quantum field theories. In the Batalin-Vilkovisky (BV) formalism, one finds that a factorization algebra of classical observables possesses, in addition to its factorization-algebraic structure, a compatible Poisson bracket of cohomological degree +1. Given a ``sufficiently nice'' such factorization algebra on a manifold $N$, one may associate to it a factorization algebra on $N\times \mathbb{R}_{\geq 0}$. The aim of the talk is to explain the sense in which the latter factorization algebra ``knows all the classical data'' of the former. This is the bulk-boundary correspondence of the title. Time permitting, we will describe how such a correspondence appears in the deformation quantization of Poisson manifolds.

Posted February 4, 2022
Last modified November 29, 2022

3:30 pm – 4:30 pm Lockett 233

Armin Schikorra, University of Pittsburgh
On Calderón–Zygmund type estimates for nonlocal PDE

I will report on progress obtained for the $W^{s,p}$-regularity theory for nonlocal/fractional equations of differential order $2s$ with bounded measurable Kernel. Namely, under (not yet optimal) assumptions on the kernel we obtain $W^{t,p}$-estimates for suitable right-hand sides, where $2s>t>s$. Technically we compare such equations via a commutator estimate to a simpler fractional equation. Based on joint works with M.M Fall, T. Mengesha, S. Yeepo.

Posted February 4, 2022

3:30 pm – 4:30 pm Lockett 233

TBA

Wednesday, May 4, 2022

Posted March 6, 2022
Last modified April 26, 2022

3:30 pm Lockett 233

Rob Quarles, Louisiana State University
A new perspective on a polynomial time knot polynomial

In this talk we consider the Z_1(K) polynomial time knot polynomial defined and described by Dror Bar-Natan and Roland van der Veen in their 2018 paper "A polynomial time knot polynomial". We first look at some of the basic properties of Z_1(K) and develop an invariant of diagrams \Psi_m(D) related to this polynomial. We use this invariant as a model to prove how Z_1(K) acts under the connected sum operation. We then discuss the effect of mirroring the knot on Z_1(K) and describe a geometric interpretation of some of the building blocks of the invariant. Finally, we describe a base set of knots which can be used to build the Z_1(K), or rather its normalization \rho_1(K), showcasing some of its symmetry properties, and we use this idea to give an explicit expansion of \rho_1(K) for the family of T(2,2p+1) torus knots in terms of this base set of knot invariants.

Posted April 23, 2022

3:30 pm – 4:30 pm Lockett, 232

Rui Han, LSU
Matthew McCoy, Louisiana State University
Dylan Spedale
Fan Yang, LSU
Lp improving estimates for averages in R^d, F_q^d and Z^d

Posted April 5, 2022

3:30 pm – 4:30 pm zoom

TBA

Thursday, May 5, 2022

Posted April 21, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Michael Falk, Northern Arizona University
Hypergraphs and Orlik-Solomon algebras

We define the Orlik-Solomon algebra of a hypergraph and establish an elementary decomposition theorem. This is sufficient to allow a classification of Orlik-Solomon algebras of matroids, and consequently, cohomology rings of complements of complex hyperplane arrangements, using the hypergraphic generalization of Whitney's 2-isomorphism theorem for graphs, due to Vertigan and Whittle (1997). The talk is based on joint work with Geoff Whittle, still in progress.

Friday, May 6, 2022

Posted January 26, 2022

9:30 am – 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)

Sophie Tarboureich, Laboratoire d'Analyse et d'Architecture des Systèmes (LAAS), France
Algorithms for Event-Triggered Control

Event-triggered control consists of devising event-triggering mechanisms leading to only seldom control updates. In the context of event-triggered control, two objectives that can be pursued are (1) emulation, whereby the controller is a priori predesigned and only the event-triggering rules have to be designed and (2) co-design, where the joint design of the control law and the event-triggering conditions has to be performed. Control systems are connected to generic digital communication networks for implementation, transmission, coding, or decoding. Therefore, event-triggered control strategies have been developed to cope with communication, energy consumption, and computation constraints. The talk is within this scope. Considering linear systems, the design of event-triggering mechanisms using local information is described through linear matrix inequality (or LMI) conditions. From these conditions, the asymptotic stability of the closed loop system, together with the avoidance of Zeno behavior, are ensured. Convex optimization problems are studied to determine the parameters of the event-triggering rule with the goal of reducing the number of control updates.

Wednesday, May 11, 2022

Posted April 26, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Nurdin Takenov, Louisiana State University
On a relation between ADO and Links-Gould invariants

Akutsu-Deguchi-Ohtsuki(ADO) and Links-Gould are two link invariants. Both of them are connected to Alexander polynomial and can be considered its generalizations. In the talk I will define them, describe some of their properties and state a conjecture about a relation between them. Then I will sketch the proof of the conjecture for some classes of links and some thoughts about perspectives of a full proof of a conjecture.

Friday, May 13, 2022

Posted February 2, 2022

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Monica Motta, Università di Padova, Italy
Stabilizability in Optimal Control

We address the stabilizability of nonlinear control systems, in an optimal control theoretic framework. First, we extend the nowadays classical concepts of sampling and Euler solutions that were developed by F. Clarke, Y. Ledyaev, E. Sontag, A. Subbotin, and R.J. Stern (1997, 2000) for control systems associated to discontinuous feedbacks, by also considering corresponding costs, given by integrals of a nonnegative Lagrangian. In particular, we introduce the notions of sample and Euler stabilizability to a closed target set with regulated cost, which require the existence of a stabilizing feedback that keeps the cost of all sampling and Euler solutions starting from the same point below the same level. Then, under mild regularity hypotheses on the dynamics and on the Lagrangian, we prove that the existence of a special control Lyapunov function, to which we refer to as a minimum restraint function (or MRF), implies not only stabilizability, but also that all sample and Euler stabilizing trajectories have regulated costs. The proof is constructive, being based on the synthesis of appropriate feedbacks derived from the MRF. As in the case of classical control Lyapunov functions, this construction requires that the MRF is locally semiconcave. However, by generalizing an earlier result by L. Rifford (2000) we establish that it is possible to trade regularity assumptions on the data with milder regularity assumptions on the MRF. In particular, we show that if the dynamics and the Lagrangian are locally Lipschitz up to the boundary of the target, then the existence of a mere locally Lipschitz MRF provides sample and Euler stabilizability with regulated cost. This talk is based on a joint work with Anna Chiara Lai (from University Roma La Sapienza, Rome, Italy), which is part of an ongoing, wider investigation of global asymptotic controllability and stabilizability from an optimal control perspective.

Thursday, July 21, 2022

Posted July 11, 2022

2:30 pm – 3:30 pm Lockett Hall 232, $\\$ Zoom Link: https://lsu.zoom.us/j/94413235134

Jens Christensen, Colgate University
The Uncertainty Principle and Representation Theory

We discuss an uncertainty principle for self-adjoint operators generated by unitary representations of Lie groups. We then apply this uncertainty principle to differential operators on Bergman spaces on the unit disc. In the process we classify the self-adjoint differential operators on these spaces, and hint at extensions to higher dimensional domains.

Monday, August 15, 2022

Posted June 1, 2022

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Algebra

Wednesday, August 17, 2022

Posted June 1, 2022

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Analysis

Friday, August 19, 2022

Posted June 1, 2022

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Topology

Wednesday, August 24, 2022

Posted July 27, 2022
Last modified August 18, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Jean Pierre Mutanguha, Institute for Advanced Study
Canonical forms for free group automorphisms

The Nielsen–Thurston theory of surface homeomorphisms can be thought of as a surface analogue to the Jordan Canonical Form. I will discuss my progress in developing a similar canonical form for free group automorphisms. (Un)Fortunately, free group automorphisms can have arbitrarily complicated behaviour. This is a significant barrier to translating arguments that worked for surfaces into the free group setting; nevertheless, the overall ideas/strategies do translate!

Friday, August 26, 2022

Posted August 8, 2022

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Lorena Bociu, North Carolina State University PECASE Awardee
Analysis and Control in Poroelastic Systems with Applications to Biomedicine

Fluid flows through deformable porous media are relevant for many applications in biology, medicine and bio-engineering, including tissue perfusion, fluid flow inside cartilages and bones, and design of bioartificial organs. Mathematically, they are described by quasi-static nonlinear poroelastic systems, which are implicit, degenerate, coupled systems of partial differential equations (PDE) of mixed parabolic-elliptic type. We answer questions related to tissue biomechanics via well-posedness theory, sensitivity analysis, and optimal control for the poroelastic PDE coupled systems mentioned above. One application of particular interest is perfusion inside the eye and its connection to the development of neurodegenerative diseases.

Tuesday, August 30, 2022

Posted August 19, 2022
Last modified August 26, 2022

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm Lockett 232 and Zoom

Daniel Fretwell, University of South Wales
Definite orthogonal modular forms: Computations, Excursions and Discoveries

The theory of (positive definite) integral quadratic forms and lattices has a long and rich history. For many years it has been known how to study these objects via their theta series, modular forms whose Fourier coefficients encode arithmetic data. A less well known fact is that isometry classes of lattices (in a genus) can themselves be viewed as automorphic forms, for the corresponding (definite) orthogonal group. These forms also contain a wealth of arithmetic information. In general, algorithms for computing spaces of automorphic forms for higher rank groups are few and far between. However, the case of definite orthogonal groups is concrete enough to be amenable to computation, and provides a significant testing ground for general conjectures in the Langlands Program (e.g. explicit Functoriality). Recently, E. Assaf and J. Voight have developed a new magma package for computing spaces of orthogonal modular forms. We will take a stroll through a zoo of explicit examples computed using this package, outlining links with conjectures of Arthur on endoscopy and discoveries of new Eisenstein congruences. (Joint work with E. Assaf, C. Ingalls, A. Logan, S. Secord and J. Voight)

Wednesday, August 31, 2022

Posted August 17, 2022
Last modified August 21, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Daniel C. Cohen, Mathematics Department, LSU
Topological complexity of motion planning

Motivated by the motion planning problem from robotics, topological complexity is a mathematical invariant of the space of all configurations of a mechanical system. This invariant provides a measure of the complexity of designing a motion planning algorithm for the mechanical system, that is, the complexity of navigation in the configuration space. I will introduce this notion (as well as a recent generalization if time permits), and provide illustrations of its determination. Examples of configuration spaces considered will include familiar topological spaces such as spheres and surfaces, and possibly some classical configuration spaces of points in Euclidean spaces.

Friday, September 2, 2022

Posted August 23, 2022
Last modified October 7, 2024

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Sasa Rakovic, Beijing Institute of Technology
Minkowski, Lyapunov, and Bellman: Inequalities and Equations for Stability and Optimal Control

The classical Lyapunov and Bellman equations, and inequalities, are cornerstone objects in linear systems theory. These equations, and inequalities, are concerned with convex quadratic functions verifying stability in cases of the Lyapunov equation and inequalities as well as optimality and stability in cases of the Bellman equation and inequalities. Rather peculiarly, prior to my work in the area, very little had been known about the related Lyapunov and Bellman equations, and inequalities, within the space of the Minkowski functions of nonempty convex compact subsets containing the origin in their interior. My recent research has provided complete characterizations of the solutions to the Lyapunov and Bellman equations, and inequalities, within the space of the Minkowski functions, referred to as the Minkowski-Lyapunov and Minkowski-Bellman equations, and inequalities, respectively. The talk reports key results underpinning the study of these fundamental equations and inequalities and their generalizations. The talk also renders strong evidence of topological flexibility and theoretical correctness of the developed frameworks and consequent advantages over the traditional Lyapunov and Bellman equations and inequalities.

Tuesday, September 6, 2022

Posted August 19, 2022
Last modified September 6, 2022

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm Lockett 232 and Zoom

Michael Allen, Louisiana State University
On some supercongruence conjectures of Long

In 2003, Rodriguez Villegas conjectured 14 supercongruences between hypergeometric functions arising as periods of certain families of rigid Calabi-Yau threefolds and the Fourier coefficients of weight 4 modular forms. Uniform proofs of these supercongruences were given in 2019 by Long, Tu, Yui, and Zudilin. In 2020 Long conjectured a number of further supercongruences for hypergeometric functions of a similar shape. In this talk, we extend the approach of Long, Tu, Yui, and Zudilin towards establishing six of Long's conjectures, and also discuss possible future directions and further generalizations.

Posted September 6, 2022

3:30 pm DMC 1034

Casey Cavanaugh, Louisiana State University
Structure-Preserving Discretizations for Partial Differential Equations

Models arising from partial differential equations (PDEs) often include physical laws such as conservation of energy or source-free flows, and theoretical properties such as the maximum principle. To accurately capture these types of features in numerical simulation, we consider structure-preserving discretization methods which guarantee that continuous level properties are satisfied exactly on the discrete level. This talk will focus on building connections between two known structure-preserving methods: the mimetic finite-difference (MFD) method, where discrete differential operators "mimic" their continuous level counterparts, and a mixed finite-element method (FEM) based on finite-element exterior calculus. First, we examine MFD discretizations for two PDE models: Maxwell's equations, describing the coupling between electric and magnetic fields, and convection-dominated diffusion equations, which are typically challenging to solve due to numerical oscillations from shocks and boundary layers. Then, by exploiting the connections between MFD and FEM, we demonstrate how a FE framework can provide the MFD method with supplementary theory such as well-posedness, stability, error estimates, and multigrid solvers.

Wednesday, September 7, 2022

Posted August 29, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Mike Wong, Louisiana State University
Annular link Floer homology and gl(1|1)

In earlier work by Ellis, Petkova, and Vertesi, tangle Floer bimodules (a combinatorial generalization of link Floer homology) are shown to decategorify to the Reshetikhin–Turaev invariants arising in the representation theory of gl(1|1). In this talk, we describe how this can give rise to a gl(1|1) action on annular link Floer homology, viewed as the Hochschild homology—or horizontal trace—of a tangle Floer bimodule. The gl(1|1) action turns out to be closely related to a known basepoint action in Floer theory. This is based on joint work in progress with Andy Manion and Ina Petkova.

Friday, September 9, 2022

Posted September 4, 2022

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Michael Margaliot, Tel Aviv University
Revisiting Totally Positive Differential Systems: A Tutorial and New Results

A matrix is called totally nonnegative (TN) if all of its minors are nonnegative, and totally positive (TP) if all its minors are positive. Multiplying a vector by a TN matrix does not increase the number of sign variations in the vector. In a largely forgotten paper, Schwarz (1970) considered matrices whose exponentials are TN or TP. He also analyzed the evolution of the number of sign changes in the vector solutions of the corresponding linear system. In a seemingly different line of research, Smillie (1984), Smith (1991), and others analyzed the stability of nonlinear tridiagonal cooperative systems by using the number of sign variations in the derivative vector as an integer-valued Lyapunov function. We provide a tutorial on these topics and show that they are intimately related. This allows us to derive generalizations of the results by Smillie (1984) and Smith (1991) while simplifying the proofs. This also opens the door to many new and interesting research directions. This is joint work with Eduardo D. Sontag from Northeastern University.

Tuesday, September 13, 2022

Posted August 19, 2022
Last modified September 6, 2022

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm Lockett 232 and Zoom

Olivia Beckwith, Tulane University
Ramanujan-type congruences for Hurwitz class numbers

The Ramanujan congruences, discovered over a century ago, state that the partition function is annihilated modulo p on a certain arithmetic progression if p is 5, 7, or 11. The work of Ono, Ahlgren, and Treneer shows the coefficients of any weakly holomorphic modular form have infinitely many similar congruence properties. We examine congruences for Hurwitz class numbers, in which case the generating series are mock modular instead of modular. We prove that congruences for Hurwitz class numbers exist on square classes, and we classify the arithmetic progressions appearing in such congruences. This is joint work with Martin Raum and Olav Richter.

Wednesday, September 14, 2022

Posted July 21, 2022
Last modified August 29, 2022

3:30 pm Lockett 233

Jeff Hicks, University of Edinburgh
Cute constructions from Lagrangian cobordisms

The symplectic squeezing problem asks: What kinds of subsets "fit" inside a symplectic manifold X. The most famous example comes from Gromov's non-squeezing theorem, which shows that the symplectic 4-ball of radius R cannot be symplectically embedded inside the product of two balls of radius A,B whenever A is less than R. In this talk, we will look at squeezing problems related to Lagrangian submanifolds. Let X be the product of two disks of radius A and B. A Lagrangian submanifold L of X is called integral if the symplectic form takes integer values on H2(X,L). The Lagrangian packing problem asks how many disjoint integral Lagrangian tori can we fit inside X. It is easy to construct (⌊A⌋-1)(⌊B⌋-1) such tori, by taking the products of circles bounding integer areas. When A,B are less than 2 of Richard Hind shows that you can do no better. In this talk, I will discuss how to fit an additional integral Lagrangian torus into this space whenever A is greater than 2. The main insight is to treat Lagrangian submanifolds in X as Lagrangian cobordisms (with Lagrangian ends) and employ tools used to construct Lagrangian cobordisms. Time permitting, I will discuss 2 other examples where techniques from Lagrangian cobordisms can be used to improve known constructions for squeezing problems. This is joint work with Cheuk Yu Mak.

Monday, September 19, 2022

Posted August 15, 2022
Last modified September 16, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Zoom Meeting

Shibin Dai, University of Alabama
Degenerate Diffusion and Interface Motion of Single Layer and Bilayer Structures

Degenerate diffusion plays an important role in the interface motion of complex structures. The degenerate Cahn-Hilliard equation is a widely used model for single layer structures. It has been commonly believed that degenerate diffusion eliminates diffusion in the bulk phases and results in surface diffusion only. We will show that due to the curvature effect there is porous medium diffusion in the bulk phases, and the geometric evolution of single layer structures is mediated by the porous medium diffusion process. We will also discuss the existence of weak solutions for the degenerate CH equation. For bilayer structures the Functionalized Cahn-Hilliard (FCH) equation is a new model that has been extensively studied in recent years. We will discuss the existence and nonnegativity of weak solutions for the degenerate FCH equation, and the corresponding interface motions.

Tuesday, September 20, 2022

Posted August 19, 2022
Last modified November 29, 2022

3:10 pm – 4:00 pm Lockett 232 and Zoom

Ayla Gafni, University of Mississippi
Uniform distribution and geometric incidence theory

The Szemerédi–Trotter Incidence Theorem, a central result in geometric combinatorics, bounds the number of incidences between $n$ points and $m$ lines in the Euclidean plane. Replacing lines with circles leads to the unit distance problem, which asks how many pairs of points in a planar set of $n$ points can be at a unit distance. The unit distance problem breaks down in dimensions $4$ and higher due to degenerate configurations that attain the trivial bound. However, nontrivial results are possible under certain structural assumptions about the point set. In this talk, we will give an overview of the history of these and other incidence results. Then we will introduce a quantitative notion of uniform distribution and use that property to obtain nontrivial bounds on unit distances and point-hyperplane incidences in higher-dimensional Euclidean space. This is based on joint work with Alex Iosevich and Emmett Wyman.

Posted September 15, 2022

4:15 pm – 5:15 pm 232 Lockett

Faculty Meeting: Courses and Curricula

Wednesday, September 21, 2022

Posted August 17, 2022
Last modified September 19, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Akram Alishahi, University of Georgia
Khovanov homology and involutive Heegaard Floer homology

Heegaard Floer theory is a package is invariants for 3- and 4-manifolds, knots, links, contact structure, etc. Khovanov homology is a knot (link) invariant defined around the same time as Heegaard Floer homology. Studying the interaction between these invariants has been the subject of many research works over the past two decades. In 2003, Ozsváth and Szabó construct a spectral sequence from Khovanov homology to the Heegaard Floer homology of the branched double cover of the knot. In 2017, Hendricks and Manolescu, incorporate the conjugation action on Heegaard Floer homology to produce a richer 3-manifold invariant, called involutive Heegaard Floer homology. In this talk, we will discuss an involutive version of Ozsváth-Szabó’s spectral sequence that converges to the involutive Heegaard Floer homology of the branched double cover of the knot. This is a work in progress, joint with Linh Truong and Melissa Zhang.

Friday, September 23, 2022

Posted September 14, 2022
Last modified September 15, 2022

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Maria Teresa Chiri, Queen's University
Soil Searching by an Artificial Root

We model an artificial root which grows in the soil for underground prospecting. Its evolution is described by a controlled system of two integro-partial differential equations: one for the growth of the body and the other for the elongation of the tip. At any given time, the angular velocity of the root is obtained by solving a minimization problem with state constraints. We prove the existence of solutions to the evolution problem, up to the first time where a "breakdown configuration" is reached. Some numerical simulations are performed, to test the effectiveness of our feedback control algorithm. This is a joint work with Fabio Ancona (University of Padova) and Alberto Bressan (Penn State University).

Tuesday, September 27, 2022

Posted August 19, 2022
Last modified September 26, 2022

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm Zoom

Hasan Saad, University of Virginia
Explicit Sato-Tate type distribution for a family of $K3$ surfaces

In the 1960s, Birch proved that the traces of Frobenius for elliptic curves taken at random over a large finite field is modeled by the semicircular distribution (i.e. the usual Sato-Tate for non-CM elliptic curves). In analogy with Birch's result, a recent paper by Ono, the author, and Saikia proved that the limiting distribution of the normalized Frobenius traces $A_{\lambda}(p)$ of a certain family of $K3$ surfaces $X_\lambda$ with generic Picard rank $19$ is the $O(3)$ distribution. This distribution, which we denote by $\frac{1}{4\pi}f(t),$ is quite different from the semicircular distribution. It is supported on $[-3,3]$ and has vertical asymptotes at $t=\pm1.$ Here we make this result explicit. We prove that if $p\geq 5$ is prime and $-3 \leq a \lt b \leq 3$, then $$ \left|\frac{\#\{\lambda\in\mathbb{F}_p :A_{\lambda}(p)\in[a,b]\}}{p}-\frac{1}{4\pi}\int_a^b f(t)dt\right|\leq \frac{110.84}{p^{1/4}}. $$ As a consequence, we are able to determine when a finite field $\mathbb{F}_p$ is large enough for the discrete histograms to reach any given height near $t=\pm1.$ To obtain these results, we make use of the theory of Rankin-Cohen brackets in the theory of harmonic Maass forms.

Posted September 21, 2022

3:30 pm – 4:30 pm Digital Media Center 1034

Frederic Marazzato, Louisiana State University
Homogenized Origami Surfaces

Origami folds have found a large range of applications in Engineering as, for instance, solar panels for satellites, or the folding of airbags for optimal deployment or metamaterials. A homogenization process turning origami folds into smooth surfaces, developed in [Nassar et al, 2017], is first discussed. Then, its application to two specific folds is presented alongside the PDEs characterizing the associated smooth surfaces. The talk will then focus on the PDEs describing Miura surfaces by studying existence and uniqueness of solutions and by proposing a numerical method to approximate them. Finally, some numerical examples are presented. div

Posted September 27, 2022

4:15 pm – 5:15 pm Lockett 232

Faculty Meeting: Courses and Curricula

Wednesday, September 28, 2022

Posted July 21, 2022
Last modified September 15, 2022

3:30 pm Lockett 233

Ipsita Datta, Institute for Advanced Study
Lagrangian cobordisms, enriched knot diagrams, and algebraic invariants

We introduce new invariants to the existence of Lagrangian cobordisms in R^4. These are obtained by studying holomorphic disks with corners on Lagrangian tangles, which are Lagrangian cobordisms with flat, immersed boundaries.

Posted July 28, 2022
Last modified August 30, 2022

3:30 pm – 4:30 pm Zoom https://lsu.zoom.us/j/94413235134

Howard Cohl, National Institute of Standards and Technology
Representations and special values for nonsymmetric and symmetric Poisson kernels of the Askey-Wilson polynomials

We discuss the literature on symmetric and nonsymmetric representations for Poisson kernels of Askey-Wilson polynomials. This goes back to the works of Rahman, Verma, Askey, Gasper, Suslov during the 80s and 90s. The symmetric Poisson kernel for Askey-Wilson polynomials was treated in a series of papers by Rahman, Verma and Suslov, and Askey, Rahman and Suslov treated a special form of the nonsymmetric Poisson kernel for Askey-Wilson polynomials in 1996. Even though in all these papers, the analysis was correct, unfortunately, this and all previous symmetric and nonsymmetric Poisson kernels contained typographical errors. We have corrected all symmetric and nonsymmetric representations for these Poisson kernels and as well have computed a new representation of the Askey-Rahman-Suslov nonsymmetric Poisson kernel for Askey-Wilson polynomials using the method of integral representations treated in a recent paper by Cohl and Costas-Santos. We will discuss the form of these representations and as well discuss generating function and arbitrary argument transformation formulas which arise by taking special values of the symmetric representations of these nonsymmetric Poisson kernels. We will also discuss future versions of these results through extension of parameter nonsymmetry.

Thursday, September 29, 2022

Posted September 29, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 232

Faculty Meeting: Courses and Curricula

Friday, September 30, 2022

Posted August 22, 2022
Last modified September 28, 2022

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Christophe Prieur, Université Grenoble Alpes
Stabilization of Nonlinear PDE by Means of Nonlinear Boundary Controls

In this presentation, the focus will be on the design of boundary controls for distributed parameter systems such as those described by linear and nonlinear partial differential equations. Saturated controllers will be discussed in this talk such as those modeling feedback laws in the presence of amplitude constraints. We will review techniques for the stability analysis and the derivation of design conditions for various PDEs such as parabolic and hyperbolic ones. An application to nuclear fusion will conclude this lecture.

Monday, October 3, 2022

Posted April 25, 2022
Last modified September 22, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Zoom: https://lsu.zoom.us/j/91528952709?pwd=UmRUQ1Rxb2IvS2l6M0l4MlMxbG15Zz09

Hao Jia, School of Mathematics, University of Minnesota
Uniform linear inviscid damping near monotonic shear flows in the whole space

In recent years tremendous progress was made in understanding the ``inviscid damping" phenomenon near shear flows and vortices, which are steady states for the 2d incompressible Euler equation, especially at the linearized level. However, in real fluids viscosity plays an important role. It is natural to ask if incorporating the small but crucial viscosity term (and thus considering the Navier Stokes equation in a high Reynolds number regime instead of Euler equations) could change the dynamics in any dramatic way. It turns out that for the perturbative regime near a spectrally stable monotonic shear flows in an infinite periodic channel (to avoid boundary layers and long wave instabilities), we can prove uniform-in-viscosity inviscid damping. The proof introduces techniques that provide a unified treatment of the classical Orr-Sommerfeld equation in a way analogous to Rayleigh equations.

Tuesday, October 4, 2022

Posted August 21, 2022
Last modified September 28, 2022

3:10 pm – 4:00 pm Lockett 232 and Zoom

Paul Pollack, University of Georgia
Some problems on the value-distribution of arithmetic functions

We discuss two strands of questions about the value-distribution of arithmetic functions. In the first half, we consider distribution in arithmetic progressions. For instance, let $A(n)$ denote the sum of the primes dividing $n$ (with multiplicity). I will sketch a proof that the values of $A(n)$, sampled for $n \leq x$ (with $x \to \infty$), are equidistributed $\pmod{q}$ both for every fixed modulus $q$ (as was known already) and for $q$ that grow slowly with $x$. A result about distribution $\pmod{q}$ is really a result about `trailing digits' working in base $q$. The second half of the talk concerns leading digits. After recalling `Benford's Law' I will describe why the leading digits of the divisor function $d(n)$ tend to follow Benford's law but why the leading digits of the sum-of-divisors function $\sigma(n)$ do not. This is joint work with Fai Chandee and Xiannan Li (Kansas State) and Akash Singha Roy (UGA).

Posted October 2, 2022

3:30 pm – 4:30 pm Zoom

Zi Yang, University of California, Santa Barbara
The Multi-Objective Polynomial Optimization

The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies multi-objective optimization problems that are given by polynomial functions. First, we study the convex geometry for (weakly) Pareto values and give a convex representation for them. Linear scalarization problems (LSPs) and Chebyshev scalarization problems (CSPs) are typical approaches for getting (weakly) Pareto points. For LSPs, we show how to use tight relaxations to solve them, how to detect existence or nonexistence of proper weights. For CSPs, we show how to solve them by moment relaxations. Moreover, we show how to check if a given point is a (weakly) Pareto point or not and how to detect existence or nonexistence of (weakly) Pareto points. We also study how to detect unboundedness of polynomial optimization, which is used to detect nonexistence of proper weights or (weakly) Pareto points. ZOOM: Meeting ID958 6951 8026 SecurityPasscode BRENNER https://lsu.zoom.us/j/95869518026?pwd=T2U3R0J1WGdMUFlKNEVhbkJndXZQZz09

Wednesday, October 5, 2022

Posted July 28, 2022
Last modified September 26, 2022

3:30 pm – 4:30 pm Lockett Hall 232

Camilo Montoya, National Institute of Standards and Technology
Laplace eigenfunctions on Riemannian symmetric spaces and the Borel-Weil Theorem

We identify a geometric relation between the Laplace-Beltrami spectra and eigenfunctions on compact Riemannian symmetric spaces and the Borel-Weil theory using ideas from symplectic geometry and geometric quantization. This is done by associating to each compact Riemannian symmetric space, via Marsden-Weinstein reduction, a generalized flag manifold which covers the space parametrizing all of its maximal totally geodesic tori. In the process we notice a direct relation between the Satake diagram of the symmetric space and the painted Dynkin diagram of its associated flag manifold. We consider in detail the examples of the classical simply-connected spaces of rank one and the space SU(3)/SO(3). In the second part of the talk, with the aid of harmonic polynomials, we induce Laplace-Beltrami eigenfunctions on the symmetric space from holomorphic sections of the associated line bundle on the generalized flag manifold. In the examples we consider we show that our construction provides all of the eigenfunctions.

Posted July 23, 2022
Last modified September 30, 2022

3:30 pm Lockett 233

Emily Stark, Wesleyan University
Graphically discrete groups and rigidity

Rigidity theorems in geometric group theory prove that a group’s geometric type determines its algebraic type, typically up to virtual isomorphism. We study graphically discrete groups, which impose a discreteness criterion on the automorphism groups of graphs the group acts on and are well suited to studying rigidity problems. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; nonabelian free groups are non-examples. We will present new families of graphically discrete groups and demonstrate this property is not a quasi-isometry invariant. We will discuss rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.

Thursday, October 6, 2022

Posted September 30, 2022
Last modified October 3, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Marco Marengon, Alfréd Rényi Institute of Mathematics
Sliceness and the rank of some knot homologies

A popular notion in knot theory is that of “sliceness”: a knot in S^3 is called slice if it bounds a smooth disc in B^4. There are various reasons why this concept is so fundamental: for example, sliceness is at the core of a trendy strategy proposed to disprove the smooth 4-dimensional Poincaré conjecture, and it has recently been shown that a generalisation of this concept to 4-manifolds other than B^4 can detect exotic pairs, i.e. 4-manifolds that are homeomorphic but not diffeomorphic to each other. We study whether sliceness poses any restrictions on the rank of certain homology theories associated with knots. We prove some results and formulate some curious conjectures. This is joint work with Hockenhull and Willis, and partly also with Dunfield and Gong.

Friday, October 7, 2022

Posted August 16, 2022
Last modified September 24, 2022

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Matthew Peet, Arizona State University
An Algebraic Framework for Representation, Analysis, Control and Simulation of Delayed and PDEs

We explain the recently proposed partial integral equation representation and show how it enables us to solve many problems in analysis, control, and simulation of delayed and partial differential equations. We start by defining the *-algebra of partial integral (PI) operators. Next, we show that through a similarity transformation, the solution of a broad class of delayed and partial differential equations may be equivalently represented using a partial integral equation (PIE) - an equation parameterized by PI operators. We then show that many analysis and control problems for systems represented as a PIE may be solved through convex optimization of PI operators. Finally, we discuss software which automates the process of conversion to PIE, analysis, optimal controller synthesis, implementation, and simulation.

Monday, October 10, 2022

Posted January 25, 2022
Last modified October 4, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett Hall 233

Kasso Okoudjou, Tufts University
Topics in analysis on fractals and self-similar graphs

The goal of this talk is to present some topics related to what is known as analysis on fractal sets such as the Sierpinski gasket. This theory is based on the spectral analysis of a corresponding Laplace operator which we will introduce in the first part of the talk. We will then review certain fractal analogs of topics from classical analysis, including the Heisenberg uncertainty principle, the spectral theory of Schr\"odinger operators, and the theory of orthogonal polynomials. In the last part of the talk, I will introduce a self-similar analog of the almost Mathieu operators (AMO), and present some results pertaining to their spectral properties. These results are obtained by using the so-called spectral decimation method which is one of the important tools in the spectral analysis of fractal Laplacians.

Tuesday, October 11, 2022

Posted August 19, 2022
Last modified September 30, 2022

3:10 pm – 4:00 pm Lockett 232 and Zoom

Catherine Hsu, Swarthmore College
Explicit non-Gorenstein $R=T$ via rank bounds

In his seminal work on modular curves and the Eisenstein ideal, Mazur studied the existence of congruences between certain Eisenstein series and newforms, proving that Eisenstein ideals associated to weight $2$ cusp forms of prime level are locally principal. In this talk, we'll explore generalizations of Mazur's result to squarefree level, focusing on recent work, joint with P. Wake and C. Wang-Erickson, about a non-optimal level $N$ that is the product of two distinct primes and where the Galois deformation ring is not expected to be Gorenstein. First, we will outline a Galois-theoretic criterion for the deformation ring to be as small as possible, and when this criterion is satisfied, deduce an $R=T$ theorem. Then we'll discuss some of the techniques required to computationally verify the criterion.

Posted October 4, 2022
Last modified October 7, 2022

4:10 pm Lockett Hall 233

Matthew Faust, TX A&M University
Reducibility of Bloch and Fermi varieties via discrete geometry

Given an infinite ZZ^n periodic graph G, the Schrödinger operator acting on G is a graph Laplacian perturbed by a potential at every vertex. Complexifying and choosing a potential periodic to a full rank subgroup of ZZ^n fixes a representation of the operator as a finite matrix whose entries are Laurent polynomials. The vanishing set of the characteristic polynomial of this matrix yields the Bloch variety, and the vanishing set for a fixed eigenvalue gives the Fermi variety. We will focus our attention on the reducibility of these varieties. Understanding the reducibility of Bloch and Fermi varieties is important in the study of the spectrum of periodic operators, providing insight into the structure of spectral edges, embedded eigenvalues, and other applications. In this talk we will present several new criteria for determining when Bloch and Fermi varieties are irreducible for infinite families of discrete periodic operators. This is joint work with Jordy Lopez.

Wednesday, October 12, 2022

Posted July 29, 2022
Last modified October 5, 2022

3:30 pm Lockett 233

Caitlin Leverson, Bard College
Lagrangian Realizations of Ribbon Cobordisms

Similarly to how every smooth knot has a Legendrian representative (in fact, infinitely many different representatives), in this talk we will discuss why every ribbon cobordism has a Legendrian representative. Meaning, if $C$ is a ribbon cobordism in $[0,1]\times S^3$ from the link $K_0$ to $K_1$, then there are Legendrian realizations $\Lambda_0$ and $\Lambda_1$ of $K_0$ and $K_1$, respectively, such that $C$ may be isotoped to a decomposable Lagrangian cobordism from $\Lambda_0$ to $\Lambda_1$. We will also give examples of some interesting constructions of such decomposable Lagrangian cobordisms. This is joint work with John Etnyre.

Monday, October 17, 2022

Posted October 13, 2022
Last modified October 16, 2022

2:30 pm – 3:30 pm Lockett 241

Meeting of Tenured Faculty

Posted October 16, 2022

3:30 pm 233 Lockett Hall

Rose McCarty, Princeton University
Local structure for vertex-minors

Roughly, the vertex-minors of a graph $G$ are the graphs that can be obtained from $G$ by deleting vertices and by performing certain local moves within the neighborhood of a vertex. We are interested in classes of graphs which are closed under vertex-minors and isomorphism and which do not contain all graphs. Geelen conjectures that the graphs in any such class have a simple structural description. We discuss progress towards proving this conjecture and its relationship with binary matroids. This is part of an ongoing project with Jim Geelen and Paul Wollan.

Posted September 21, 2022
Last modified October 17, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett Hall 233

Doosung Choi, LSU
Inverse problem in potential theory using Faber polynomials

This presentation concerns the inverse problem of determining a planar conductivity inclusion. We analytically reconstruct from the generalized polarization tensors (GPTs), which can be obtained from exterior measurements. The primary result is an inversion formula in terms of the GPTs for conformal mapping coefficients associated with the inclusion.

Tuesday, October 18, 2022

Posted August 19, 2022
Last modified October 15, 2022

3:10 pm – 4:00 pm Lockett 232 and Zoom

Kim Klinger-Logan, Kansas State University
An application of automorphic forms to string theory

Recently, physicists Green, Russo, and Vanhove have discovered solutions to differential equations involving automorphic forms appear as the coefficients to the 4-graviton scattering amplitude in type IIB string theory. We will discuss a particular form of equation that appears in this context and different approaches to the solution. Time permitting, we will also discuss a connection to a shifted convolution sum that appears in this context. This is joint work with Stephen D. Miller, Danylo Radchenko and Ksenia Fedosova.

Wednesday, October 19, 2022

Posted August 18, 2022
Last modified October 14, 2022

3:30 pm Lockett 233

Pallavi Dani, Department of Mathematics, LSU
Divergence, thickness, and hypergraph index for Coxeter groups

Divergence and thickness are geometric properties of finitely generated groups that are invariant under quasi-isometry. In general, they can be quite difficult to compute. In the case of right-angled Coxeter groups, Levcovitz introduced the notion of hypergraph index, which can be algorithmically computed from the defining graph, and proved that it determines the thickness and divergence of the group. After introducing the basics, I will talk about joint work with Yusra Naqvi, Ignat Soroko, and Anne Thomas, in which we propose a definition of hypergraph index for general Coxeter groups. We show that it determines the divergence and thickness in an infinite family of non-right-angled Coxeter groups.

Thursday, October 20, 2022

Posted September 6, 2022
Last modified October 12, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 232

Peter Schauenburg, Université de Bourgogne
Prime factorization(s) of modular categories

The raison d'être of modular categories is in their rôle (or rather in their many rôles) in mathematics and mathematical physics; the most direct perhaps in topological quantum field theory. Forgetting about all the exciting applications they are (finite, in a sense) algebraic structures with a categorical but not overly complicated definition. They are impossible to classify, but there are ongoing and very active investigations into partial (but still rich, hard, and interesting) classification results. We will humbly study an early general structural result by Michael Müger: A (semisimple) modular category can be written as a Deligne product of prime factors. This immediately begs the question whether the factors are unique. Along with the existence of the factorization it was already proved that it is in fact unique if the category does not contain invertible objects. If all the simples of the category are invertible on the other hand, the factorization was already known to be non-unique before modular categories were ever defined (sic). In joint work with Michael Müger we try to find out what exactly can happen between these extreme cases. This is work in progress, since between partial positive uniqueness results and some counterexamples there remains uncharted territory.

Friday, October 21, 2022

Posted September 12, 2022
Last modified October 17, 2022

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Craig Woolsey, Virginia Tech
Port-Hamiltonian Modeling and Energy-Based Control of Ocean and Atmospheric Vehicles

The dynamics of a wide variety of vehicles can be represented using noncanonical Hamiltonian system models with dissipation and exogenous inputs. The Hamiltonian structure captures energy exchange among subsystem elements, the noncanonical form accommodates rotating reference frames, and the exogenous inputs allow for control commands and for disturbances that are not readily incorporated into the Hamiltonian form. Because these models typically describe a system's behavior within a large region of state space, and because the system structure provides a natural starting point for Lyapunov-based control design, noncanonical Hamiltonian models are especially well-suited to developing large-envelope nonlinear control laws. The presentation will include several examples from the speaker's experience, such as space vehicles, autonomous underwater vehicles (AUVs), and uncrewed air vehicles (UAVs). A particular emphasis will be recent theoretical results, supported by experimental demonstrations, of passivity-based control laws for fixed-wing aircraft. In considering these examples, a unifying theme will emerge: recognizing and exploiting the nonlinear mechanical system structure of the governing equations to obtain provably effective control strategies.

Tuesday, October 25, 2022

Posted August 19, 2022
Last modified October 14, 2022

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm Lockett 232 and Zoom

Lawrence Washington, University of Maryland
Heuristics for anticyclotomic $\mathbb{Z}_p$-extensions

For an imaginary quadratic field, there are two natural $\mathbb{Z}_p$-extensions, the cyclotomic and the anticyclotomic. We'll start with a brief description of Iwasawa theory for the cyclotomic extensions, and then describe some computations for anticyclotomic $\mathbb{Z}_p$-extensions, especially the fields and their class numbers.

Wednesday, October 26, 2022

Posted October 16, 2022
Last modified October 23, 2022

3:30 pm – 4:30 pm https://lsu.zoom.us/j/94413235134

Howard Cohl, National Institute of Standards and Technology
Jacobi functions of the first and second kind. II

We continue our review of properties of the Jacobi functions of the first and second kind which are generalizations of the Jacobi polynomials and the Jacobi function of the second kind for integer degrees, where the degree is now allowed to be an arbitrary complex number. We also describe the properties of the Jacobi functions of the first and second kind on-the-cut (-1,1) which are obtained from the standard functions through a limiting process. Various properties that we include are hypergeometric representations, symmetry and anti-symmetry relations (and their relations to Gegenbauer, associated Legendre and Ferrers functions), linear and quadratic transformations, connection formulas, infinite series, and expressions for evaluating these functions when all the degree and parameters are all integers.

Posted August 11, 2022
Last modified October 19, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Miriam Kuzbary, Georgia Institute of Technology
Asymptotic bounds on the d-invariant

As shown by Morita, every integral homology 3-sphere Y has a Heegaard decomposition into two handlebodies where the gluing map along the boundary is an element of the Torelli subgroup of the mapping class group of the boundary composed with the standard gluing map for the 3-sphere. In work in progress with Santana Afton and Tye Lidman, we show that the d-invariant of Y, a homology cobordism invariant of homology spheres defined using Heegaard Floer homology, is bounded above by a linear function of the word length of a corresponding gluing element in the Torelli group for any fixed, finite generating set when the genus is larger than 2. Moreover, we show the d-invariant is bounded for homology spheres corresponding to various large families of mapping classes.

Friday, October 28, 2022

Posted September 11, 2022
Last modified October 21, 2022

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Na (Lina) Li, Harvard University Donald P. Eckman, AFOSR YIP, NSF CAREER, and ONR YIP Awardee
Scalable Distributed Control and Learning of Networked Dynamical Systems

Recent radical evolution in distributed sensing, computation, communication, and actuation has fostered the emergence of cyber-physical network systems. Regardless of the specific application, one central goal is to shape the network's collective behavior through the design of admissible local decision-making algorithms. This is nontrivial due to various challenges such as local connectivity, system complexity and uncertainty, limited information structure, and the complex intertwined physics and human interactions. In this talk, I will present our recent progress in formally advancing the systematic design of distributed coordination in network systems via harnessing special properties of the underlying problems and systems. In particular, we will present three examples and discuss three types of properties: i) how to use network structure to ensure the performance of the local controllers; ii) how to use the information and communication structure to develop distributed learning rules; iii) how to use domain-specific properties to further improve the efficiency of the distributed control and learning algorithms.

Monday, October 31, 2022

Posted October 24, 2022
Last modified January 7, 2025

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 232

Hal Schenck, Auburn University
Combinatorics and Commutative Algebra

This talk will give an overview of the spectacular success of algebraic methods in studying problems in discrete geometry and combinatorics. First we'll discuss the face vector (number of vertices, edges, etc.) of a convex polytope and recall Euler's famous formula for polytopes of dimension 3. Then we'll discuss graded rings, focusing on polynomial rings and quotients. Associated to a simplicial polytope P (every face is "like" a triangle) is a graded ring called the Stanley-Reisner ring, which "remembers" everything about P, and gives a beautiful algebra/combinatorics dictionary. I will sketch Stanley's solution to a famous conjecture using this machinery, and also touch on connections between P and objects from algebraic geometry (toric varieties).

This talk will be accessible to undergraduates. No prior knowledge of any of the terms above will be assumed or needed for the talk.

Tuesday, November 1, 2022

Posted October 15, 2022
Last modified October 31, 2022

3:10 pm – 4:00 pm Lockett 232 and Zoom

Emma Lien, Louisiana State University
Galois Representations and Weight One Eta-Quotients

A classical problem in number theory is to determine the primes $p$ for which a polynomial splits into linear factors modulo $p$. One is then naturally led to consider the Artin representations associated to the polynomial, i.e, the complex representations of the finite Galois group of its splitting field. Serre and Deligne showed that the representations associated to a weight one Hecke eigenforms are Artin representations. Thus, we wish to examine some easily computable examples of weight 1 Hecke eigenforms coming from eta-quotients with the goal of determining the explicit polynomials associated to them. For example, let $f(\tau)=\eta(6\tau)\eta(18\tau)$; then if $a_n$ denotes the $n$-th coefficient in the Fourier expansion of $f$ and $p>3$ is a prime, then $a_p = 2$ if and only if $x^3-2$ splits modulo $p$. In particular, the representations give us information about certain abelian extensions of imaginary quadratic extensions of $\mathbb{Q}$ and we can even express certain cases as a theta series associated to a quadratic form twisted by a grossencharacter.

Posted October 24, 2022
Last modified January 7, 2025

3:30 pm – 4:30 pm Locket 276

Hal Schenck, Auburn University
Numerical Analysis meets Topology

One of the fundamental tools in numerical analysis and PDE is the finite element method (FEM). A main ingredient in FEM are splines: piecewise polynomial functions on a mesh. Even for a fixed mesh in the plane, there are many open questions about splines: for a triangular mesh T and smoothness order one, the dimension of the vector space $C^1_3(T)$ of splines of polynomial degree at most three is unknown. In 1973, Gil Strang conjectured a formula for the dimension of the space $C^1_2(T)$ in terms of the combinatorics and geometry of the mesh T, and in 1987 Lou Billera used algebraic topology to prove the conjecture (and win the Fulkerson prize). I'll describe recent progress on the study of spline spaces, including a quick and self contained introduction to some basic but quite useful tools from topology, as well as interesting open problems.

Thursday, November 3, 2022

Posted October 20, 2022
Last modified October 21, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Hal Schenck, Auburn University
Calabi-Yau threefolds in P^n and Gorenstein rings

In physics, String Theory posits a symmetry between certain pairs of geometric objects: Calabi-Yau threefolds. In algebra, Gorenstein rings are objects possessing an intrinsic, internal symmetry. We’ll discuss connections between the two sets of objects, going from the basic algebraic construction to computation, culminating in smooth Calabi-Yau threefolds with new Hodge numbers. The talk will start from ground zero, and anything we need along the way will be illustrated with examples. Joint work with M. Stillman and B. Yuan.

Friday, November 4, 2022

Posted June 12, 2022
Last modified September 14, 2022

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Naomi Leonard, Princeton University MacArthur Fellow, and Fellow of ASME, IEEE, IFAC, and SIAM.
Nonlinear Opinion Dynamics on Networks: Agreeing, Disagreeing, and Avoiding Indecision

I will present continuous-time multi-option nonlinear opinion dynamics for a group of agents that observe or communicate opinions over a network. Nonlinearity is introduced by saturating opinion exchanges: this enables a wide range of analytically tractable opinion-forming behaviors, including agreement and disagreement, deadlock breaking, tunable sensitivity to input, oscillations, flexible transition between opinion configurations, and opinion cascades. I will discuss how network-dependent tuning rules can robustly control the system behavior and how state-feedback dynamics for model parameters make the behavior adaptive to changing external conditions. The model provides new means for systematic study and design of dynamics on networks in nature and technology, including the dynamics of decision-making, spreading processes, polarization, games, navigation, and task allocation. I will demonstrate with applications to multi-robot teams. This is joint work with Anastasia Bizyaeva and Alessio Franci and based on the paper https://doi.org/10.1109/TAC.2022.3159527 with reference to other key papers with additional collaborators, including https://doi.org/10.1109/LCSYS.2022.3185981 and https://doi.org/10.1109/LCSYS.2021.3138725.

Monday, November 7, 2022

Posted October 3, 2022
Last modified October 31, 2022

3:30 pm – 4:30 pm Zoom: https://lsu.zoom.us/j/5494314978

Donatella Danielli, Arizona State University
Regularity properties in obstacle-type problems for higher-order fractional powers of the Laplacian

In this talk we will discuss a sampler of obstacle-type problems associated with the fractional Laplacian. Our goals are to establish regularity properties of the solution and to describe the structure of the free boundary. To this end, we combine classical techniques from potential theory and the calculus of variations with more modern methods, such as the localization of the operator and monotonicity formulas. This is joint work with A. Haj Ali (Arizona State University) and A. Petrosyan (Purdue University).

Wednesday, November 9, 2022

Posted July 28, 2022
Last modified November 7, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Alex Margolis, Vanderbilt University
Model geometries of groups and discretisability

The central theme of geometric group theory is to study groups via their actions on metric spaces. A model geometry of a finitely generated group is a proper geodesic metric space admitting a geometric group action. Every finitely generated group has a model geometry that is a locally finite graph, namely its Cayley graph with respect to a finite generating set. In this talk, I investigate which finitely generated groups G have the property that all model geometries of G are (essentially) locally finite graphs. I introduce the notion of domination of metric spaces and give necessary and sufficient conditions for all model geometries of a finitely generated group to be dominated by a locally finite graph. Among groups of cohomological dimension two, the only such groups are surface groups and generalised Baumslag-Solitar groups. Time permitting, I will discuss applications to quasi-isometric rigidity.

Friday, November 11, 2022

Posted August 8, 2022

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Nader Motee, Lehigh University AFOSR YIP and ONR YIP Awardee
Finite-Section Approximation of Carleman Linearization and Its Exponential Convergence

The Carleman linearization is one of the mainstream approaches to lift a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear system with the promise of providing accurate finite-dimensional linear approximations of the original nonlinear system over larger regions around the equilibrium for longer time horizons with respect to the conventional first-order linearization approach. Finite-section approximations of the lifted system has been widely used to study dynamical and control properties of the original nonlinear system. In this context, some of the outstanding problems are to determine under what conditions, as the finite-section order (i.e., truncation length) increases, the trajectory of the resulting approximate linear system from the finite-section scheme converges to that of the original nonlinear system and whether the time interval over which the convergence happens can be quantified explicitly. In this talk, I will present explicit error bounds for the finite-section approximation and prove that the convergence is indeed exponential as a function of finite-section order. For a class of nonlinear systems, it is shown that one can achieve exponential convergence over the entire time horizon up to infinity. Our results are practically plausible, including approximating nonlinear systems for model predictive control and reachability analysis of nonlinear systems for verification, control, and planning purposes, as our proposed error bound estimates can be used to determine proper truncation lengths for a given sampling period.

Monday, November 14, 2022

Posted September 22, 2022
Last modified November 11, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Zoom: https://lsu.zoom.us/j/92890365678?pwd=SlJmN0JnQnRvTFYxd1QyUjhqR0tqQT09

Arghir Zarnescu, Basque Center for Applied Mathematics
On the motion of several small rigid bodies in a viscous incompressible fluid

We consider the motion of N rigid bodies contained in a domain in dimension two or three. We show the fluid flow is not influenced by the presence of the bodies in the asymptotic limit as the size of the bodies tends to zero. The result depends solely on the geometry of the bodies and is independent of their mass densities. Collisions are allowed and the initial data are arbitrary with finite energy. This is joint work with Eduard Feireisl and Arnab Roy.

Tuesday, November 15, 2022

Posted October 15, 2022
Last modified November 9, 2022

1:40 pm – 2:30 pm Lockett 241 and Zoom

Abbey Bourdon, Wake Forest University
Sporadic Torsion on Elliptic Curves

An elliptic curve is a curve in projective space whose points can be given the structure of an abelian group. In this talk, we will focus on torsion points, which are points having finite order under this group law. While we can generally determine the torsion points of a fixed elliptic curve defined over a number field, there are several open problems which require controlling the existence of torsion points within infinite families of elliptic curves. Success stories include Merel's Uniform Boundedness Theorem, which states that the order of a torsion point can be bounded by the degree of its field of definition. On the other hand, a proof of Serre's Uniformity Conjecture---which has been open for 50 years---would in particular imply that for sufficiently large primes $p$, there do not exist points of order $p^2$ arising on elliptic curves defined over field extensions of ``unusually low degree." In this talk, I will give a brief introduction to the arithmetic of elliptic curves before addressing the problem of identifying elliptic curves producing a point of large order in usually low degree, i.e., those possessing a sporadic torsion point. More precisely, let $E$ be an elliptic curve defined over a field extension $F/\mathbb{Q}$ of degree $d$, and let $P$ be a point of order $N$ with coordinates in $F$. Such a point is called ``rational" since it is defined over the same field as $E$. We say $P$ is sporadic if, as one ranges over all fields $F/\mathbb{Q}$ of degree at most $d$ and all elliptic curves $E/F$, there are only finitely many elliptic curves which possess a rational point of order $N$. Sporadic pairs $(E,P)$ correspond to exceptional points on modular curves, which are points whose existence is not explained by standard geometric constructions.

Posted October 15, 2022
Last modified November 9, 2022

Algebra and Number Theory Seminar Questions or comments?

3:10 pm – 4:00 pm Lockett 232 and Zoom

Nicole Looper, University of Illinois at Chicago
Diophantine Techniques in Arithmetic Dynamics

This talk will explore some of the most important relationships between Diophantine geometry and arithmetic dynamics. Many questions in arithmetic dynamics are inspired by classical problems in arithmetic geometry, and many dynamical consequences follow from well-known Diophantine inputs such as the abc conjecture. Moreover, ideas drawn from dynamics are often useful in tackling number-theoretic questions. I will give an overview of these links, and then will discuss some concrete illustrative examples. I will also point out some areas of difficulty that appear key to future progress.

Posted November 11, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Zoom

Tongtong Li, Dartmouth College
Improving Numerical Accuracy for the Viscous-plastic Formulation of Sea Ice

Accurate modeling of sea ice dynamics is critical for predicting environmental variables, which in turn is important in applications such as navigating ice breaker ships, and has led to extensive research in both modeling and simulating sea ice dynamics. The most widely accepted model is the one based on the viscous-plastic formulation introduced by Hibler, which is intrinsically difficult to solve numerically due to highly nonlinear features. In particular, sea ice simulations often significantly differ from satellite observations. In this study we focus on improving the numerical accuracy of the viscous-plastic sea ice model. We explore the convergence properties for various numerical solutions of the sea ice model and in particular examine the poor convergence seen in existing numerical methods. To address these issues, we demonstrate that using higher order methods for solving conservation laws, such as the weighted essentially non-oscillatory (WENO) schemes, is critical for numerically solving viscous-plastic formulations whenever the solution is not smooth. Moreover, WENO yields higher order convergence for smooth solutions than standard central differencing does. Our numerical examples verify this, and in particular by using WENO, we are able to resolve the discontinuities in the sharp features of sea ice covers. We also propose an approach utilizing the idea of phase field method to develop a potential function method which naturally incorporates the physical restrictions of ice thickness and ice concentration in transport equations. Our approach results in modified transport equations with extra forcing terms coming from potential energy function, and has the advantage of not requiring any post-processing procedure that might introduce discontinuities and thus ruin the solution behavior. Zoom: Meeting ID958 6951 8026 SecurityPasscode BRENNER https://lsu.zoom.us/j/95869518026?pwd=T2U3R0J1WGdMUFlKNEVhbkJndXZQZz09

Posted November 9, 2022

4:15 pm – 5:45 pm Lockett 232 and Zoom

BARD 1 Lightning Talks

Short talks (up to 10 minutes) by Prerna Agarwal (LSU), Andrea Bourque (LSU), Pranabesh Das (Xavier University of Louisiana), Brian Grove (LSU), Emma Lien (LSU), Evangelos Nastas (State University of New York), Matthias Storzer (Max Planck Institute), and Kalani Thalagoda (University of North Carolina Greensboro)

Wednesday, November 16, 2022

Posted July 23, 2022
Last modified November 11, 2022

3:30 pm Lockett 233

Hannah Turner , Georgia Institute of Technology
Generalizing the (fractional) Dehn twist coefficient

The fractional Dehn twist coefficient (FDTC) is a rational number associated to a mapping class on a (finite-type) surface with boundary. This 2-dimensional invariant has many applications to 3-manifold topology and contact geometry. One way to think of the FDTC is as a real-valued function on the mapping class group of a surface with many nice properties. In this talk, we will give sufficient conditions on a more general group to admit a function which behaves like the FDTC. In particular, we use this to generalize the FDTC to infinite-type surfaces (with boundary); in this setting, we show that the "fractional" Dehn twist coefficient need not be rational. This is joint work with Peter Feller and Diana Hubbard.

Thursday, November 17, 2022

Posted November 16, 2022
Last modified November 17, 2022

Seminar

3:10 pm – 4:00 pm Lockett 232

Evangelos Nastas, SUNY Albany
On generalizing a model of the Fluid-Porohyperelastic Structure Interaction by Seboldt, et al to higher dimensions

This talk is devoted to reviewing and the exploration of ideas to generalize to higher dimensions, staring with the 3-dimensional case, of a model of the Fluid-Porohyperelastic Structure Interaction in the article,``Numerical Modeling of the Fluid-Porohyperelastic Structure Interaction'' by Seboldt, et al, 2021. In addition, applying those same methods by Seboldt, et al to different scenarios will be discussed.

Monday, November 21, 2022

Posted July 7, 2022
Last modified November 20, 2022

3:30 pm Zoom: https://lsu.zoom.us/j/8811458211?pwd=Um1DV3J6YkFSbkkzSldwSXU1cFJqQT09

Thomas Chen, University of Texas at Austin
On the emergence of a quantum Boltzmann equation near a Bose-Einstein condensate

The mathematically rigorous derivation of nonlinear Boltzmann equations from first principles in interacting physical systems is an extremely active research area in Analysis, Mathematical Physics, and Applied Mathematics. In classical physical systems, rigorous results of this type have been obtained for some models. In the quantum case on the other hand, the problem has essentially remained open. In this talk, I will explain how a cubic quantum Boltzmann equation arises within the fluctuation dynamics around a Bose-Einstein condensate, within the quantum field theoretic description of an interacting Boson gas. This is based on joint work with Michael Hott.

Monday, November 28, 2022

Posted October 2, 2022
Last modified November 29, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Zoom

James Scott, Columbia University
Geometric Rigidity Theorems for Nonlocal Continuum Theories of Linear and Nonlinear Elasticity

We present several quantitative results that generalize known nonlocal rigidity relations for vector fields representing deformations of elastic media. We show that the distance in Lebesgue norm of a deformation from a rigid motion is bounded by a multiple of a strain energy associated to the deformation. This nonconvex energy is a nonlocal constitutive relation that represents the extent to which the deformation stretches and shrinks distances. This inequality can be thought of as a nonlinear fractional Poincaré-Korn inequality. We linearize this inequality to obtain a fractional Poincaré-Korn inequality for Lipschitz domains with an explicit universal bounding constant. This inequality is also valid for more general interaction kernels of non-fractional type, which we demonstrate by using a compactness argument. We apply these inequalities to obtain quantitative statements for solutions to variational problems arising in peridynamics, dislocation models, and phase transition dynamics.

Tuesday, November 29, 2022

Posted October 15, 2022
Last modified November 22, 2022

3:10 pm – 4:00 pm Lockett 232 and Zoom

Louis Gaudet, Rutgers University
The least Euler prime via sieve

Euler primes are primes of the form $p = x^2+Dy^2$ with $D>0$. In analogy with Linnik’s theorem, we can ask if it is possible to show that $p(D)$, the least prime of this form, satisfies $p(D) \ll D^A$ for some constant $A>0$. Indeed Weiss showed this in 1983, but it wasn’t until 2016 that an explicit value for $A$ was determined by Thorner and Zaman, who showed one can take $A=694$. Their work follows the same outline as the traditional approach to proving Linnik’s theorem, relying on log-free zero-density estimates for Hecke L-functions and a quantitative Deuring-Heilbronn phenomenon. In an ongoing work (as part of my PhD thesis) we propose an alternative approach to the problem via sieve methods that (as far as results about zeros of the Hecke $L$-functions) only requires the classical zero-free region. We hope that such an approach may result in a better value for the exponent $A$.

Posted November 11, 2022
Last modified November 22, 2022

3:30 pm – 4:30 pm DMC 1034

Jose Garay, Louisiana State University
DD-LOD: A Localized Orthogonal Decomposition Method for Elliptic Problems with Rough Coefficients Based on Domain Decomposition Techniques

The solution of multi-scale elliptic problems with non-separable scales and high contrast in the coefficients by standard Finite Element Methods (FEM) is typically prohibitively expensive since it requires the resolution of all characteristic lengths to produce an accurate solution. Numerical homogenization methods such as Localized Orthogonal Decomposition (LOD) methods provide access to feasible and reliable simulations of such multi-scale problems. These methods are based on the idea of a generalized finite element space whose basis functions are obtained by modifying standard coarse standard FEM basis functions to incorporate relevant microscopic information in a computationally feasible procedure. Using this enhanced basis one can solve a much smaller problem to produce an approximate solution whose accuracy is comparable to the solution obtained by the expensive standard FEM. We present a variant of the LOD method that utilizes domain decomposition techniques and its applications in the solution of elliptic partial differential equations with rough coefficients as well as elliptic optimal control problems with rough coefficients with and without control constraints.

Wednesday, November 30, 2022

Posted September 6, 2022
Last modified November 28, 2022

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Agniva Roy, Georgia Institute of Technology
On the doubling construction for Legendrian submanifolds

In high dimensional contact and symplectic topology, finding interesting constructions for Legendrian submanifolds is an active area of research. Further, it is desirable that the constructions lend themselves nicely to computation of invariants. The doubling construction was defined by Ekholm, which uses Lagrangian fillings of a Legendrian knot in R^{2n-1} to produce a Legendrian in R^{2n+1}. Later Courte-Ekholm showed that symmetric doubles of embedded fillings are "uninteresting". In recent work the symmetric doubling construction was generalised to any contact manifold, giving two isotopic constructions related to open book decompositions of the ambient manifold. In a separate joint work with James Hughes, we explore the asymmetric doubling construction through Legendrian weaves.

Friday, December 2, 2022

Posted August 31, 2022
Last modified November 27, 2022

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Wei Ren, University of California Riverside IEEE Fellow
Distributed Average Tracking and Continuous-time Optimization in Multi-agent Networks

We introduce a distributed average tracking problem and present distributed discontinuous control algorithms to solve the problem. The idea of distributed average tracking is that multiple agents track the average of multiple time-varying reference signals in a distributed manner based only on local information and local communication with adjacent neighbors. We study cases where the time-varying reference signals have bounded derivatives and accelerations. We also use the distributed average tracking idea to solve a continuous-time distributed convex optimization problem. Tools from nonsmooth analysis are used to analyze the stability of the systems. Simulation and experimental results are presented to illustrate the theoretical results.

Friday, December 9, 2022

Posted September 14, 2022
Last modified September 27, 2022

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Maryam Yashtini, Georgetown University
Counting Objects by Diffused Index: Geometry-Free and Training-Free Approach

Counting objects is a fundamental but challenging problem. In this talk, we propose diffusion-based, geometry-free, and learning-free methodologies to count the number of objects in images. The main idea is to represent each object by a unique index value regardless of its intensity or size, and to simply count the number of index values. First, we place different vectors, referred to as seed vectors, uniformly throughout the mask image. The mask image has boundary information of the objects to be counted. Secondly, the seeds are diffused using an edge-weighted harmonic variational optimization model within each object. We propose an efficient algorithm based on an operator splitting approach and alternating direction minimization method, and theoretical analysis of this algorithm is given. An optimal solution of the model is obtained when the distributed seeds are completely diffused such that there is a unique intensity within each object, which we refer to as an index. For computational efficiency, we stop the diffusion process before a full convergence, and propose to cluster these diffused index values. We refer to this approach as Counting Objects by Diffused Index (CODI). We explore scalar and multi-dimensional seed vectors. For scalar seeds, we use Gaussian fitting in a histogram to count, while for vector seeds, we exploit a high-dimensional clustering method for the final step of counting via clustering. The proposed method is flexible even if the boundary of the object is not clear nor fully enclosed. We present counting results in various applications such as biological cells, agriculture, concert crowds, and transportation. Some comparisons with existing methods are presented.

Monday, January 9, 2023

Posted December 3, 2022

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam in Analysis

Wednesday, January 11, 2023

Posted December 3, 2022

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam in Topology

Friday, January 13, 2023

Posted December 3, 2022

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam in Algebra

Friday, January 20, 2023

Posted January 17, 2023
Last modified February 14, 2023

3:30 pm – 4:20 pm Lockett 232

Naga Manasa Vempati, Georgia Tech
Weighted Inequalities for Singular Integral Operators

Weighted inequalities for singular integral operators are central in the study of non-homogeneous harmonic analysis. Two weight inequalities for singular integral operators, in particular attracted attention as they can be essential in the perturbation theory of unitary matrices, spectral theory of Jacobi matrices and PDE's. In this talk, I will discuss several results concerning the two weight inequalities for various Calderón-Zygmund operators in both Euclidean setting and in the more generic setting of spaces of homogeneous type in the sense of Coifman and Weiss. The two-weight conjecture for singular integral operators T was first raised by Nazarov, Treil and Volberg on finding the real variable characterization of the two weights u and v so that T is bounded on the weighted L^2 spaces. This conjecture was only solved completely for the Hilbert transform on R until recently. In this talk, I will describe our result that resolves a part of this conjecture for any Calderón-Zygmund operator on the spaces of homogeneous type by providing a complete set of sufficient conditions on the pair of weights. We will also discuss the existence of similar analogues for multilinear Calderón-Zygmund operators.

Monday, January 23, 2023

Posted January 11, 2023
Last modified January 18, 2023

2:30 pm – 3:20 pm Lockett 285

Zhongjian Wang, University of Chicago
Deep learning of multi-scale PDEs based on data generated from particle methods

Abstract: Solving multi-scale PDEs is difficult in high-dimensional and/or convection-dominant cases. The interacting particle methods (IPM) are shown to outperform solving PDEs directly. Examples include computing effective diffusivities, KPP front speed, and asymptotic transport properties in topological insulators. However, the particle simulation takes a long time before convergence and is lack of surrogate models for physical parameters. In this regard, we introduce the DeepParticle methods, which learn the pushforward map from arbitrary distribution to IPM-generated distribution by minimizing the Wasserstein distance. In particular, we formulate an iterative scheme to find the transport map and prove the convergence. On the application side, in addition to KPP invariant measures, our method also applies to investigate the blow-up behavior in chemotaxis models.

Posted November 10, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Zoom

Jeffrey Rauch, University of Michigan
Earnshaw’s Theorem in Electrostatics

This result dating to 1842 asserts that a charge in a static electrostatic field can never be in a stable equilibrium. In spite of many partial results a complete proof was first given in 1987. The present talk concerns generalizations from Section 116 of Maxwell’s treatise. There Maxwell explains (but does not prove) why a rigid charged body or a perfect conducting body or a dielectric body in a static field can never be in a stable equilibrium. We prove the result for conductors and dielectrics. The charged rigid body remains open. This joint work with G. Allaire appeared in the Archive for Rational Mechanics in 2017.

Tuesday, January 24, 2023

Posted January 16, 2023
Last modified January 20, 2023

6:00 pm – 6:50 pm Zoom

Xin Wan, Chinese Academy of Sciences
[NOTE UNUSUAL TIME] Iwasawa main conjecture for universal families

We formulate and prove the Iwasawa main conjecture for the universal family for ${\rm GL}_2/\mathbb{Q}$ in the $p$-adic Langlands program. As a consequence we prove the Iwasawa main conjecture and rank 0 BSD formula at bad primes. This is joint work with Olivier Fouquet.

Friday, January 27, 2023

Posted December 12, 2022

Control and Optimization Seminar Questions or comments?

10:30 am – 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Giulia Giordano, University of Trento, Italy SIAG on Control and Systems Theory Prize Awardee
What We Can Learn from the System Structure in Biology and Epidemiology

Biological, ecological and epidemiological systems can be seen as dynamical networks, namely dynamical systems that are naturally endowed with an underlying network structure, because they are composed of subsystems that interact according to an interconnection. Despite their large scale and complexity, natural systems often exhibit extraordinary robustness that preserves fundamental properties and qualitative behaviors even in the presence of huge parameter variations and environmental fluctuations. First, we focus on biochemical reaction networks and look for the source of the amazing robustness that often characterizes them, by identifying properties and emerging behaviors that exclusively depend on the system structure (i.e., the graph structure along with qualitative information), regardless of parameter values. We introduce the BDC-decomposition to capture the system structure and enable the parameter-free assessment of important properties, including the stability of equilibria and the sign of steady-state input-output influences, thus allowing structural model falsification and structural comparison of alternative mechanisms proposed to explain the same phenomenon. Then, inspired by the COVID-19 pandemic and the observation that compartmental models for epidemics can be seen as a special class of chemical reaction networks, we consider epidemiological systems describing the spread of infectious diseases within a population, along with control approaches to curb the contagion. We illustrate strategies to cope with the deep uncertainty affecting parameter values and optimally control the epidemic.

Posted January 18, 2023
Last modified February 14, 2023

3:30 pm – 4:20 pm Lockett 232

Oishee Banerjee, IAS, Princeton
Cohomology and arithmetic of Mapping spaces

How do we describe the topology of the space of all nonconstant holomorphic (respectively, algebraic) maps F: X->Y from one complex manifold (respectively, variety) to another? What is, for example, its cohomology? Such problems are old but difficult, and are nontrivial even when the domain and range are Riemann spheres. In this talk I will explain how these problems relate to other parts of mathematics such as spaces of polynomials, arithmetic (e.g. the geometric Batyrev-Manin type conjectures) and algebraic geometry (e.g. moduli spaces of elliptic fibrations, of smooth sections of a line bundle, etc). I will show how one can fruitfully attack such problems by incorporating techniques from homotopy theory to the holomorphic/algebraic world (e.g. by constructing a new spectral sequence). Most of this talk should be understandable to first year graduate students.

Tuesday, January 31, 2023

Posted January 18, 2023
Last modified January 23, 2023

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Nick Rozenblyum, University of Chicago
Langlands duality and higher traces

A central theme in arithmetic geometry over finite fields is the passage from geometric invariants to arithmetic information by taking the trace of Frobenius. I will describe a higher version of this procedure with a particular focus on applications to the Langlands correspondence over function fields. In this case, this procedure relates the geometric Langlands correspondence with the classical one. Specifically, we obtain that the space of automorphic functions is the categorical trace (aka Hochschild homology) of Frobenius acting on an appropriate version of the automorphic category. This leads to a localization of the space of automorphic functions on a moduli space of Langlands parameters, giving a refinement of V. Lafforgue's spectral decomposition. This is based on joint works with Arinkin, Gaitsgory, Kazhdan, Raskin, and Varshavsky.

Wednesday, February 1, 2023

Posted January 27, 2023

1:30 pm Lockett 233

Amit Kumar, Louisiana State University
Invariants and Moduli

This talk will be an introduction to Theory of invariants and its evolution to the theory of moduli spaces. I will begin from the works of the invariant triple: Cayley, Sylvester, and Soloman, and will end at David Mumford's point of view that gives us the theory of Moduli spaces. No specific prerequisite is required.

Posted January 25, 2023
Last modified January 27, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Yeonjong Shin, KAIST
Towards Trustworthy Scientific Machine Learning: Theory, Algorithms, and Applications

Abstract: Machine learning (ML) has achieved unprecedented empirical success in diverse applications. It now has been applied to solve scientific problems, which has become an emerging field, Scientific Machine Learning (SciML). Many ML techniques, however, are very complex and sophisticated, commonly requiring many trial-and-error and tricks. These result in a lack of robustness and interpretability, which are critical factors for scientific applications. This talk centers around mathematical approaches for SciML, promoting trustworthiness. The first part is about how to embed physics into neural networks (NNs). I will present a general framework for designing NNs that obey the first and second laws of thermodynamics. The framework not only provides flexible ways of leveraging available physics information but also results in expressive NN architectures. The second part is about the training of NNs, one of the biggest challenges in ML. I will present an efficient training method for NNs - Active Neuron Least Squares (ANLS). ANLS is developed from the insight gained from the analysis of gradient descent training.

Friday, February 3, 2023

Posted January 27, 2023
Last modified January 29, 2023

10:30 am – 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Raphael Jungers, Université Catholique de Louvain
Data-Driven Control of Hybrid Systems and Chance-Constrained Optimization

Control systems are increasingly complex, often to the point that obtaining a model for them is out of reach. In some situations, (parts of) the systems are proprietary, so that the very equations that rule their behavior cannot be known. On the other hand, the ever-growing progress in hardware technologies often enables one to retrieve massive data, e.g., from embedded sensors. Due to these evolutions, control theory can alternatively be viewed as a model-free and data-driven paradigm. For linear time-invariant systems, classical results from identification theory provide a rather straightforward approach. However, these approaches become least inefficient if one relaxes the assumptions they rely upon, e.g., linearity, Gaussian noise, etc. This is especially the case in safety-critical applications, where one needs guarantees on the performance of the obtained solution. Despite these difficulties, one may sometimes recover firm guarantees on the behavior of the system. This may require changing one's point of view on the nature of the guarantees we seek. I will provide examples of such results for different control tasks and different complex systems, and will raise the question of theoretical fundamental barriers for these problems.

Posted January 23, 2023

3:30 pm – 4:20 pm Lockett 232

Xingting Wang, Howard University
Quantum groups and their invariants in positive characteristic

Abstract: The theory of quantum groups originated in algebraic topology and algebraic geometry in mid-twentieth century. Nowadays, it has applications in a wide rage of settings across mathematics and physics, including quantum invariants of links and 3-manifolds and solutions of the quantum Yang-Baxter equation. In this talk, I will discuss the theory of quantum groups and their invariants in positive characteristic. As an application, I will investigate their connections to different areas of mathematics and physics.

Monday, February 6, 2023

Posted October 12, 2022
Last modified November 9, 2022

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett Hall 233 and Zoom

Yue Yu, Lehigh University
Learning Nonlocal Neural Operators for Complex Physical System Modeling

For many decades, physics-based PDEs have been commonly employed for modeling complex system responses, then traditional numerical methods were employed to solve the PDEs and provide predictions. However, when governing laws are unknown or when high degrees of heterogeneity present, these classical models may become inaccurate. In this talk we propose to use data-driven modeling which directly utilizes high-fidelity simulation and experimental measurements to learn the hidden physics and provide further predictions. In particular, we develop PDE-inspired neural operator architectures, to learn the mapping between loading conditions and the corresponding system response. By parameterizing the increment between layers as an integral operator, our neural operator can be seen as the analog of a time-dependent nonlocal equation, which captures the long-range dependencies in the feature space and is guaranteed to be resolution-independent. Moreover, when applying to (hidden) PDE solving tasks, our neural operator provides a universal approximator to a fixed point iterative procedure, and partial physical knowledge can be incorporated to further improve the model’s generalizability and transferability. As an application, we learn the material models directly from digital image correlation (DIC) displacement tracking measurements on a porcine tricuspid valve leaflet tissue, and show that the learnt model substantially outperforms conventional constitutive models.

Tuesday, February 7, 2023

Posted January 27, 2023
Last modified February 5, 2023

3:10 pm – 4:00 pm Lockett 233 and Zoom

Jeffrey Lagarias, University of Michigan
The Floor Quotient Partial Order

We say that a positive integer $m$ is a floor quotient of $n$ if $m = [n/k]$ for some integer $k$, where $[\, \cdot \,]$ denotes the floor function. We show this relation between $m$ and $n$ defines a partial order on the positive integers. This partial order refines the multiplicative divisor order on the positive integers and is refined by the additive total order. We describe results on the internal structure of this partial order, especially on its initial intervals. We study the (two-variable) Möbius function of this partial order. This is joint work with David Harry Richman (see $\texttt{arXiv:2212.11689}$).

Posted January 17, 2023
Last modified January 20, 2023

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:20 pm LDMC: room 1034

Daniel Massatt, Louisiana State University
Convergence of the Planewave Approximations for Quantum Incommensurate Systems

Incommensurate structures arise from stacking single layers of low-dimensional materials on top of one another with misalignment such as an in-plane twist in orientation. While these structures are of significant physical interest, they pose many theoretical challenges due to the loss of periodicity. In this paper, we characterize the density of states of Schrödinger operators in the weak sense for the incommensurate system and develop novel numerical methods to approximate them. In particular, we (i) justify the thermodynamic limit of the density of states in the real space formulation; and (ii) propose efficient numerical schemes to evaluate the density of states based on planewave approximations and reciprocal space sampling. We present both rigorous analysis and numerical simulations to support the reliability and efficiency of our numerical algorithms.

Wednesday, February 8, 2023

Posted January 30, 2023
Last modified February 6, 2023

1:30 pm Lockett 233

Justin Murray, Louisiana State University
On the Homotopy Cardinality of the Legendrian Representation Category

Given a Legendrian knot in the standard contact R^3, one can assign an n-dimensional representation category. This A-infinity category encodes n-dimensional representations of the Legendrian contact homology DGA (LCH DGA). In this talk, I will discuss the relationship between a categorical count of representations, and other holomorphic curve invariants called colored ruling polynomials. In particular, I will present a formula relating these two invariants. This formula is generalizes results known for augmentations (1-dimensional representations). Towards the end I will discuss some related applications to concordance and a few open conjectures.

Posted February 6, 2023

3:30 pm – 4:20 pm Lockett 232

Meeting of the Professorial Faculty

Thursday, February 9, 2023

Posted February 9, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Meeting of the Professorial Faculty

Friday, February 10, 2023

Posted December 12, 2022
Last modified February 8, 2023

10:30 am – 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Patrick L. Combettes, North Carolina State University IEEE Fellow
Perspective Functions

I will discuss mathematical and computational issues pertaining to perspective functions, a powerful concept that makes it possible to extend a convex function to a jointly convex one in terms of an additional scale variable. Recent results on perspective functions with nonlinear scales will also be discussed. Applications to inverse problems and statistics will also be presented.

Posted January 31, 2023
Last modified February 6, 2023

3:30 pm – 4:20 pm Lockett 232

Nadia Drenska, Johns Hopkins University
A PDE Interpretation of Prediction with Expert Advice

Abstract: We study the problem of prediction of binary sequences with expert advice in the online setting, which is a classic example of online machine learning. We interpret the binary sequence as the price history of a stock, and view the predictor as an investor, which converts the problem into a stock prediction problem. In this framework, an investor, who predicts the daily movements of a stock, and an adversarial market, who controls the stock, play against each other over N turns. The investor combines the predictions of n ≥ 2 experts in order to make a decision about how much to invest at each turn, and aims to minimize their regret with respect to the best-performing expert at the end of the game. We consider the problem with history-dependent experts, in which each expert uses the previous d days of history of the market in making their predictions. The prediction problem is played (in part) over a discrete graph called the d-dimensional de Bruijn graph. We focus on an appropriate continuum limit. Using methods from optimal control, graph theory, and partial differential equations, we discuss strategies for the investor and the adversarial market. We prove that the value function for this game, rescaled appropriately, converges as N goes to infinity at a rate of O(N^−1/2) (for C^4 payoff functions) to the viscosity solution of a nonlinear degenerate parabolic PDE. It can be understood as the Hamilton-Jacobi-Issacs equation for the two-person game. As a result, we are able to deduce asymptotically optimal strategies for the investor. This is joint work with Robert Kohn and Jeff Calder.

Monday, February 13, 2023

Posted February 11, 2023

12:45 pm – 2:00 pm Keisler Lounge

Informal discussion on probability research topics

Posted February 8, 2023

3:30 pm – 4:20 pm Lockett 232

Xiaoqi Huang, University of Maryland
Spectral Cluster and Weyl Remainder Estimates for the Laplacian and on compact manifolds

Abstract: In the first part of the talk, we shall discuss generalizations of classical versions of the Weyl formula involving Schrödinger operators on compact boundaryless Riemannian manifolds with critically singular potentials V. In particular, we extend the classical results of Avakumović, Levitan and Hörmander by obtaining sharp bounds for the error term in the Weyl formula when we merely assume that V belongs to the Kato class, which is the minimal assumption to ensure that H_V is essentially self-adjoint and bounded from below or has favorable heat kernel bounds. In the second part, we will discuss the problem of trying to obtain improved eigenfunction estimates under geometric assumptions, such as the presence of negative sectional curvatures, which is based on the use of microlocal Kakeya-Nikodym estimates along with a combination of local and global harmonic analysis that further exploit geometric assumptions. We will also discuss some new sharp estimates involving the tori eigenfunctions.

Tuesday, February 14, 2023

Posted February 13, 2023
Last modified February 14, 2023

1:00 pm – 2:00 pm Zoom

Benjamin Moore, Charles University, Prague
Quantum field theory, colouring, and the Strong Nine Dragon Tree Conjecture

Abstract: I'll discuss various aspects of structural graph theory which I have worked on. In particular, I'll describe how certain nice Feynman Integrals correspond with a minor closed class, allowing structural graph theory to show up in Quantum field theory. I'll also discuss the Strong Nine Dragon Tree Conjecture, and Sebastian Mies and my recent progress has led to towards the thin tree conjecture, and finish with a counterexample to a conjecture of Galvin and Rodl from 1977, by describing graphs with arbitrarily large chromatic number, have no clique of size four, and all triangle-free induced subgraphs have chromatic number at most 4.

Posted February 13, 2023

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Meeting of the Professorial Faculty

Wednesday, February 15, 2023

Posted January 30, 2023
Last modified February 10, 2023

1:30 pm Lockett 233

Adithyan Pandikkadan, Louisiana State University
On the Contact Class in Heegaard Floer Homology

Ozsvath and Szabo defined an invariant of a contact 3-manifold, an element in the Heegaard Floer Homology of the manifold. In this talk, I will give an alternate description of this contact invariant which was introduced by K. Honda, W.H. Kazez, and G. Matic in their paper “On the Contact Class in Heegaard Floer Homology”. We will also see how the contact class helps to prove certain properties of the contact structure.

Posted February 12, 2023

2:30 pm Lockett 285

Summer Internship and Math Bootcamp Information Seminar

Posted September 29, 2022

4:00 pm – 5:00 pm Lockett 232

Meeting with Provost

Thursday, February 16, 2023

Posted January 19, 2023
Last modified January 20, 2023

3:30 pm – 4:20 pm Lockett 232

Irina Markina, University of Bergen
On rolling of manifolds

In the talk, we will introduce the notion of rolling one manifold over another. The idea of the rolling map originated as a simple mathematical model of rolling a ball over a plate with the constraints of no-slip and no-twist motion in the works of S. Chaplygin (1897), K. Nomizu (1978), R.Bryan and L.Hsu (1993). The geometric features are closely related to the distributions of E.Cartan type (1910). Later this idea was extended to the rolling of Riemannian manifolds of any dimension, as an isometry map preserving the parallelism of vector fields. After a historical overview and necessary definitions, we also mention some applications in the interpolation on nonlinear spaces and construction of stochastic processes on manifolds.

Tuesday, February 21, 2023

Posted December 1, 2023

3:30 pm Lockett 233

Katherine Goldman, Ohio State University
TBA

Posted December 1, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Katherine Goldman, Ohio State University
TBA

Friday, February 24, 2023

Posted February 3, 2023
Last modified February 6, 2023

10:30 am – 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Enrique Zuazua, Friedrich-Alexander-Universität Erlangen-Nürnberg 2022 SIAM W.T. and Idalia Reid Prize Winner
Control and Machine Learning

In this lecture, we present some recent results on the interplay between control and machine learning, and more precisely, supervised learning and universal approximation. We adopt the perspective of the simultaneous or ensemble control of systems of residual neural networks (or ResNets). Roughly, each item to be classified corresponds to a different initial datum for the Cauchy problem of the ResNets, leading to an ensemble of solutions to be driven to the corresponding targets, associated to the labels, by means of the same control. We present a genuinely nonlinear and constructive method, allowing us to show that such an ambitious goal can be achieved, estimating the complexity of the control strategies. This property is rarely fulfilled by the classical dynamical systems in mechanics and the very nonlinear nature of the activation function governing the ResNet dynamics plays a determinant role. It allows deformation of half of the phase space while the other half remains invariant, a property that classical models in mechanics do not fulfill. The turnpike property is also analyzed in this context, showing that a suitable choice of the cost functional used to train the ResNet leads to more stable and robust dynamics. This lecture is inspired in joint work, among others, with Borjan Geshkovski (MIT), Carlos Esteve (Cambridge), Domènec Ruiz-Balet (IC, London) and Dario Pighin (Sherpa.ai).

Monday, February 27, 2023

Posted February 11, 2023
Last modified February 24, 2023

1:00 pm – 2:00 pm Lockett 135

Arnab Ganguly, LSU
Optimal learning via large deviation

Abstract: Statistical decision theory typically involves learning or estimation of a cost function from available data. The cost function in turn depends on the parameters of the underlying mathematical model of the system. We will discuss how large deviation theory can be used to develop an optimal estimator in these problems. This is a joint work with Tobias Sutter. Most of the talk should be accessible to students with only elementary knowledge of probability and statistics.

Posted January 8, 2023
Last modified February 12, 2023

3:30 pm Zoom

Justin Holmer, Brown University
Well/Ill-posedness of the Boltzmann equation with constant collision kernel

Drawing upon methods from the field of nonlinear dispersive PDEs, we investigate well/ill-posedness for the 3D Boltzmann equation with constant collision kernel in the Sobolev spaces. We find that the threshold space is one-half derivative above the scale invariant space, and prove ill-posedness below this threshold by constructing a family of special solutions, which are neither near equilibrium nor self-similar, and exhibit a "norm deflation" behavior -- a rapid drop in the Sobolev norm that breaks the uniform continuity of the data-to-solution map. This is joint work with Xuwen Chen (University of Rochester)

Posted February 21, 2023

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett 233

Nir Gadish, University of Michigan
(Lots of) unstable cohomology of moduli spaces of curves with marked points

The moduli spaces of smooth projective curves with marked points have cohomology that attaches characteristic classes to surface bundles with disjoint sections. As such, this cohomology plays a fundamental role in algebraic geometry and topology. However, only a tiny fraction of the cohomology is understood. I will present joint works with Bibby, Chan and Yun, and with Hainaut, in which we gain access to the least algebraic part of the cohomology for curves of genus 2, using tropical geometry and configuration spaces on graphs. In particular we find the first examples of families of cohomology classes in the top cohomological dimension, which seem to tell a geometric story that is yet to be understood.

Tuesday, February 28, 2023

Posted January 16, 2023
Last modified February 24, 2023

3:10 pm – 4:00 pm Lockett 233 and Zoom

Pranabesh Das, Xavier University of Louisiana
Perfect Powers in Power Sums

Let $k \geq 1$, $n \geq 2$ be integers. A power sum is a sum of the form $x_1^k+x_2^k+\cdots +x_n^k$ where $x_1, x_2, \cdots, x_n$ are all integers. Perfect powers appearing in power sums have been well studied in the literature and are an active field of research. In this talk, we consider the Diophantine equation of the form $$ (x+r)^k + (x+2r)^k + \cdots + (x+nr)^k = y^m \ \ \ \ \ \ \ \ \ (1) $$ where $x, y, r \in \mathbb{Z}$, $n, k \in \mathbb{N}$, and $m \geq 2$. We begin with discussing the literature on the Diophantine equation (1). Then we consider explicit solutions for a particular case of the Diophantine equation (1); more precisely, we consider the Diophantine equation $$ \ \ \ (x-r)^5 + x^5 + (x+r)^5 = y^n, \ \ \ \ n \geq 2, \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) $$ where $r, x, y \in \mathbb{Z}$ and $r$ is composed of certain fixed primes. The talk is based on a joint work with Dey, Koutsianas, and Tzanakis where we determine the integral solutions of the Diophantine equation (2) as an application of the modular method.

Wednesday, March 1, 2023

Posted January 30, 2023
Last modified February 24, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233

Nilangshu Bhattacharyya, Louisiana State University
Morse theory and Flow Category

The aim is to discuss the basics of Morse theory with an eye towards understanding the flow category of a Morse function. For a compact Riemannian manifold, the classifying space of the flow category of a Morse function on that manifold completely captures the topological structure of the manifold up to Homotopy (result by Cohen-Jones-Segal). I will try to show a few examples.

Posted February 23, 2023
Last modified August 7, 2023

3:30 pm – 4:30 pm Lockett 232; https://lsu.zoom.us/j/94413235134

Khalid Bdarneh, Louisiana State University
Analytic continuation of Toeplitz operators and their spectral representation on the weighted Bergmann spaces

Weighted Bergman spaces on the unit ball $A_{\lambda}^2(\mathbb{B}^n)$ are defined when the weight $\lambda>n$. In this talk we will discuss how the weighted Bergmann spaces can be extended to $\lambda>0$, and we will present a characterization of commuting families of $C^*-$algebras in terms of restriction to multiplicity free representations. Moreover, we will describe the spectral representation of Toeplitz operators that acts on $A_{\lambda}^2(\mathbb{B}^n)$ by extending the restriction principal to the analytic continuation case for suitable maximal abelian subgroups of $\widetilde{SU(n,1)}$. This is a joint work with Dr. Gestur \'Olafsson.

Posted January 10, 2023
Last modified August 7, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Jingyin Huang, Ohio State University
Integral measure equivalence versus quasi-isometry for some right-angled Artin groups

Recall that two finitely generated groups G and H are quasi-isometric, if they admit a topological coupling, i.e. an action of G times H on a locally compact topological space such that each factor acts properly and cocompactly. This topological definition of quasi-isometry was given by Gromov, and at the same time he proposed a measure theoretic analogue of this definition, called the measure equivalence, which is closely related to the notion of orbit equivalence in ergodic theory. Despite the similarity in the definition of measure equivalence and quasi-isometry, their relationship is rather mysterious and not well-understood. We study the relation between these two notions in the class of right-angled Artin groups. In this talk, we show if H is a countable group with bounded torsion which is integrable measure equivalence to a right-angled Artin group G with finite outer automorphism group, then H is finitely generated, and H and G are quasi-isometric. This allows us to deduce integrable measure equivalence rigidity results from the relevant quasi-isometric rigidity results for a large class of right-angled Artin groups. Interestingly, this class of groups are rigid for a reason which is quite different from other cases of measure equivalence rigidity. We will also do a quick survey of relevant measure equivalence rigidity and quasi-isometric rigidity results of other classes of groups, motivating our choice of right-angled Artin groups as a playground. This is joint work with Camille Horbez.

Friday, March 3, 2023

Posted January 17, 2023
Last modified February 27, 2023

10:30 am – 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Spring Berman, Arizona State University DARPA Young Faculty and ONR Young Investigator Awardee
Scalable Control of Robotic Swarms with Limited Information

Robotic swarms are currently being developed for many applications, including environmental sensing, exploration and mapping, infrastructure inspection, disaster response, agriculture, and logistics. However, significant technical challenges remain before they can be robustly deployed in uncertain, dynamic environments. We are addressing the problem of controlling swarms of robots that lack prior data about the environment and reliable inter-robot communication. As in biological swarms, the highly resource-constrained robots would be restricted to information obtained through local sensing and signaling. We are developing scalable control strategies that enable swarms to operate largely autonomously, with user input consisting only of high-level directives that map to a small set of robot parameters. In this talk, I describe control strategies that we have designed for collective tasks that include coverage, mapping, and cooperative manipulation. We develop and analyze models of the swarm at different levels of abstraction based on differential equations, Markov chains, and graphs, and we design robot controllers using feedback control theory and optimization techniques. We validate our control strategies in simulation and on experimental test beds with small mobile robots.

Monday, March 6, 2023

Posted March 2, 2023

Mathematical Physics and Representation Theory Seminar

1:00 pm Lockett 135

Arnab Ganguly, LSU
Optimal learning via large deviation (Part II)

Statistical decision theory typically involves learning or estimation of a cost function from available data. The cost function in turn depends on the parameters of the underlying mathematical model of the system. We will discuss how large deviation theory can be used to develop an optimal estimator in these problems. This is a joint work with Tobias Sutter. Most of the talk should be accessible to students with only elementary knowledge of probability and statistics.

Posted January 9, 2023
Last modified February 28, 2023

2:30 pm – 3:20 pm 233 Lockett

Nadia Ott, University of Pennsylvania
Period maps for super Riemann surfaces with Ramond punctures

Super Riemann surfaces and their moduli spaces $\mathfrak{M}_g$ are supersymmetric generalizations of the classical notions of Riemann surfaces. In physics, super Riemann surfaces are the worldsheets of propagating superstrings and once can define important quantities in superstring theory, e.g., vacuum and scattering amplitudes, as integrals over $\mathfrak{M}_g$. However, computing these integrals has proved to be extremely difficult and answers are known only up to genus 2. D’Hoker and Phong’s computation in genus 2 relied on the super period map for genus 2 super Riemann surfaces. Naturally, we look to the period map for answers in the higher genus. However, the period map in $g > 2$ behaves in ways quite distinct from its ordinary counterpart. Most dramatically, it blows up along a certain divisor in supermoduli space. It is also not fully defined for either the Ramond punctured variants of super Riemann surfaces, or for the compactification. In both cases, one expects the map to blow up along a divisor, called the bad locus. In my talk, I will discuss some of the open problems as well as recent progress concerning the super period map and its relation to the supermeasure. In addition, I will talk about my joint work with Ron Donagi in which we describe the “bad locus” on the supermoduli space with Ramond punctures.

Posted February 10, 2023
Last modified February 20, 2023

3:30 pm – 4:30 pm Zoom

TBA

Posted February 10, 2023
Last modified March 3, 2023

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Zoom: https://lsu.zoom.us/j/5494314978?pwd=SmpvVDRpaFY2dGxqcGlIT0kxTzVMdz09

Zihui Zhao, University of Chicago
Counter-example in boundary unique continuations

Unique continuation property is a fundamental property for harmonic functions, as well as a large class of elliptic and parabolic PDEs. It says that if a harmonic function vanishes at a point to infinite order, it must vanish everywhere. In the same spirit, we are interested in quantitative unique continuation problems, where we use the growth rate of a harmonic function to deduce some global estimates, such as estimating the size of its singular set. In this talk, I will talk about some boundary unique continuation results, and show that these results are sharp by giving explicit examples using harmonic measures. This is joint work with C. Kenig

Tuesday, March 7, 2023

Posted January 27, 2023
Last modified March 5, 2023

3:10 pm – 4:00 pm Lockett 233 and Zoom

Wijit Yangjit, University of Michigan
On the Montgomery–Vaughan weighted generalization of Hilbert's inequality

Hilbert's inequality states that $$ \left\vert\sum_{m=1}^N\sum_{\substack{n=1\\n\neq m}}^N\frac{z_m\overline{z_n}}{m-n}\right\vert\le C_0\sum_{n=1}^N\left\vert z_n\right\vert^2, $$ where $C_0$ is an absolute constant. In 1911, Schur showed that the optimal value of $C_0$ is $\pi$. In 1974, Montgomery and Vaughan proved a weighted generalization of Hilbert's inequality and used it to estimate mean values of Dirichlet series. This generalized Hilbert inequality is important in the theory of the large sieve. The optimal constant $C$ in this inequality is known to satisfy $\pi\le C \lt \pi+1$. It is widely conjectured that $C=\pi$. In this talk, I will describe the known approaches to obtain an upper bound for $C$, which proceed via a special case of a parametric family of inequalities. We analyze the optimal constants in this family of inequalities. A corollary is that the method in its current form cannot imply an upper bound for $C$ below $3.19$.

Wednesday, March 8, 2023

Posted January 30, 2023
Last modified March 3, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233

Aneek Maiti, Louisiana State University
Kazhdan-Lusztig polynomials

Intersection cohomology is an important tool in the theory of Perverse sheaves. It satisfies Poincare duality and the Kunneth formula. For a Schubert variety corresponding to a reductive linear algebraic group the computation of the Intersection cohomology is not very easy without extra tools. During the 1970s in Kazhdan Lusztig conjectured (which has been proved later) a problem in representation theory of Verma modules and introduced Kazdan Lusztig polynomials. These Kazhdan Lusztig polynomials are very important tool to compute the intersection cohomology of Schubert varieties. In my talk I will give a brief overview of Kazhdan Lusztig polynomials.

Posted February 23, 2023
Last modified March 5, 2023

3:30 pm – 4:30 pm Lockett 232; https://lsu.zoom.us/j/94413235134

Iswarya Sitiraju, Louisiana State University
Wavefront Sets: Spectral Analysis of singularities

Let u be a distribution with compact support. We know that u cannot be a smooth function if and only if its Fourier transform does not decay in some direction. For example, the Dirac Delta distribution is not smooth at 0 as its Fourier transform which is 1 does not decay in all directions. This concept can be generalized to distributions, which describes the set of points having no neighbourhood where u is smooth and the direction in which the singularity occurs. One of the many applications of wavefront set is, it tells us when we can define a a pull back of a distribution/ restrict a distribution to a submanifold, which in general is not defined. In this talk I will briefly introduce the concept of wavefront sets, mostly following the book by H\"ormander: \it{The Linear Partial Differential Operators I}.

Posted January 12, 2023
Last modified March 1, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Catherine Cannizzo, University of California, Riverside
Homological Mirror Symmetry for Theta Divisors

Symplectic geometry is a relatively new branch of geometry. However, a string theory-inspired duality known as “mirror symmetry” reveals more about symplectic geometry from its mirror counterparts in complex geometry. M. Kontsevich conjectured an algebraic version of mirror symmetry called “homological mirror symmetry” (HMS) in his 1994 ICM address. HMS results were then proved for symplectic mirrors to Calabi-Yau and Fano manifolds. Those mirror to general type manifolds have been studied in more recent years, including my research. In this talk, we will introduce HMS through the example of the 2-torus T^2. We will then outline how it relates to HMS for a hypersurface of a 4-torus T^4, in joint work with Haniya Azam, Heather Lee, and Chiu-Chu Melissa Liu. From there, we generalize to hypersurfaces of higher dimensional tori, otherwise known as “theta divisors.” This is also joint with Azam, Lee, and Liu.

Friday, March 10, 2023

Posted November 30, 2022
Last modified February 28, 2023

10:30 am – 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Jacquelien Scherpen, University of Groningen IEEE Fellow, Automatica Best Paper Prize Awardee
Model Reduction for Nonlinear Control Systems Based on Differential Balancing and Data

We present the standard balancing theory for nonlinear systems, which is based on an analysis around equilibrium points. Its extension to the contraction framework offers computational advantages, and is presented as well. We provide definitions for controllability and observability functions and their differential versions which can be used for simultaneous diagonalization procedures, providing a measure for importance of the states, as can be shown by the relation to the Hankel operator. In addition, we propose a data-based model reduction method based on differential balancing for nonlinear systems whose input vector fields are constants by utilizing its variational system. The difference between controllability and reachability for the variational system is exploited for computational reasons. For a fixed state trajectory, it is possible to compute the values of the differential Gramians by using impulse and initial state responses of the variational system. Therefore, differential balanced truncation is doable along state trajectories without solving nonlinear partial differential equations.

Posted January 31, 2023

1:00 pm – 4:00 pm Saturday, March 11, 2023 Tulane University

Scientific Computing Around Louisiana - SCALA 2023

http://www.math.tulane.edu/scala/index.html

Monday, March 20, 2023

Posted February 11, 2023
Last modified March 20, 2023

1:00 pm – 2:00 pm Zoom

Pratima Hebbar, Grinnell College
Branching Diffusion in Periodic Media

We describe the behavior of branching diffusion processes in periodic media. For a super-critical branching process, we distinguish two types of behavior for the normalized number of particles in a bounded domain, depending on the distance of the domain from the region where the bulk of the particles is located. At distances that grow linearly in time, we observe intermittency (i.e., the k-th moment dominates the k-th power of the first moment for some k), while, at distances that grow sub-linearly in time, we show that all the moments converge. A key ingredient in our analysis is a sharp estimate of the transition kernel for the branching process, valid up to linear in time distances from the location of the initial particle.

Posted February 20, 2023
Last modified March 3, 2023

3:30 pm – 4:30 pm Zoom: https://lsu.zoom.us/j/5494314978?pwd=SmpvVDRpaFY2dGxqcGlIT0kxTzVMdz09

Max Engelstein, University of Minnesota
On global graphical solutions to free boundary problems

The Bernstein problem for minimal surfaces asks whether a globally defined minimal hypersurface given by the graph of a function in dimension $n$ must be a hyperplane. This was resolved by the combined work of De Giorgi, Simons and then De Giorgi-Bombieri-Giusti; showing that the answer is yes when $n \leq 8$ and no when $n\geq 9$. In this talk we will discuss recent progress towards this question for one-phase free boundary problems of Bernoulli type. This is joint with Xavier Fernandez-Real (EPFL) and Hui Yu (NUS).

Posted November 29, 2023

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm Lockett 233

Katherine Raoux, University of Arkansas
TBA

Wednesday, March 22, 2023

Posted January 31, 2023
Last modified March 17, 2023

1:30 pm Lockett 233

Colton Sandvick, Louisiana State University
Singular Support of Constructible Sheaves on Manifolds

Given a sheaf F on a real manifold X, one can assign closed, conic, Lagrangian subset of the cotangent bundle T*X, called the singular support. Singular support is a powerful invariant of sheaves and behaves well with regard to many common sheaf operations. In this talk, we will discuss singular support in the context of constructible sheaves, describe many of its fundamental properties, and give some examples. As an application, we will discuss some classes of sheaves which can be described by their singular support. We will not assume any prior knowledge of sheaf theory; although, some familiarness with differential geometry and singular (or de Rham) cohomology will be helpful.

Posted February 23, 2023
Last modified August 7, 2023

3:30 pm – 4:30 pm Lockett 232; https://lsu.zoom.us/j/94413235134

Iswarya Sitiraju, Louisiana State University
Analytic Wavefront Sets of Spherical Distributions on De Sitter space

A De Sitter space is a one sheeted hyperboloid with Lorentzian metric. For $G$ the orthochronous Lorentzian group of dimension $n+1$ and the subgroup $H$, the orthochronous Lorentzian group of dimension $n$, the De Sitter space is homogeneous space $G/H$. A distribution $u$ is said to be a spherical distribution if it is H-invariant eigendistribution of the Laplace-Beltrami operator $\square$ on De Sitter space. The dimension of the space of spherical distribution turns out to be 2. I will construct the basis for this space and hence characterize the analytic wavefront set of these distributions.

Posted January 10, 2023
Last modified March 14, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Grigori Avramidi, Max Planck Institute for Mathematics
Division, group rings, and negative curvature

In 1997 Delzant observed that fundamental groups of hyperbolic manifolds with large injectivity radius have nicely behaved group rings. In particular, these rings have no zero divisors and only the trivial units. In this talk I will discuss an extension of this observation showing that such rings have a division algorithm (generalizing the division algorithm for group rings of free groups discovered by Cohn) and ``freedom theorems’’ saying ideals generated by two elements are free (which can be viewed as generalizations from subgroups to ideals of some freedom theorems of Delzant and Gromov). This has geometric consequences to the homotopy classification of 2-complexes with surface fundamental groups and to complexity of cell structures on hyperbolic manifolds.

Friday, March 24, 2023

Posted February 14, 2023

10:30 am – 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Frank Allgower, University of Stuttgart IFAC Fellow
Data-driven Model Predictive Control: Concepts, Algorithms and Properties

While recent years have shown rapid progress of learning-based and data-driven methods to effectively utilize data for control tasks, providing rigorous theoretical guarantees for such methods is challenging and an active field of research. This talk will be about a recently developed framework for model predictive control (MPC) of unknown systems based only on input-output data which admits exactly such guarantees. The proposed approach relies on the Fundamental Lemma of Willems et al. which parametrizes trajectories of unknown linear systems using data. First, we cover MPC schemes for linear systems with a focus on theoretical guarantees for the closed loop, which can be derived even if the data are noisy. Building on these results, we then move towards the general, nonlinear case. Specifically, we present a data-driven MPC approach which updates the data used for prediction online at every time step and, thereby, stabilizes unknown nonlinear systems using only input-output data. In addition to introducing the framework and the theoretical results, we also report on successful applications of the proposed framework in simulation and real-world experiments.

Monday, March 27, 2023

Posted March 2, 2023
Last modified March 23, 2023

Mathematical Physics and Representation Theory Seminar

1:00 pm Lockett 135

Scott McKinley, Tulane University
Modeling, analysis and inference for the Generalized Langevin Equation

Fluctuating microparticles in biological fluids exhibit a wide range of anomalous behavior. From state switching (where the states cannot be directly observed) to memory effects, these particles are intrinsically Non-Markovian. In this talk, I will give a brief introduction to experimental observations that motivate using the generalized Langevin equation to model microparticle movement in mucus. In studying these paths a number of mathematical challenges arise, including determining the regularity and asymptotic behavior of these particles, and quantifying uncertainty when conducting inference.

Posted March 23, 2023

2:30 pm – 3:20 pm Lockett 233

Simon Riche, Université Clermont Auvergne
Characters of modular representations of reductive algebraic groups

One of the main questions in the representation theory of reductive algebraic groups is the computation of characters of simple modules. A conjectural solution to this problem was proposed by G. Lusztig in 1980, and later shown to be correct assuming the base field has large characteristic. However in 2013 G. Williamson found (counter)examples showing that this answer is not correct without this assumption. In this talk I will explain a new solution to this problem, obtained in a combination of works involving (among others) P. Achar and G. Williamson, which is less explicit but has the advantage of being valid in all characteristics.

Wednesday, March 29, 2023

Posted January 31, 2023
Last modified March 17, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233

Colton Sandvick, Louisiana State University
Singular Support of Étale Constructible Sheaves and Applications to Representation Theory

In this talk, we will discuss a generalization of singular support for constructible sheaves on manifolds where we instead consider étale constructible sheaves on algebraic varieties. Singular support in this setting was only recently defined by Beilinson in 2015. We will detail the nuances in working with étale sheaves on algebraic varieties rather than sheaves on manifolds. We will investigate a few classical applications of singular support which provides a geometric description of character sheaves in characteristic 0. We will then use Beilinson's generalization to explain some recent work of Psaromiligkos which generalizes one of these results to character sheaves on reductive groups in positive characteristic.

Posted February 23, 2023
Last modified August 7, 2023

3:30 pm – 4:30 pm zoom: https://lsu.zoom.us/j/94413235134

Vishwa Dewage, Clemson University
Dense subsets of the Toeplitz algebra on the Fock space

We study the full Toeplitz algebra via convolutions of operators and the Laplacian of the Berezin transform. We present a new class of operators that are dense in the Toeplitz algebra. We use this new dense class of operators to provide a new proof for the fact that the radial Toeplitz algebra is isomorphic to the space of bounded sequences that are uniformly continuous with respect to the square-root metric. This is a joint work with Mishko Mitkovski.

Posted January 10, 2023
Last modified March 13, 2023

3:30 pm Lockett 233

Jonathan Johnson, Oklahoma State University
Non-standard orders on torus bundles with one boundary

Consider a torus bundle over the circle with one boundary. Perron-Rolfsen shows that having an Alexander polynomial with real positive roots is a sufficient condition for a surface bundle with one boundary to have bi-orderable fundamental group. This is done by showing the action induced by the monodromy preserves a "standard" bi-ordering of the fundamental group of the surface. In this talk, we discuss if there are other ways to bi-order the fundamental group of a torus bundle with one boundary component. This work is joint with Henry Segerman. This work is partially funded by NSF grant DMS-2213213.

Thursday, March 30, 2023

Posted February 9, 2023
Last modified February 24, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Melody Chan, Brown University
Moduli spaces of graphs

My goal is to share with you a broad view on the topic of moduli spaces of graphs. A metric graph is a graph—a finite network of vertices and edges—together with a prescription of a positive real length on each edge. I’ll use the term “moduli space of graphs’’ to refer to certain combinatorial spaces—think simplicial complexes—that furnish parameter spaces for metric graphs. There are different flavors of spaces depending on some additional choices of decorations on the graphs, but roughly, each cell parametrizes all possible metrizations of a fixed combinatorial graph. Many flavors of these moduli spaces have been in circulation for a while, starting with the work of Culler-Vogtmann in the 1980s on Outer Space. They have also recently played an important role in some recent advances using tropical geometry to study the topology of moduli spaces of curves and other related spaces. These advances give me an excuse to give what I hope will be an accessible introduction to moduli spaces of graphs and their connections with geometry.

Friday, March 31, 2023

Posted February 13, 2023
Last modified April 9, 2023

10:30 am – 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Ningshi Yao, George Mason University
Resolving Contentions Through Real-Time Control and Scheduling for Cyber Physical Human Systems

Shared resources, such as cloud computing and communication networks, are widely used in large-scale real-time systems to increase modularity and flexibility. When multiple systems need to access a shared resource at the same time and the demands exceed the total supply, a contention occurs. A scheduling strategy is needed to determine which systems can access the resource first to resolve contentions. However, such a scheduling mechanism inevitably introduces time-varying delays and may degrade the system performance or even sabotage the stability of control systems. Considering the coupling between scheduling and control, this talk presents a novel sample-based method to co-design scheduling strategies and control laws for coupled control systems with shared resources, which aims to minimize the overall performance degradation caused by contentions. The co-design problem is formulated as a mixed integer optimization problem with a very large search space, rendering difficulty in computing the optimal solution. To solve this challenge, we describe a contention resolving model predictive control (CRMPC) method to dynamically design optimal scheduling and control in real-time. With fundamental assumptions in scheduling theory, the solution computed by CRMPC can be proved to be globally optimal. CRMPC is a theoretical framework that is general and can be applied to many applications in cyber-physical-human systems. The effectiveness of CRMPC has been verified in real-world applications, such as networked control systems, traffic intersection management systems, and human multi-robot collaboration systems. The performance of CRMPC was compared with well-known scheduling methods and demonstrated significant improvements.

Posted February 25, 2023
Last modified March 22, 2023

Association for Women in Mathematics Student Colloquium

1:30 pm – 2:30 pm Lockett Hall 277

Melody Chan, Brown University
Counting in the presence of symmetry (counting with groupoids)

Objects with symmetry are special. In many situations arising in nature, they tend to appear less frequently, in fact with frequency inverse proportional to the order of the symmetry group. I will explain some combinatorics in the presence of symmetry that can be summarized as "counting with groupoids." The student colloquium will be preceded by lunch and an informal "Ask me anything!" discussion with the speaker.

Monday, April 3, 2023

Posted February 11, 2023
Last modified March 26, 2023

Algebra and Number Theory Seminar Questions or comments?

1:00 pm – 2:00 pm Lockett 135

Wasiur KhudaBukhsh, University of Nottingham
Large-graph approximations for interacting particles on graphs and their applications

In this talk, we will consider stochastic processes on (random) graphs. They arise naturally in epidemiology, statistical physics, computer science and engineering disciplines. In this set-up, the vertices are endowed with a local state (e.g., immunological status in case of an epidemic process, opinion about a social situation). The local state changes dynamically as the vertex interacts with its neighbours. The interaction rules and the graph structure depend on the application-specific context. We will discuss (non-equilibrium) approximation methods for those systems as the number of vertices grow large. In particular, we will discuss three different approximations in this talk: i) approximate lumpability of Markov processes based on local symmetries (local automorphisms) of the graph, ii) functional laws of large numbers in the form of ordinary and partial differential equations, and iii) functional central limit theorems in the form of Gaussian semi-martingales. We will also briefly discuss how those approximations could be used for practical purposes, such as parameter inference from real epidemic data (e.g., COVID-19 in Ohio), designing efficient simulation algorithms etc.

Tuesday, April 4, 2023

Posted January 16, 2023
Last modified March 27, 2023

3:10 pm – 4:00 pm Zoom (click here)

Piper H, University of Toronto
Joint Shapes of Quartic Fields and Their Cubic Resolvents

In studying the (equi)distribution of shapes of quartic number fields, one relies heavily on Bhargava’s parametrizations which brings with it a notion of resolvent ring. Maximal rings have unique resolvent rings so it is possible to live a long and healthy life without understanding what they are. The authors have decided, however, to forsake such bliss and look into what ever are these rings and what happens if we consider their shapes along with our initial number fields. What happens is very nice! Until it isn't! We'd have more to say if our respective jobs had treated us humanely during the global pandemic, which coincidentally, is ongoing. (with Christelle Vincent)

Wednesday, April 5, 2023

Posted March 29, 2023
Last modified April 3, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233

Amit Kumar, Louisiana State University
Legendrian Weaves and Manifold with decoration

In the paper titled 'Legendrian Weaves' Casals and Zaslow introduced the idea of N-graph and used it to construct Legendrian surfaces in the jet space of the surface associated with the N - graph. I will first talk about this construction and will then show that how the N-graph is an example of a more general 'manifold with decoration'. On a heuristic level a manifold with decoration is a manifold with defect where the defect facilitates decoration with other mathematical objects e.g., local systems, groups, etc. For this talk, I will focus on the decoration with groups and will show how such manifolds capture processes like Reidemeister moves. I will end the talk with an approach to TQFT of manifolds with decoration. This is research in progress.

Posted February 23, 2023
Last modified March 29, 2023

3:30 pm – 4:30 pm https://lsu.zoom.us/j/94413235134

Markus Hunziker, Baylor University
Associated varieties and unitarizability of highest weight Harish-Chandra modules

In the first part of this talk, we will explain how to determine the associated variety of any highest weight Harish-Chandra module directly from its highest weight by computing the width of a poset. In the second part, we will see how this leads to a simple new characterization of unitarizability of some highest weight Harish-Chandra modules. This is a joint work with Zhangqiang Bai.

Posted January 18, 2023
Last modified August 7, 2023

3:30 pm Lockett 233

Allison Miller, Swarthmore
Generalizing sliceness

A knot in the 3-sphere is said to be smoothly slice if it bounds a smoothly embedded disc in the 4-ball. Sliceness questions are closely related to interesting phenomena in 4-manifold topology: for example, the existence of a non smoothly slice knot that bounds a flatly embedded disc can be used to give a relatively quick proof of the existence of nonstandard smooth structures on 4-dimensional euclidean space. There are (at least!) two reasonable generalizations of sliceness to arbitrary 4-manifolds: in each of these directions, we will highlight open questions and give some results from joint work with Kjuchukova-Ray-Sakallı and Marengon-Ray-Stipsicz.

Monday, April 10, 2023

Posted March 26, 2023
Last modified April 6, 2023

1:00 pm Zoom (Click “Questions or Comments?” to request a Zoom link)

Samy Tindel, Purdue University
Hyperbolic Anderson model in the Skorohod and rough settings

In this talk I will start by giving a brief overview of some standard results concerning the stochastic heat equation, for which existence and uniqueness results are well established for a large class of Gaussian noises. Then I will describe some recent advances aiming at a proper definition of noisy wave equations, when specialized to a bilinear setting (called hyperbolic Anderson model). First I will focus on the so-called Skorohod setting, where an explicit chaos decomposition of the solution is available. A good control of the chaos expansion is then achieved thanks to an exponentiation trick. Next I will turn to a pathwise approach, which is based on a novel Strichartz type estimate for the wave operator. If possible I will show the main steps of this analytic estimate.

Posted February 1, 2023
Last modified March 20, 2023

3:30 pm Lockett Hall 232

Kirill Cherednichenko, University of Bath
Operator-norm homogenisation for Maxwell equations on periodic singular structures

I will discuss a new approach to obtaining uniform operator asymptotic estimates in periodic homogenisation. Based on a novel uniform Poincaré-type inequality, it bears similarities to the techniques I developed with Cooper (ARMA, 2016) and Velcic (JLMS, 2022). In the context of the Maxwell system, the analytic framework I will present leads to a new representation for the asymptotics obtained by Birman and Suslina in 2007 for the full system and by Suslina in 2004 for the electric field in the presence of currents. As part of the new asymptotic construction, I will link the leading-order approximation to a family of "homogenised" problems, which was not possible using the earlier method. The analysis presented applies to a class of inhomogeneous structures modelled by arbitrary periodic Borel measures. However, the results are new even for the particular case of the Lebesgue measure. This is joint work with Serena D'Onofrio.

Tuesday, April 11, 2023

Posted April 10, 2023

3:30 pm – 4:30 pm Zoom

Jia-Jie Zhu, Weierstrass Institute for Applied Analysis and Stochastics
Distributionally Robust Optimization in Kernel and Unbalanced Transport Geometry

This distribution shift in machine learning (ML) can happen as a consequence of causal confounding, unfairness due to data biases, and adversarial attacks. In such cases, recent optimizers adopt robustification strategies derived from distributionally robust optimization (DRO). For example, one of the most interesting directions of DRO is the adoption of the optimal transport distance, the Wasserstein distance. While the Wasserstein DRO literature has exploded, it is restricted to the pure transport regime, often similar to existing regularization techniques already used by machine learners. To make matters worse, many state-of-the-art Wasserstein DRO methods based place severe limitations on the learning models and scalability, making them inapplicable to modern ML tasks. With those limitations in mind, I will introduce mathematical tools beyond the Wasserstein DRO using unbalanced optimal transport and kernel geometry. I will also discuss ML applications such as robust learning under distribution shift. Zoom link: https://lsu.zoom.us/j/6653973295

Wednesday, April 12, 2023

Posted April 10, 2023

3:30 pm – 4:30 pm Locket 232; zoom: https://lsu.zoom.us/j/94413235134

Li Chen, LSU
Dimension-free bounds of Riesz transforms and multiplies

In this talk, I will first briefly introduce how probabilistic tools lead to sharp $L^p$ bound of Riesz transforms on Euclidean spaces. The main idea is to use the martingale transform representation of Gundy-Varopoulos and sharp martingale inequality. Then I will discuss several results on dimension-free bounds of Riesz transforms and multipliers in various geometric settings.

Posted January 10, 2023
Last modified April 4, 2023

3:30 pm Lockett 233

Giovanni Paolini, Caltech
The K(π,1) conjecture

Artin groups are a generalization of braid groups, and arise as the fundamental groups of configuration spaces associated with Coxeter groups. A long-standing open problem, called the K(π,1) conjecture, states that these configuration spaces are classifying spaces for the corresponding Artin groups. In the case of finite Coxeter groups, this was proved by Deligne in 1972. In the first part of this talk I will introduce Coxeter groups, Artin groups, and the K(π,1) conjecture. Then I will outline a recent proof of the K(π,1) conjecture in the affine case and further developments in the hyperbolic case. This is joint work with Mario Salvetti and Emanuele Delucchi.

Monday, April 17, 2023

Posted February 11, 2023
Last modified April 12, 2023

Mathematical Physics and Representation Theory Seminar

1:00 pm – 2:00 pm Zoom (Click “Questions or Comments?” to request a Zoom link)

Adina Oprisan, New Mexico State University
On the exit time of the Brownian motion with a power law drift

We will discuss the power law drift influence on the exit time of the Brownian motion from the half-line. The power law drift considered will emphasize the fact that the behavior of the process far away from zero will have the greatest influence. We are evaluating the time it takes for the perturbed process to hit zero using large deviations techniques. This talk is based on a joint work with D. DeBlassie and R. Smits.

Posted January 11, 2023
Last modified April 9, 2023

2:30 pm – 3:20 pm Lockett 233

Melissa Sherman-Bennett, MIT
The m=2 amplituhedron and the hypersimplex

I'll discuss a curious correspondence between the m=2 amplituhedron, a 2k-dimensional subset of Gr(k, k+2), and the hypersimplex, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map, respectively), but are different dimensions and live in very different ambient spaces. I'll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and certain matroidal decompositions of the hypersimplex (originally conjectured by Lukowski—Parisi—Williams). We also give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers, inspired by an analogous hypersimplex decomposition. No background knowledge on the amplituhedron, the totally nonnegative Grassmannian, or the hypersimplex will be assumed.

Wednesday, April 19, 2023

Posted March 29, 2023
Last modified April 10, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233

Jake Murphy, LSU
Quasiconvex subgroups of Coxeter groups

A subgroup of a hyperbolic group whose inclusion map is a quasi-isometric embedding is called quasiconvex. Various algorithmic problems are decidable for these quasiconvex subgroups, such as the membership problem and computing the index of the subgroup. In this talk, I will show techniques for determining when a subgroup is quasiconvex by Dani and Levcovitz for right-angled Coxeter groups and by Schupp for extra-large type Coxeter groups.

Posted January 10, 2023
Last modified August 7, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Chindu Mohanakumar, Duke University
DGA maps Induced by Decomposable Fillings with Z-coefficients

To every Legendrian link in R3, we can assign a differential graded algebra (dga) called the Chekanov-Eliashberg DGA. An exact Lagrangian cobordism between two Legendrian links induces a DGA map between the corresponding Chekanov-Eliashberg DGAs, and this association is functorial. This DGA map was written down explicitly for exact, decomposable Lagrangian fillings as Z2-count of certain pseudoholomorphic disks by Ekholm, Honda, and Kálmán, and this was combinatorially upgraded to an integral count by Casals and Ng. However, this upgrade only assigned an automorphism class of DGA maps. We approach the same problem of integral lifts by a different strategy, first done for the differential in the Chekanov-Eliashberg DGA by Ekholm, Etnyre, and Sullivan. Here, we find the precise DGA maps for all exact, decomposable Lagrangian cobordisms through this more analytic method.

Friday, April 21, 2023

Posted December 12, 2022
Last modified April 11, 2023

10:30 am – 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Maria Elena Valcher, University of Padova Fellow of IEEE and of IFAC
On the Influence of Homophily on the Friedkin-Johnsen Model

Over the last few decades, the modelling and analysis of sociological phenomena have attracted the interests of researchers from various fields, such as sociology, economics, and mathematics. Opinion dynamics models aim to describe and predict the evolution of the opinions of a group of individuals as a result of their mutual influence/appraisal. One of the most celebrated opinion dynamics models is the Friedkin-Johnsen (FJ) model, that captures the attitude of individuals to form their opinions by balancing exogenous and endogenous influences. On the one hand they value the opinions of the other individuals, weighted by the appraisals they have of them, and on the other hand they tend to adhere to their original opinions, that represent a permanent bias, to an extent that depends on the agent stubbornness. In the classical FJ model the weights that each agent gives to the opinions of the others are fixed. However, this is not consistent with other opinion dynamics models, where the weight matrix is time varying and it updates based on a homophily model: individuals decide which individuals they want to be influenced by (and on the contrary which individuals they want to distance their opinions from) based on the correlation between their opinion vectors. In this talk we will explore some recent results regarding this extended FJ model and present some future directions and challenges related to opinion dynamics models.

Monday, April 24, 2023

Posted January 21, 2023
Last modified March 8, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:20 pm Lockett 233

Svetlana Makarova, University of Pennsylvania
Quiver moduli and effective global generation

Moduli problems are ubiquitous and related to all areas of mathematics in one way or another. In this talk, I will focus on the algebro-geometric picture: namely, I would like to view the set of objects of classification as a scheme, called a moduli scheme. I will provide a framework that allows to recover the algebraic structure on this set, and then I will talk about modern methods of studying moduli problems. The modern theory "Beyond GIT", introduced by Alper and being developed by Alper, Halpern-Leistner, Heinloth and others, provides a "coordinate-free" way of thinking about classification problems. Among giving a uniform philosophy, this allows to treat problems that can't necessarily be described as global quotients. Our result about moduli of quiver representations is a particularly nice example where this modern theory can be applied. After a reminder on quiver representations, I will explain how we refine a classical result of King that moduli spaces of semistable representations of acyclic quivers are projective by proving it over an arbitrary noetherian base. Our methods allow us to obtain new results about the geometry of these moduli: I will define a determinantal line bundle which descends to a semiample line bundle on the moduli space and provide effective bounds for its global generation. For an acyclic quiver, we can observe that this line bundle is ample and thus the adequate moduli space is projective over an arbitrary noetherian base. This talk is based on a preprint with Belmans, Damiolini, Franzen, Hoskins, Tajakka (https://arxiv.org/abs/2210.00033).

Posted February 28, 2023
Last modified April 23, 2023

3:30 pm – 4:30 pm Zoom: https://lsu.zoom.us/j/5494314978

Hung Tran, University of Wisconsin Madison
Periodic homogenization of Hamilton-Jacobi equations: some recent progress.

I first give a quick introduction to front propagations, Hamilton-Jacobi equations, and homogenization theory. I will then show that the optimal rate of convergence is $O(\varepsilon)$ in the convex setting and some nonconvex cases. I will also mention finer results on the effective fronts in two dimensions. Connections to stable norms in Riemannian geometry will also be made. Based on various joints work with W. Jing and Y. Yu.

Tuesday, April 25, 2023

Posted April 24, 2023

1:30 pm – 2:30 pm Zoom

Meeting of the Tenured Faculty

Posted January 12, 2023
Last modified April 20, 2023

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:20 pm LDMC: room 1034

Matthias Maier, Department of Mathematics Texas A&M University
Structure-preserving finite-element schemes for the Euler-Poisson equations

We discuss structure-preserving numerical discretizations for the repulsive and attractive Euler-Poisson equations. The scheme is fully discrete and structure preserving in the sense that it maintains a discrete energy law, as well as hyperbolic invariant domain properties, such as positivity of the density and a minimum principle of the specific entropy. We discuss the underlying algebraic discretization technique based on collocation and convex limiting that maintain hyperbolic invariants and a discrete energy law, and discuss recovery strategies to maintain the discrete Gauss law.

Wednesday, April 26, 2023

Posted January 31, 2023
Last modified April 13, 2023

1:30 pm Lockett 233

Megan Farrell, Louisiana State University
Smooth versus Topological Concordance via Whitehead Doubles

We examine the difference between smooth and topological concordance using Knot Floer Homology. We do this using whitehead doubles, which can provide examples of knots which are topologically slice but not smoothly slice. We will be following Knot Floer Homology and Whitehead Doubles, written by Matt Hedden.

Posted January 10, 2023
Last modified April 19, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Ying Hu, University of Nebraska Omaha
Left-orderability of branched covers and link orientations

A non-trivial group G is called left-orderable (LO) if G admits a total linear order invariant under left-multiplication. We call a 3-manifold is LO if its fundamental group is. In this talk, we will discuss the (in)dependence of the left-orderability of cyclic branched covers of a link on the orientation of the link. We show that for certain links, such as fibered strongly quasi-positive hyperbolic links, changing the link's orientation does not affect the LO of the cyclic branched covers. Our proof involves a construction that mutates the Homeo(S^1) representations obtained from "pseudo-Anosov" flows on $3$-orbifolds. We will discuss additional applications of this construction. This is joint work with Steve Boyer and Cameron Gordon.

Friday, April 28, 2023

Posted January 17, 2023
Last modified April 16, 2023

10:30 am – 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Weiwei Hu, University of Georgia
Optimal Control for Suppression of Singularity in Chemotaxis

In this talk, we discuss the problem of optimal control for chemotaxis governed by the parabolic-elliptic Patlak-Keller-Segel (PKS) system via flow advection. The main idea is to utilize flow advection for enhancing diffusion as to control the nonlinear behavior of the system. The objective is to determine an optimal strategy for adjusting flow strength for advection so that the local in time blow up of the solution can be suppressed. Rigorous proof of existence of an optimal solution and derivation of first-order optimality conditions for solving such a solution are presented. Numerical experiments based on 2D cellular flows in a rectangular domain are conducted to demonstrate our ideas and designs.

Monday, May 1, 2023

Posted January 9, 2023
Last modified August 7, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:20 pm Lockett 233

Anne Dranowski, University of Southern California
Canonical bases in representation theory and mathematical physics

The fusion of two Mirković-Vilonen cycles is a degeneration of their product, defined using the Beilinson-Drinfeld Grassmannian. We describe a conceptually friendly approach to computing this product in type A, by transferring the problem to a fusion of generalized orbital varieties using the Mirković-Vybornov isomorphism. We explain how using this fusion product we are able to verify a conjecture about cluster monomials and the MV basis in the coordinate ring of the upper-triangular subgroup of GL(4). Based on joint work with R. Bai and J. Kamnitzer.

Wednesday, May 3, 2023

Posted January 31, 2023
Last modified April 28, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233

Matthew McCoy, Louisiana State University
An Introduction to Buildings and BN Pairs

This talk will introduce a special class of simplicial complexes called buildings. We will discuss some basic properties of buildings along with some examples. Then, we will discuss group actions on buildings. In particular, group actions by algebraic groups. As it turns out, algebraic groups are the historical motivation behind the study of buildings, and there are lots of relations between buildings and the structure theory of algebraic groups. In particular, we will discuss BN pairs associated with algebraic groups acting on buildings and how these BN pairs relate to the group action.

Posted January 11, 2023
Last modified April 29, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Ben Knudsen, Northeastern University
Farber's conjecture and beyond

Topological complexity is a numerical invariant quantifying the difficulty of motion planning; applied to configuration spaces, it measures the difficulty of collision-free motion planning. In many situations of practical interest, the environment is reasonably modeled as a graph, and the topological complexity of configuration spaces of graphs has received significant attention for this reason. This talk will discuss a proof of a conjecture of Farber, which asserts that this invariant is as large as possible in the stable range, and of an analogue of this result in the setting of unordered configuration spaces.

Friday, May 5, 2023

Posted January 26, 2023
Last modified April 2, 2023

10:30 am – 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Wim Michiels, KU Leuven
Strong Relative Degree of Time-Delay Systems with Non-Commensurate Delays

The presentation addresses the notion of relative degree for linear time-delay systems of retarded type, when the common assumption of commensurate delays is dropped. Algebraic conditions are provided that fully exploit the delay dependence structure. It is shown that the relative degree may be sensitive to delay perturbations, which is the basis of a novel notion of relative degree, called strong relative degree. This notion is characterized algebraically and computationally in the SISO and MIMO settings. Using the obtained characterizations and a benchmark problem, which illustrates that invariant zeros may be characterized as zeros of quasi-polynomials of retarded, neutral or advanced type, light is shed on existence conditions of a normal form. The novel concepts and theoretical results also play a role in the design and analysis of extended PD controllers, as illustrated. Finally, connections are established with the notion of strong stability and strong H2-norm for delay equations of neutral type and delayed descriptor systems. This work is in collaboration with Bin Zhou from Harbin University of Technology.

Wednesday, May 10, 2023

Posted April 3, 2023
Last modified May 8, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Oleg Lazarev, University of Massachusetts Boston
Localization and flexibilization in symplectic geometry

Localization is an important construction in algebra and topology that allows one to study global phenomena a single prime at a time. Flexibilization is an operation in symplectic topology introduced by Cieliebak and Eliashberg that makes any two symplectic manifolds that are diffeomorphic (plus a bit of tangent bundle data) become symplectomorphic. In this talk, I will explain joint work with Sylvan and Tanaka that shows that flexibilization is a localization functor of a certain category of symplectic manifolds and also constructs new localization functors of symplectic manifolds associated to primes P. These P-flexibilization functors interpolate between rigidity and flexibility and are a symplectic analog of topological localization of Sullivan, Quillen, and Bousfield. I will also describe work joint work with Datta, Mohanakumar, and Wu that gives explicit descriptions of Legendrians used to create P-flexible symplectic manifolds.

Friday, May 12, 2023

Posted February 13, 2023
Last modified April 25, 2023

10:30 am – 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)

Matthew Hale, University of Florida AFOSR Young Investigator, ONR Young Investigator, and NSF CAREER Program Awardee
Resilient Multi-Agent Coordination: From Theory to Practice

A multi-agent system is any collection of decision-makers that collaborates on a common task. A distinguishing feature is that communications among agents provide the feedback signals needed for autonomous decision-making. For example, a team of drones may exchange location data and images to jointly map an area. There is now a large literature on multi-agent systems, though practical implementations are often fragile or only done in controlled environments. A fundamental challenge is that agents’ communications in realistic environments can be impaired, e.g., by delays and intermittency, and thus agents must rely on impaired feedback. To transition theory to practice, such systems need novel coordination techniques that are provably resilient to such impairments and validated in practice under realistic conditions. In this talk, I will cover two recent developments in my group that have successfully transitioned novel theory to practice for multi-agent systems facing asynchronous communications. The first considers a class of geometrically complex coordination tasks – namely those given by constrained nonconvex programs – and provides provable guarantees of performance that are borne out in practice onboard teams of drones. The second considers a class of time-varying task specifications for agents that can change unpredictably. Theoretical results show that agents can complete this class of task under mild restrictions, and validation is provided by a team of lighter-than-air agents in a contested environment.

Monday, May 22, 2023

Posted May 14, 2023

http://automorphicformsworkshop.org/

until Friday, May 26, 2023 Lockett 277 (5/22), 006 (5/23-5/26)

35th Automorphic Forms Workshop

Monday, August 14, 2023

Posted April 26, 2023

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Algebra

Wednesday, August 16, 2023

Posted April 26, 2023

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Analysis

Friday, August 18, 2023

Posted April 26, 2023

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Topology

Monday, August 21, 2023

Posted August 20, 2023

3:30 pm – 4:20 pm Lockett 232

Fabrice Baudoin, University of Connecticut
Dirichlet forms on metric measure spaces as Mosco limits of Korevaar-Schoen energies

We will give sufficient general conditions for the existence of Mosco limits of Korevaar-Schoen L2 energies, first in the context of Cheeger spaces and then in the context of fractal-like spaces with walk dimension greater than 2. Among the ingredients, a new Rellich- Kondrachov type theorem for Korevaar-Schoen-Sobolev spaces is of independent interest. The talk will be based on a joint work with Patricia Alonso-Ruiz (TAMU)

Wednesday, August 23, 2023

Posted July 7, 2023
Last modified August 23, 2023

1:30 pm Lockett 233

Rima Chatterjee, University of Cologne
Knots in overtwisted manifolds

Knots in contact manifolds are interesting objects to study. In this talk, I'll focus on knots in overtwisted manifolds with tight complements also known as non-loose knots. These knots play an important role in contact topology as one can get interesting tight contact manifolds by doing surgery on them, though they appear to be rare. I'll discuss some of their classification results and how they differ from knots in tight manifolds. Next I’ll show that the cabling construction of these knots will give us a family of non-loose knots but only under certain conditions. Part of this is joint work with Geiges-Onaran and with Etnyre, Min and Mukherjee.

Posted July 7, 2023
Last modified August 23, 2023

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett 233

Yu Chan Chang, Wesleyan University
The RAAG Recognition Problem for Bestvina–Brady Groups

Right-angled Artin groups (RAAGs) have been a central object of study in geometric group theory because they contain many interesting subgroups. The RAAG Recognition Problem seeks to determine whether a given group is isomorphic to a RAAG. In this talk, we will discuss this recognition problem for Bestvina–Brady groups (BBGs). I will describe a graph-theoretic condition that certifies a BBG as a RAAG. On the other hand, I will use the BNS-invariants of BBGs to demonstrate that certain BBGs are not RAAGs. Finally, we will see a complete solution to the RAAG Recognition Problem for the BBGs defined on 2-dimensional flag complexes. This is joint work with Lorenzo Ruffoni.

Tuesday, August 29, 2023

Posted August 22, 2023
Last modified August 24, 2023

3:10 pm – 4:00 pm Lockett 233 or click here to attend on Zoom

Xingting Wang, Louisiana State University
What are automorphism groups and where to find them?

We will discuss the automorphism problem in number theory, algebraic geometry, Poisson geometry, and quantum algebras from both classical and quantum group perspectives. The focus will be on recent progress and open conjectures in specific topics.

Wednesday, August 30, 2023

Posted August 21, 2023
Last modified January 7, 2025

1:30 pm Lockett 138

John Etnyre, Georgia Institute of Technology
Invariants of embeddings and immersions via contact geometry

There is a beautiful idea that one can study topological spaces by studying associated geometric objects. In this talk I will begin by reviewing the Whitney-Graustein theorem that tells you precisely when two immersed curves in the plane can be deformed into each other. We will then see how this result can be interpreted in terms of contact geometry and Legendrian knots, so we see how one can turn a topological problem (deforming immersed curves) into a geometric one (isotoping Legendrian knots). Along the way I will give a brief introduction to contact geometry and end by discussing how one can try to study immersions and embeddings in all dimensions using contact geometry.

Posted July 31, 2023
Last modified January 7, 2025

3:30 pm Lockett 232

John Etnyre, Georgia Institute of Technology
The Job Process

In this talk I will discuss academic jobs for people with a math PhD, focusing on postdoctoral positions and beginning tenure track jobs. We will discuss what these jobs entail and how to apply for them, and most importantly, what you can be doing now to maximize your chance at getting such a position.

Thursday, August 31, 2023

Posted August 8, 2023
Last modified August 27, 2023

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

John Etnyre, Georgia Institute of Technology
Contact geometry and Legendrian knots

In this talk, I will discuss the current state of our understanding of contact structures on 3-manifolds and the related problem of Legendrian knots in contact manifolds. We will begin the talk by recalling basic definitions and examples in contact geometry, discuss natural occurrences of contact structures in everyday life, and then survey the long history of contact geometry and its connections to many areas of math and science. After this, we will focus on recent advances in our understanding of Legendrian knots in contact manifolds and how this is relevant to trying to classify the types of contact structures a 3-manifold might support.

Tuesday, September 5, 2023

Posted August 22, 2023
Last modified September 4, 2023

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom

Dermot McCarthy, Texas Tech University
The number of $\mathbb{F}_q$-points on diagonal hypersurfaces with monomial deformation

In this talk, we consider the problem of counting the number of solutions to equations over finite fields using character sums. We start with a review of standard techniques and discuss Weil's seminal 1949 paper, which gives an exposition on the topic up to that point by examining diagonal hypersurfaces. We then consider the family of diagonal hypersurfaces with monomial deformation $$D_{d, \lambda, h}: x_1^d + x_2^d \dots + x_n^d - d \lambda \, x_1^{h_1} x_2^{h_2} \dots x_n^{h_n}=0$$ where $d = h_1+h_2 +\dots + h_n$ with $\gcd(h_1, h_2, \dots h_n)=1$, which was studied by Koblitz over $\mathbb{F}_{q}$ in the case ${d \mid {q-1}}$. We outline recent results where we provide a formula for the number of $\mathbb{F}_{q}$-points on $D_{d, \lambda, h}$ in terms of Gauss and Jacobi sums, which generalizes Koblitz's result. We then express the number of $\mathbb{F}_{q}$-points on $D_{d, \lambda, h}$ in terms of a $p$-adic hypergeometric function previously defined by the speaker. The parameters in this hypergeometric function mirror exactly those described by Koblitz when drawing an analogy between his result and classical hypergeometric functions.

Posted August 30, 2023

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Benjamin Fehrman, Louisiana State University
Non-equilibrium fluctuations and parabolic-hyperbolic PDE with irregular drift

Non-equilibrium behavior in physical systems is widespread. A statistical description of these events is provided by macroscopic fluctuation theory, a framework for non-equilibrium statistical mechanics that postulates a formula for the probability of a space-time fluctuation based on the constitutive equations of the system. This formula is formally obtained via a zero noise large deviations principle for the associated fluctuating hydrodynamics, which postulates a conservative, singular stochastic PDE to describe the system far-from-equilibrium. In this talk, we will focus particularly on the fluctuations of the zero range process about its hydrodynamic limit. We will show how the associated MFT and fluctuating hydrodynamics lead to a class of conservative SPDEs with irregular coefficients, and how the study of large deviations principles for the particles processes and SPDEs leads to the analysis of parabolic-hyperbolic PDEs in energy critical spaces. The analysis makes rigorous the connection between MFT and fluctuating hydrodynamics in this setting, and provides a positive answer to a long-standing open problem for the large deviations of the zero range process.

Wednesday, September 6, 2023

Posted September 6, 2023

1:30 pm – 2:30 pm Lockett 233

Organizational

Posted August 15, 2023
Last modified August 31, 2023

3:30 pm Lockett 233

David Sheard, King's College London
Reflection and Nielsen equivalence in Coxeter groups

Nielsen equivalence – the natural notion of equivalence between generating sets of finitely generated groups – has been studied for the last century. Early techniques were often combinatorial, however more modern approaches use algebra and geometric/topological methods. In the last decade significant progress has been made studying it in surface and Fuchsian groups. In this talk I will introduce Nielsen equivalence in Coxeter groups, a class of groups with very rich geometry, and a related notion called reflection equivalence which is specialised for reflections. I will prove that any reflect generating set of a Coxeter group is equivalent to a “geometrically simple” generating set and provide a complete classification in some classes of Coxeter groups. Time permitting, I will also mention one approach to Nielsen equivalence in the right-angled case based on recent work generalising Stallings’ folds to RACGs.

Thursday, September 7, 2023

Posted August 8, 2023
Last modified August 28, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Emanuele Delucchi, University of Applied Sciences and Arts of Southern Switzerland (SUPSI)
On polytopes associated to metric spaces

In 2010, Vershik proposed a new combinatorial invariant of metric spaces given by a class of polytopes that arise in the theory of optimal transport, called “Wasserstein polytopes” or “Kantorovich-Rubinstein polytopes” (KRP). Recently such polytopes have been shown to play an important role in a host of contexts, from machine learning to computational biology. However, little is known in general to date about their structure. In this talk I will state the definitions in the case of finite metric spaces and by outlining some context. I will then show some examples and survey some recent results and open questions about the combinatorial structure of such polytopes. The talk includes joint work with Linard Hössly, Alessio D'Alì, Mateusz Michalek, Lukas Kühne and Leonie Mühlherr.

Friday, September 8, 2023

Posted August 25, 2023
Last modified August 12, 2024

10:30 am – 11:20 am Zoom (click here to join)

Cristopher Hermosilla, Universidad Técnica Federico Santa María
Hamilton-Jacobi-Bellman Approach for Optimal Control Problems of Sweeping Processes

This talk is concerned with a state constrained optimal control problem governed by a Moreau's sweeping process with a controlled drift. The focus of this work is on the Bellman approach for an infinite horizon problem. In particular, we focus on the regularity of the value function and on the Hamilton-Jacobi-Bellman equation it satisfies. We discuss a uniqueness result and we make a comparison with standard state constrained optimal control problems to highlight a regularizing effect that the sweeping process induces on the value function. This is a joint work with Michele Palladino (University of L’Aquila, Italy) and Emilio Vilches (Universidad de O’Higgins, Chile).

Monday, September 11, 2023

Posted August 1, 2023
Last modified September 10, 2023

3:30 pm Zoom (https://lsu.zoom.us/j/96065057555)

Gautam Iyer, Carnegie Mellon University
Using mixing to accelerate convergence of Langevin systems, and applications to Monte Carlo methods

A common method used to sample from a distribution with density proportional to $p = e^{-V/\kappa}$ is to run Monte Carlo simulations on an overdamped Langevin equation whose stationary distribution is also proportional to $p$. When the potential $V$ is not convex and the temperature $\kappa$ is small, this can take an exponentially large (i.e. of order $e^{C/\kappa}$) amount of time to generate good results. I will talk about a method that introduces a "mixing drift" into this system, which allows us to rigorously prove convergence in polynomial time (i.e. a polynomial in $1/\kappa$). This is joint work with Alex Christie, Yuanyuan Feng and Alexei Novikov.

Tuesday, September 12, 2023

Posted August 22, 2023
Last modified September 5, 2023

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Digital Media Center 1034
(Originally scheduled for Tuesday, September 5, 2023, 3:30 pm)

Xiaoliang Wan, Louisiana State University
Adaptive Sampling for the Neural Network Approximation of PDEs

Abstract: Deep learning-based numerical methods are being actively investigated for the approximation of PDEs from different perspectives including numerical analysis, algorithm development and applications. One common key component of these learning-based approximation methods is the training set, which consists of random samples in the computation domain. These random samples define a discrete optimization problem for the optimal neural network approximate solution. In this talk, we pay particular attention to the training set and demonstrate that adaptive sampling can improve significantly the accuracy of the neural network approximation especially for low-regularity and high-dimensional problems. https://www.cct.lsu.edu/lectures/adaptive-sampling-neural-network-approximation-pdes

Wednesday, September 13, 2023

Posted September 6, 2023

1:30 pm – 2:30 pm Lockett 233

Shea Vela-Vick, Louisiana State University
Characteristic Classes - Lecture 1

Posted September 6, 2023
Last modified September 11, 2023

3:30 pm Lockett 233

Agniva Roy, Louisiana State University
Symplectic fillings of lens spaces and torus bundles

Classifying minimal strong symplectic fillings of contact manifolds is a problem with a rich history. The first result was by Eliashberg who showed that the 4-ball is the unique such filling of the standard tight contact 3-sphere. Since then, various techniques have been developed, by Eliashberg, McDuff, Wendl, Lisca, Christian-Menke, and Lisi-van Horn-Morris-Wendl, among others, to study this problem using holomorphic curves, and the literature has seen complete classifications for certain families of 3-manifolds -- notably lens spaces. I will discuss the primary techniques that are used to study these problems and talk about some of my own work in classifying fillings of lens spaces and developing techniques to understand fillings of torus bundles -- the former joint with Etnyre, and the latter joint with Min and Wang.

Friday, September 15, 2023

Posted September 12, 2023

Informal Geometry and Topology Seminar Questions or comments?

2:30 pm – 3:30 pm Lockett Hall 239

Zhiyu Wang, Louisiana State University
$\chi$-boundedness and $\chi$-binding functions of graph classes

Abstract: A graph class is called $\chi$-bounded if there is a fixed function $f$ (called the $\chi$-binding function) such that for every graph G in that graph class, $\chi(G)\leq f(\omega(G))$, where $\chi(G)$ and $\omega(G)$ denote the chromatic number and clique number of $G$ respectively. The well-known Gy\'arf\'as-Sumner Conjecture states that for every tree $T$, the class of $T$-free graphs is $\chi$-bounded. The existence of a polynomial $\chi$-binding function for a graph class also implies the Erd\H{o}s-Hajnal Conjecture for that graph class. In this talk, we survey some recent results on $\chi$-boundedness and $\chi$-binding functions of certain graph classes.

Wednesday, September 20, 2023

Posted September 6, 2023

1:30 pm – 2:30 pm Lockett 233

Adithyan Pandikkadan, Louisiana State University
Characteristic Classes - Lecture 2

Posted August 1, 2023
Last modified September 12, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

James Hughes, Duke University
Legendrian loops and cluster modular groups

Given a Legendrian link L in the contact 3-sphere, one can hope to classify the set of exact Lagrangian fillings of L, i.e. exact Lagrangian surfaces in the symplectic 4-ball with boundary equal to L. Much of the recent progress towards this classification relies on the theory of cluster algebras. In this talk, I will describe a cluster structure on the augmentation variety of Legendrian positive braid closures. I will then discuss how Legendrian loops -- Legendrian isotopies fixing L setwise -- yield cluster automorphisms of the augmentation variety. These automorphism groups behave very similarly to mapping class groups and I will use this connection to describe generating sets, fixed point properties, and some applications to the mapping tori of Legendrian loops.

Friday, September 22, 2023

Posted August 18, 2023
Last modified August 12, 2024

10:30 am – 11:20 am Zoom (click here to join)

Mario Sznaier, Northeastern University IEEE Fellow, IEEE Control Systems Society Distinguished Member Awardee
Why Do We Need Control in Control Oriented Learning?

Despite recent advances in machine learning (ML), the goal of designing control systems capable of fully exploiting the potential of these methods remains elusive. Modern ML can leverage large amounts of data to learn powerful predictive models, but such models are not designed to operate in a closed-loop environment. Recent results on reinforcement learning offer a tantalizing view of the potential of a rapprochement between control and learning, but so far proofs of performance and safety are mostly restricted to limited cases. Thus, learning elements are often used as black boxes in the loop, with limited interpretability and less than completely understood properties. Further progress hinges on the development of a principled understanding of the limitations of control-oriented machine learning. This talk will present some initial results unveiling the fundamental limitations of some popular learning algorithms and architectures when used to control a dynamical system. For instance, it shows that even though feed forward neural nets are universal approximators, they are unable to stabilize some simple systems. We also show that a recurrent neural net with differentiable activation functions that stabilizes a non-strongly stabilizable system must itself be open loop unstable, and discuss the implications of this for training with noisy, finite data. Finally, we present a simple system where any controller based on unconstrained optimization of the parameters of a given structure fails to render the closed loop system input-to-state stable. The talk finishes by arguing that when the goal is to learn stabilizing controllers, the loss function should reflect closed loop performance, which can be accomplished using gap-metric motivated loss functions, and presenting initial steps towards that goal.

Posted September 18, 2023

2:30 pm – 3:30 pm Lockett Hall 239

Brittian Qualls, Louisiana State University
Unavoidable Immersions in 4-edge-connected Graphs

A graph H is called an immersion of a graph G if H can be obtained from a subgraph of G by repeated liftings, which means replacing two adjacent edges xy, xz by one edge yz. In this talk, we discuss results on unavoidable topological minors and their analogous results for immersions. In particular, we discuss our main result: that every sufficiently large 4-edge-connected graph contains a doubled cycle of length k, $C_{2,k}$, as an immersion. We will also discuss other results on immersions and possible avenues of further research.

Tuesday, September 26, 2023

Posted August 23, 2023

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Digital Media Center 1034

Zequn Zheng, Louisiana State University
Generating Polynomial Method for Non-symmetric Tensor Decomposition

Abstract: Tensors or multidimensional arrays are higher order generalizations of matrices. They are natural structures for expressing data that have inherent higher order structures. Tensor decompositions play an important role in learning those hidden structures. There exist both optimization-based methods and algebraic methods for the tensor decomposition problem, optimization-based methods regard the tensor decomposition problem as a nonconvex optimization problem and apply optimization methods to solve it. Hence, they usually suffer from local minimum and may not be able to find a satisfactory tensor decomposition. Algebraic methods usually require the tensor rank to be not too large and the running time is not so satisfying for large tensors. In this talk, we present a novel algorithm to find the tensor decompositions utilizing generating polynomials. Under some conditions on the tensor's rank, we prove that the exact tensor decomposition can be found by our algorithm. Numerical examples successfully demonstrate the robustness and efficiency of our algorithm. https://www.cct.lsu.edu/lectures/generating-polynomial-method-non-symmetric-tensor-decomposition

Wednesday, September 27, 2023

Posted September 6, 2023

1:30 pm – 2:30 pm Lockett 233

Nilangshu Bhattacharyya, Louisiana State University
Characteristic Classes - Lecture 3

Posted August 30, 2023
Last modified September 18, 2023

3:30 pm – 4:30 pm Lockett 232

Xiaoqi Huang, Louisiana State University
Curvature and growth rates of log-quasimodes on compact manifolds

We will discuss the relation between curvature and L^q norm estimates of spectral projection operators on compact manifolds. We will present a new way that one can hear the shape of a connected compact manifold of constant sectional curvatures, if the shape refers to curvature, and the radios used are the L^q norm of quasimodes. This is based on ongoing work with Christopher Sogge.

Posted August 30, 2023
Last modified September 1, 2023

3:30 pm – 4:30 pm Lockett 232

Xiaoqi Huang, Louisiana State University
Curvature and growth rates of log-quasimodes on compact manifolds

Posted September 6, 2023
Last modified September 22, 2023

3:30 pm Lockett 233

Ana Bălibanu, Louisiana State University
Moment maps and multiplicative reduction

Symplectic reduction is a process that eliminates the symmetries of a Poisson manifold equipped with a Hamiltonian group action. Many algebraic varieties which are of interest to representation theory arise as reductions of symplectic spaces associated to algebraic groups. We introduce several new reduction procedures, some of which are multiplicative analogues of ”classical” examples of symplectic reduction. This is joint work with Maxence Mayrand.

Thursday, September 28, 2023

Posted September 18, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Wilhelm Schlag, Yale University
Lyapunov exponents, Schrödinger cocycles, and Avila’s global theory

In the 1950s Phil Anderson made a prediction about the effect of random impurities on the conductivity properties of a crystal. Mathematically, these questions amount to the study of solutions of differential or difference equations and the associated spectral theory of self-adjoint operators obtained from an ergodic process. With the arrival of quasicrystals, in addition to random models, nonrandom lattice models such as those generated by irrational rotations or skew-rotations on tori have been studied over the past 30 years. By now, an extensive mathematical theory has developed around Anderson’s predictions, with several questions remaining open. This talk will attempt to survey certain aspects of the field, with an emphasis on the theory of SL(2,R) cocycles with an irrational or Diophantine rotation on the circle as base dynamics. In this setting, Artur Avila discovered about a decade ago that the Lyapunov exponent is piecewise affine in the imaginary direction after complexification of the circle. In fact, the slopes of these affine functions are integer valued. This is easy to see in the uniformly hyperbolic case, which is equivalent to energies falling into the gaps of the spectrum, due to the winding number of the complexified Lyapunov exponent. Remarkably, this property persists also in the non-uniformly hyperbolic case, i.e., on the spectrum of the Schrödinger operator. This requires a delicate continuity property of the Lyapunov exponent in both energy and frequency. Avila built his global theory (Acta Math. 2015) on this quantization property. I will present some recent results with Rui HAN connecting Avila’s notion of acceleration (the slope of the complexified Lyapunov exponent in the imaginary direction) to the number of zeros of the determinants of finite volume Hamiltonians relative to the complex toral variable. This connection allows one to answer questions arising in the supercritical case of Avila’s global theory concerning the measure of the second stratum, Anderson localization on this stratum, as well as settle a conjecture on the Hölder regularity of the integrated density of states.

Friday, September 29, 2023

Posted August 18, 2023
Last modified August 12, 2024

10:30 am – 11:20 am Zoom (click here to join)

Cristina Pignotti, Università degli Studi dell'Aquila
Consensus Results for Hegselmann-Krause Type Models with Time Delay

We study Hegselmann-Krause (HK) opinion formation models in the presence of time delay effects. The influence coefficients among the agents are nonnegative, as usual, but they can also degenerate. This includes, e.g., the case of on-off influence, namely the agents do not communicate over some time intervals. We give sufficient conditions ensuring that consensus is achieved for all initial configurations. Moreover, we analyze the continuity type equation obtained as the mean-field limit of the particle model when the number of agents goes to infinity. Finally, we analyze a control problem for a delayed HK model with leadership and design a simple control strategy steering all agents to any fixed target opinion.

Posted September 25, 2023

Algebra and Number Theory Seminar Questions or comments?

2:30 pm – 3:30 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)

Xiaonan Liu, Vanderbilt University
Counting Hamiltonian cycles in planar triangulations

Whitney showed that every planar triangulation without separating triangles is Hamiltonian. This result was extended to all $4$-connected planar graphs by Tutte. Hakimi, Schmeichel, and Thomassen showed the first lower bound $\log _2 n$ for the number of Hamiltonian cycles in every $n$-vertex $4$-connected planar triangulation and, in the same paper, they conjectured that this number is at least $2(n-2)(n-4)$, with equality if and only if $G$ is a double wheel. We show that every $4$-connected planar triangulation on $n$ vertices has $\Omega(n^2)$ Hamiltonian cycles. Moreover, we show that if $G$ is a $4$-connected planar triangulation on $n$ vertices and the distance between any two vertices of degree $4$ in $G$ is at least $3$, then $G$ has $2^{\Omega(n^{1/4})}$ Hamiltonian cycles. Joint work with Zhiyu Wang and Xingxing Yu.

Tuesday, October 3, 2023

Posted September 24, 2023
Last modified September 29, 2023

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom

Cheng Chen, University of Minnesota
Progresses on the local Gan-Gross-Prasad conjecture

The local Gan-Gross-Prasad conjecture speculates the generalization of branching problems for classical groups over local fields using classification in the Langlands problem. It has global applications related to automorphic forms and arithmetic. Works of Waldspurger, Moeglin, Beuzart-Plessis, Gan, Ichino, and Atobe completed the conjecture over non-archimedean local fields. Based on the local trace formula results in the work of Beuzart-Plessis and Luo, I will introduce an approach for the conjecture over archimedean local fields, including joint work with Luo and joint work with Chen and Zou.

Wednesday, October 4, 2023

Posted September 6, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm – 2:30 pm Lockett 233

Colton Sandvick, Louisiana State University
Characteristic Classes - Lecture 4

Posted August 23, 2023
Last modified September 27, 2023

3:30 pm Lockett 233

Yuan Yao, Sorbonne University
Morse-Bott theory and embedded contact homology

Embedded contact homology (ECH) is a Floer theory associated to a contact 3-manifold $(Y,\lambda)$. Its generators are orbits of the Reeb vector field and its differential counts pseudo-holomorphic curves. It has been shown to be isomorphic to versions of Heegaard Floer homology and monopole Floer homology. It has wide ranging applications in the study of symplectic topology and dynamics, for example in finding obstructions to symplectic embeddings and studying periodic orbits of Reeb vector fields. In this talk I will first give an overview of ECH, then explain how to compute ECH in certain Morse-Bott settings via enumerations of J-holomorphic cascades. One of the main technical tools will be how to do Morse-Bott theory in the pseudo-holomorphic curves setting.

Posted September 28, 2023

3:30 pm – 4:30 pm Lockett 232

Boris Rubin, Louisiana State University
Offbeat Radon Transforms

One of the most attractive problems of L. Zalcman's offbeat integral geometry is whether a function on a constant curvature space X can be reconstructed from its integrals over geodesic spheres (or balls) of fixed radius. The problem acquires a new flavor if the (0-dimensional) centers of the spheres (or balls) are replaced by the totally geodesic submanifolds of positive dimension. This way of thinking paves the way to a number of exotic Radon type transforms, like those over strips of fixed width d>0 in the 2-plane. The case d=0 corresponds to the classical problem by J. Radon (1917) for lines in the 2-plane. One can also consider pipes or solid tubes of fixed diameter in the 3-space, slabs of constant thickness, hoops on the sphere, and similar objects in higher dimensions. I am planning to show some recent injectivity results for these "offbeat" Radon transforms in the cases when X is the Euclidean space and the unit sphere. Open problems will be discussed. If time allows, I will also speak about intriguing connections to the inverse problems for the Euler-Poisson-Darboux Equations with $L^p$ initial data. The results were delivered at the Conference "Harmonic and Complex Analysis: modern and classical" dedicated to the memory of Prof. Lawrence Zalcman, Bar-Ilan University, Ramat Gan, Israel, June 18-23, 2023.

Tuesday, October 10, 2023

Posted October 2, 2023
Last modified October 3, 2023

Algebra and Number Theory Seminar Questions or comments?

9:00 am Zoom (email dmassatt@lsu.edu for link)

Huajie Chen, Beijing Normal University
Multi-level Monte Carlo methods in stochastic density functional theory

The stochastic density functional theory (sDFT) has become an attractive approach in electronic structure calculations. The computational complexity of Hamiltonian diagonalization is replaced by introducing a set of random orbitals leading to sub-linear scaling of evaluating the ground-state observables. This work investigates the convergence and acceleration of the self-consistent field (SCF) iterations for sDFT in the presence of statistical error. We also study some variance reduction schemes by multi-level Monte Carlo methods that can accelerate the SCF convergence.

Posted September 24, 2023
Last modified October 5, 2023

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom

Tewodros Amdeberhan, Tulane University
Generalized divisor sums and integer partitions

Our story and motivation go back to MacMahon, in which divisor sums are generalized and connections were made to partitions. We extend the argument for a variation of this development where we link our multi-variable $q$-series to alternative formulation, including multiple $q$-zeta values, quasi-modular forms. This is joint work with George Andrews and Roberto Tauraso.

Posted September 26, 2023
Last modified October 3, 2023

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm Lockett 232

Jing Wang, Purdue University
Spectral bounds for exit times of diffusions on metric measure

We consider a diffusion on a metric measure space equipped with a local regular Dirichlet form. Assuming volume doubling property and heat kernel sub-Gaussian upper bound we obtain a spectral upper bound for the survival probability $\mathbb P(\tau_D >t)$ of the diffusion, where $\tau_D$ is its first exit time from domain $D$. Among other nice consequences, we are able to obtain a uniform upper bound for the product $\lambda(D) \sup_{x\in D} \mathbb E_x(\tau_D)$. This is a joint work with Phanuel Mariano.

Wednesday, October 11, 2023

Posted September 6, 2023

1:30 pm – 2:30 pm Lockett 233

Krishnendu Kar, Louisiana State University
TBA

Posted October 6, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm – 2:30 pm Lockett 233

Adithyan Pandikkadan, Louisiana State University
Continuation on characteristic classes

Posted August 20, 2023
Last modified September 28, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Wenyuan Li, Northwestern University
Conjugate fillings and Legendrian weaves

In this talk, we compare two different approaches to constructing Lagrangian fillings of Legendrian knots. The first one is conjugate Lagrangian fillings of alternating Legendrians, introduced by Shende-Treumann-Williams-Zaslow, which are characterized using bipartite graphs, and the second one is Lagrangian projections of Legendrian weaves, introduced by Casals-Zaslow, which are depicted by planar graphs encoding their wavefronts. We will develop a diagrammatic calculus to show that conjugate Lagrangian fillings are Hamiltonian isotopic to certain Lagrangian projections of Legendrian weaves. The result includes Legendrian positive braid closures and ideal triangulations on punctured surfaces. We will then explain some implications on Lagrangian mutations and cluster theory. This is joint work with Roger Casals.

Friday, October 13, 2023

Posted September 12, 2023
Last modified August 12, 2024

10:30 am – 11:20 am Zoom (click here to join)

Melvin Leok, University of California, San Diego
Connections Between Geometric Mechanics, Information Geometry, Accelerated Optimization and Machine Learning

Geometric mechanics describes Lagrangian and Hamiltonian mechanics geometrically, and information geometry formulates statistical estimation, inference, and machine learning in terms of geometry. A divergence function is an asymmetric distance between two probability densities that induces differential geometric structures and yields efficient machine learning algorithms that minimize the duality gap. The connection between information geometry and geometric mechanics will yield a unified treatment of machine learning and structure-preserving discretizations. In particular, the divergence function of information geometry can be viewed as a discrete Lagrangian, which is a generating function of a symplectic map, that arise in discrete variational mechanics. This identification allows the methods of backward error analysis to be applied, and the symplectic map generated by a divergence function can be associated with the exact time-h flow map of a Hamiltonian system on the space of probability distributions. We will also discuss how time-adaptive Hamiltonian variational integrators can be used to discretize the Bregman Hamiltonian, whose flow generalizes the differential equation that describes the dynamics of the Nesterov accelerated gradient descent method.

Posted October 6, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:30 pm Lockett Hall 239 (or email zhiyuw at lsu.edu for Zoom link)

Samuel Weiner, Louisiana State University
Unavoidable Uniform Hypergraphs

A classical extension of Ramsey's Theorem states that every infinite graph must contain either an infinite clique or infinite coclique as an induced subgraph. There are three similar results detailing the unavoidable induced subgraphs for 1) graphs with infinitely many edges, 2) graphs with a vertex of infinite degree, and 3) locally finite, connected, infinite graphs. We now generalize all three of these results to hypergraphs for which every edge contains a uniform number of vertices. We also obtain the corresponding results for finite hypergraphs.

Monday, October 16, 2023

Posted August 14, 2023
Last modified October 9, 2023

2:30 pm – 3:20 pm Lockett 233

Konstantin Aleshkin, Columbia University
Crossing the walls in GLSM

Gauged Linear Sigma Models (GLSM) are curve counting theories that have been studied recently. Conceptually, they capture the enumerative geometry of the critical locus of a holomorphic function on a quotient of a simple variety by an algebraic Lie group. I plan to explain how to construct and compute certain genus 0 invariants and their generating functions called central charges. Analytic continuation of these functions produces invariants of certain birational GLSM that are related to the original one by wall-crossing.

Posted September 11, 2023
Last modified January 7, 2025

3:30 pm Lockett 232

Allison Miller, Swarthmore
Algebra and topology in dimension four.

In order to understand and distinguish complicated topological spaces, we often compute algebraic invariants: if two spaces have different invariants, then they are certainly different themselves. (For example, for those who recognize them: the Euler characteristic of a surface, the Alexander polynomial of a knot, the fundamental group of a manifold.) But one might also wonder about the converse: are there algebraic invariants that completely determine something about the topological structure of a space? We will talk about this question in dimension four, where the answer is a resounding "Sometimes!". Knots, surfaces, and 4-dimensional spaces will all play important roles.

Posted September 5, 2023
Last modified October 9, 2023

3:30 pm Zoom (https://lsu.zoom.us/j/93676311052?pwd=ZnRuOGxMVGpIVjVvdzRLTGNSM05CQT09)

Camil Muscalu, Cornell University
A new approach to the Fourier Extension Problem for the paraboloid

The plan of the talk is to describe a new approach to the so-called Restriction Conjectures, that Itamar Oliveira and I have developed recently. Without entering into details, this new point of view allows one to prove that (essentially) all the relevant conjectures (linear or multi-linear) are true, provided that one of the functions involved has a tensor structure.

Tuesday, October 17, 2023

Posted October 12, 2023

Algebra and Number Theory Seminar Questions or comments?

2:00 pm – 2:45 pm TBA

Meeting of Full Professors

Posted September 4, 2023
Last modified October 15, 2023

2:30 pm – 3:20 pm Lockett 233 or click here to attend on Zoom

Tong Liu, Purdue University
Prismatic crystals and $p$-adic Galois representations

$p$-adic Galois representations are an important object and a very power tool in number theory. In this talk, I will explain how to use prismatic theory, recently developed by Bhatt and Scholze, to understand $p$-adic Galois representations. In particular, I will explain how to use prismatic crystal to understand crystalline and semi-stable $p$-adic local systems.

Posted September 11, 2023
Last modified October 1, 2023

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm Lockett 285

Allison Miller, Swarthmore
Teaching ethics and/or social justice in mathematics

This talk comes out of my experience teaching "Ethics in Mathematics" (Rice University, Spring 2021) and "Mathematics and Social Justice" (Swarthmore College, Spring 2022), both of which dealt with human aspects and impacts of mathematical practices in somewhat different ways. I will describe key content and "big questions" and lay out some considerations for those interested in developing similar courses, leaving plenty of time for questions and discussion.

Wednesday, October 18, 2023

Posted September 6, 2023
Last modified October 11, 2023

1:30 pm – 2:30 pm Lockett 233

Megan Fairchild, Louisiana State University
The Non-Oriented 4-Genus of Knots

The non-oriented 4-genus of a knot K in the three-sphere is defined to be the minimum first betti number of a surface F so that K bounds F. We will be discussing bounds on the non-oriented 4-genus given by knot invariants such as the signature and Arf invariant, as well as bounds given by unoriented band moves. We also will discuss obstructions to a knot bounding a Mobius band given by the double branched cover of the three-sphere branched over K.

Posted August 17, 2023
Last modified October 15, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Laura Wakelin, Imperial College London
Characterising slopes for knots of hyperbolic type

A slope p/q is characterising for a knot K in the 3-sphere if the oriented homeomorphism type of the manifold obtained by performing Dehn surgery of slope p/q on K uniquely determines the knot K. Sorya showed that for any knot K, there exists a constant C(K) such that any slope p/q with |q|≥C(K) is characterising for K. However, the proof of the existence of C(K) in the general case is non-constructive, which naturally evokes the question of how to compute explicit values for C(K). In this talk, I will explore methods for finding C(K) in the case where K is a knot of hyperbolic type (meaning that the JSJ decomposition of its complement has a hyperbolic outermost JSJ piece). This is ongoing joint work with Patricia Sorya.

Friday, October 20, 2023

Posted August 22, 2023
Last modified August 12, 2024

10:30 am – 11:20 am Zoom (click here to join)

Eduardo Cerpa, Pontificia Universidad Católica de Chile SIAM Activity Group on Control and Systems Theory Prize Recipient
Control and System Theory Methods in Neurostimulation

Electrical stimulation therapies are used to treat the symptoms of a variety of nervous system disorders. Recently, the use of high frequency signals has received increased attention due to its varied effects on tissues and cells. In this talk, we will see how some methods from Control and System Theory can be useful to address relevant questions in this framework when the FitzHugh-Nagumo model of a neuron is considered. Here, the stimulation is through the source term of an ODE and the level of neuron activation is associated with the existence of action potentials which are solutions with a particular profile. A first question concerns the effectiveness of a recent technique called interferential currents, which combines two signals of similar kilohertz frequencies intended to activate deeply positioned cells. The second question is about how to avoid the onset of undesirable action potentials originated when signals that produce conduction block are turned on. We will show theoretical and computational results based on methods such as averaging, Lyapunov analysis, quasi-static steering, and others.

Posted October 16, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:30 pm Lockett Hall 239 (or email zhiyuw at lsu.edu for Zoom link)

Linyuan Lu, University of South Carolina
Anti-Ramsey number of disjoint rainbow bases: from graphs to matroids

Motivated by our earlier work on the anti-Ramsey number of disjoint rainbow spanning trees on graphs, we generalize it to matroids. Consider a matroid $M=(E,\mathcal{I})$ with its elements of the ground set $E$ colored. A {\em rainbow basis} is a maximum independent set in which each element receives a different color. The {\em rank} of a subset $S$ of $E$, denoted by $r_M(S)$, is the maximum size of an independent set in $S$. A {\em flat} $F$ is a maximal set in $M$ with a fixed rank. The {\em anti-Ramsey} number of $t$ pairwise disjoint rainbow bases in $M$, denoted by $ar(M,t)$, is defined as the maximum number of colors $m$ such that there exists an $m$ coloring of the ground set $E$ of $M$ which contains no $t$ pairwise disjoint rainbow bases. We determine $ar(M,t)$ for all matroids.

Monday, October 23, 2023

Posted August 16, 2023
Last modified October 20, 2023

2:30 pm – 3:20 pm Lockett 233

Kendric Schefers, UC Berkeley
Microlocalization of homology

The difference between the homology and cohomology of a space can be seen as a measure of the singularity of that space. This measure can be made precise for special fibers of maps between smooth varieties by introducing the so-called "microlocal homology" of such a map, an object which records the singularities of the special fiber as well as the codirections along the base in which those singularities arise. In this talk, we show that the microlocal homology is in fact intrinsic to the special fiber—independent of its particular presentation—by relating it to an object of -1-shifted symplectic geometry: the canonical perverse sheaf categorifying Donaldson-Thomas invariants introduced by Joyce et al. Time permitting, we will relate the microlocal homology to the singular support theory of coherent sheaves.

Posted December 9, 2022
Last modified October 22, 2023

3:30 pm Lockett Hall 232

Nicolas Meunier, LaMME, Universite Evry Val D'Essonne
Mathematical analysis and numerical simulations on a model of cell motility

In this talk, I will present a model to describe some aspects of cell migration. Cell migration plays a key role in many physiological processes, such as embryogenesis, wound repair, or metastasis formation. It is the result of a complex activity that involves different time and space scales. I will first detail the construction of the model and then present rigorous results and numerical simulations.

Tuesday, October 24, 2023

Posted September 25, 2023

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm Lockett 232

Chuntian Wang, University of Alabama
On the impact of spatially heterogeneous human behavioral factors on 2D dynamics of infectious diseases

It is well observed that human natural and social behavior have non-negligible impacts on spread of contagious disease. For example, large scaling gathering and high level of mobility of population could lead to accelerated disease transmission, while public behavioral changes in response to pandemics may reduce infectious contacts. In order to understand spatial characteristics of epidemic outbreaks like clustering, we formulate a stochastic-statistical epidemic environment-human-interaction dynamic system, which will be called as SEEDS. In particular, a 2D agent-based biased-random-walk model with SEAIHR compartments set on a two-dimensional lattice is constructed. Two environment variables are taken into consideration to capture human natural and social behavioral factors, including population crowding effects, and public preventive measures in the presence of contagious transmissions. These two variables are assumed to guide and bias agent movement in a combined way. Numerical investigations imply that controlling mass mobility or promoting disease awareness can impede a global-scale spatial population aggregation to form, and consequently suppress disease outbreaks. Importance of coordinated public-health interventions and public compliance to these measures are explicitly demonstrated. A mechanistic interpretation of spatial geometric traits in progression of epidemic transmissions is provided through these findings, which may be useful for quantitative evaluations of a variety of public-health policies.

Wednesday, October 25, 2023

Posted September 6, 2023
Last modified October 24, 2023

1:30 pm – 2:30 pm Lockett 233

Jake Murphy, LSU
Bestvina Brady Morse Theory and Virtually Fibered Right-Angled Coxeter Groups

A group G is said to virtually algebraically fiber if there exists a finite index subgroup H and an epimorphism from H into Z with a finitely generated kernel. One technique used to show a group is virtually algebraically fibered is Bestvina-Brady Morse theory. In this talk I will give a brief introduction to Bestvina-Brady Morse theory and present a result by Jankiewicz, Norin, and Wise which shows that certain right-angled Coxeter groups are virtually algebraically fibered.

Posted August 20, 2023
Last modified October 12, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Amanda Wilkens, University of Texas
Poisson-Voronoi tessellations and fixed price in higher rank

We overview the cost of a group action and the ideal Poisson-Voronoi tessellation (IPVT), a new random limit with interesting geometric features. In recent work, we use the IPVT to prove all measure preserving and free actions of a higher rank semisimple Lie group on a standard probability space have cost 1, answering Gaboriau's fixed price question for this class of groups. This further implies results on the rank gradient and growth of first mod-p homology groups. We sketch a proof, which relies on some simple dynamics of the group action and the definition of a Poisson point process. No prior knowledge on cost or IPVTs will be assumed. This is joint work with Mikolaj Fraczyk and Sam Mellick.

Friday, October 27, 2023

Posted August 22, 2023
Last modified August 12, 2024

10:30 am – 11:20 am Zoom (click here to join)

Philip E. Paré, Purdue University
Modeling, Estimation, and Analysis of Epidemics over Networks

We present and analyze mathematical models for network-dependent spread. We use the analysis to validate a SIS (susceptible-infected-susceptible) model employing John Snow’s classical work on cholera epidemics in London in the 1850’s. Given the demonstrated validity of the model, we discuss control strategies for mitigating spread, and formulate a tractable antidote administration problem that significantly reduces spread. Then we formulate a parameter estimation problem for an SIR (susceptible-infected-recovered) networked model, where costs are incurred by measuring different nodes' states and the goal is to minimize the total cost spent on collecting measurements or to optimize the parameter estimates while remaining within a measurement budget. We show that these problems are NP-hard to solve in general and propose approximation algorithms with performance guarantees. We conclude by discussing an ongoing project where we are developing online parameter estimation techniques for noisy data and time-varying epidemics.

Posted October 23, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:30 pm Lockett Hall 239 (or email zhiyuw at lsu.edu for Zoom link)

James "Dylan" Douthitt, Louisiana State University
A matroid analogue of chordal graphs

A graph is chordal if every cycle of length four or more has a chord. In 1961, Dirac proved that a graph is chordal if and only if it can be built from complete graphs by repeated clique-unions. In this talk, I will describe a generalization of Dirac's result to binary matroids. This talk is based on joint work with James Oxley.

Monday, October 30, 2023

Posted August 11, 2023
Last modified October 22, 2023

2:30 pm – 3:20 pm 233 Lockett

Yan Zhou, Northeastern University
Irregular connections, Stokes geometry, and WKB analysis

We study the Riemann-Hilbert map of a class of meromorphic linear ODE systems on the complex projective line with irregular singularities. This class of ODE’s shows up in various contexts in geometry and representation theory. The Stokes matrices of these ODE’s encode the generalized monodromy data. First, we study the WKB leading terms of the Stokes matrices and give a definite answer for the degenerate Riemann-Hilbert map. Then, if time permits, we will establish the connection to the work of Gaiotto-Moore-Neitzke and explain how the picture of spectral networks and DT theory simplifies near the degenerate Riemann-Hilbert map. The talk is based on ongoing joint work with Anton Alekseev, Andrew Neitzke, and Xiaomeng Xu.

Posted September 1, 2023
Last modified October 13, 2023

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Zoom

Amir Sagiv, Technion Israel Institute of Technology
Floquet Hamiltonians - spectrum and dynamics

The last decade has witnessed tremendous experimental progress in the study of "Floquet media," crystalline materials whose properties are altered by time-periodic parametric forcing. Theoretical advancements, however, have so far been achieved through discrete and approximate models. Understanding these materials from their underlying, first-principle PDE models, however, remains an open problem. Specifically, semi-metals such as graphene are known to transform into insulators under periodic driving. While traditionally this phenomenon is modeled by a spectral gap, in PDE models no such gaps are conjectured to form. How do we reconcile these seemingly contradictory statements? We show that the driven Schrödinger equation possesses an “effective gap” – a novel and physically relevant relaxation of a spectral gap. Adopting a broader perspective, we study the influence of time-periodic forcing on a general band structure. A spectrally-local notion of stability is formulated and proven, using methods from periodic homogenization theory.

Tuesday, October 31, 2023

Posted August 22, 2023
Last modified September 24, 2023

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom

Kalani Thalagoda, Tulane University
Bianchi Modular Forms over $\mathbb{Q}(\sqrt{-17})$

Bianchi modular form are a generalization of classical modular forms defined over imaginary quadratic fields. A theory of modular symbols exists for computing Bianchi modular forms as Hecke eigensystems. However, when the class group of the imaginary quadratic field is nontrivial, modular symbol techniques only compute the principal part of the eigensystem. In this talk, I will explain how to extract a Hecke eigensystem for $\mathbb{Q}(\sqrt{-17})$, which has a class group of order $4$.

Posted October 23, 2023

3:30 pm – 4:30 pm Digital Media Center 1034

Summer Atkins, Louisiana State University
An Immuno-epidemiological Model of Foot-and-Mouth Disease in African Buffalo

We present a novel immuno-epidemiological model of Foot-and-Mouth Disease (FMD) in African buffalo host populations. Upon infection, the hosts can undergo two phases, namely the acute and the carrier stages. In our model, we divide the infectious population based upon these two stages so that we can dynamically capture the immunological characteristics of the disease and to better understand the carrier’s role in transmission. We first define the within-host immune kinetics dependent basic disease reproduction number and show that it is a threshold condition for the local stability of the disease-free equilibrium and existence of endemic equilibrium. By using a sensitivity analysis (SA) approach developed for multi-scale models, we assess the impact of the acute infection and carrier phase immunological parameters on the basic reproduction number. Interestingly, our numerical results show that the within-carrier infected host immune kinetics parameters and the susceptible individual recruitment rates play significant roles in disease persistence, which are consistent with experimental and field studies. This is joint work with Dr. Hayriye Gulbudak (University of Louisiana at Lafayette), Dr. Shane Welker (University of North Alabama), and Houston Smith (LSU). Further details: https://www.cct.lsu.edu/lectures/immuno-epidemiological-model-foot-and-mouth-disease-african-buffalo

Posted September 25, 2023
Last modified October 26, 2023

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm Zoom (Click “Questions or Comments?” to request a Zoom link)

Qi Feng, Florida State University
Entropy dissipation for general Langevin dynamics and its application

In this talk, I will discuss long-time dynamical behaviors of Langevin dynamics, including Langevin dynamics on Lie groups and mean-field underdamped Langevin dynamics. We provide unified Hessian matrix conditions for different drift and diffusion coefficients. This matrix condition is derived from the dissipation of a selected Lyapunov functional, namely the auxiliary Fisher information functional. We verify the proposed matrix conditions in various examples. I will also talk about the application in distribution sampling and optimization. This talk is based on several joint works with Erhan Bayraktar (University of Michigan) and Wuchen Li (University of South Carolina).

Wednesday, November 1, 2023

Posted September 6, 2023
Last modified October 29, 2023

1:30 pm – 2:30 pm Lockett 233

Krishnendu Kar, Louisiana State University
Glimpses on Virtual Knots and Virtual Knot Group

Virtual Knots are knots drawn on thickened surfaces, first introduced by Louis Kauffman. Virtual knots extend the study of classical knots by allowing crossings to become "virtual," which means they don't have a physical overpass or underpass. Instead, they can cross over without any physical connection. We extend the notion of knot equivalence (Reidemeister moves) to these knots to classify them. To distinguish between two virtual knots, we use virtual knot invariants analogous to classical knot invariants. One such invariant is the virtual knot group introduced by Boden in 2015, extending the idea of Wirtinger presentation. In this seminar, we will explore the properties of this virtual knot group and see examples of how this virtual knot invariant is useful.

Posted August 23, 2023
Last modified October 27, 2023

3:30 pm Lockett 233

Mustafa Hajij, University of San Francisco
Topological Deep Learning: Going Beyond Graph Data

Over the past decade, deep learning has been remarkably successful at solving a massive set of problems on datatypes including images and sequential data. This success drove the extension of deep learning to other discrete domains such as sets, point clouds, graphs, 3D shapes, and discrete manifolds. While many of the extended schemes have successfully tackled notable challenges in each domain, the plethora of fragmented frameworks have created or resurfaced many long-standing problems in deep learning such as explainability, expressiveness and generalizability. Moreover, theoretical development proven over one discrete domain does not naturally apply to the other domains. Finally, the lack of a cohesive mathematical framework has created many ad hoc and inorganic implementations and ultimately limited the set of practitioners that can potentially benefit from deep learning technologies. This talk introduces the foundation of topological deep learning, a rapidly growing field that is concerned with the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations including images and sequence data. It introduces the main notions while maintaining intuitive conceptualization, implementation and relevance to a wide range of practical applications. It also demonstrates the practical relevance of this framework with practical applications ranging from drug discovery to mesh and image segmentation.

Friday, November 3, 2023

Posted October 31, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:30 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)

Emily Heath, Iowa State University
Conflict-free hypergraph matchings and generalized Ramsey numbers

Given graphs $G$ and $H$ and a positive integer $q$, an $(H,q)$-coloring of $G$ is an edge-coloring in which each copy of $H$ receives at least $q$ colors. Erdős and Shelah raised the question of determining the minimum number of colors, $f(G,H,q)$, which are required for an $(H,q)$-coloring of $G$. Determining $f(K_n,K_p,2)$ for all $n$ and $p$ is equivalent to determining the classical multicolor Ramsey numbers. Recently, Mubayi and Joos introduced the use of a new method for proving upper bounds on these generalized Ramsey numbers; by finding a “conflict-free" matching in an appropriate auxiliary hypergraph, they determined the values of $f(K_n,n,C_4,3)$ and $f(K_n,K_4,5)$. In this talk, we will show how to generalize their approach to give bounds on the generalized Ramsey numbers for several families of graphs. This is joint work with Deepak Bal, Patrick Bennett, and Shira Zerbib.

Monday, November 6, 2023

Posted September 7, 2023
Last modified November 3, 2023

2:30 pm – 3:20 pm Lockett 233

Daniil Klyuev, MIT
Analytic Langlands correspondence for $G=PGL(2,\mathbb{C})$

Analytic Langlands correspondence was proposed by Etingof, Frenkel and Kazhdan based on ideas and results of Langlands, Teschner, Braverman-Kazhdan and Kontsevich. Let $X$ be a smooth irreducible projective curve over $\mathbb{C}$, $G$ be a semisimple group. On one side of this conjectural correspondence there are $G^{\vee}$-opers on $X$ satisfying a certain condition ($real$ opers), where $G^{\vee}$ is Langlands dual group. On the other side there are certain operators on $L^2(Bun_G)$, called Hecke operators, where $Bun_G$ is the variety of stable $G$-bundles on $X$ and $L^2(Bun_G)$ is a Hilbert space of square-integrable half-densities. I will describe the main picture and present new results in this direction. Partially based on joint projects with A. Wang and S. Raman.

Posted September 20, 2023
Last modified October 28, 2023

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett Hall 233

Burak Hatinoglu, Michigan State University
Quantum Graphs formulation of Elastic Beam Frames

Three-dimensional elastic frames constructed out of Euler-Bernoulli beams can be modeled as 4th order differential operators on metric graphs (also called quantum graphs). In 2021, Gregory Berkolaiko and Mahmood Ettehad formulated elastic beam frames with rigid joints as three-dimensional quantum graphs with 4th order Hamiltonians and self-adjoint vertex conditions. In this talk we will consider formulation of these quantum graph models and discuss their spectral properties in some special planar cases with periodic Hamiltonians. This talk is based on joint works with Mahmood Ettehad and Soohee Bae. (Host: Stephen Shipman)

Tuesday, November 7, 2023

Posted September 24, 2023
Last modified November 5, 2023

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom

Hui Xue, Clemson University
Coefficients of Hecke polynomials

Hecke operators play an important role in the theory of modular forms. Information about Hecke operators can be obtained through the study of their characteristic polynomials, the so-called Hecke polynomials. In this talk, I will discuss results on the nonvanishing and non-repetition properties of certain coefficients of Hecke polynomials.

Posted September 28, 2023
Last modified November 3, 2023

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm Lockett 232

Wasiur Khuda Bukhsh, University of Nottingham
Some approximations for stochastic epidemic models

I will talk about two approximations for stochastic compartmental models in infectious disease epidemiology. 1) Under the mass-action setup, I will discuss when one stochastic model can be approximated in some precise mathematical sense by another. In particular, I will provide error estimates in terms of a concentration inequality when an SEIR model is approximated by an SIR model. We will also consider the problem of parameter inference of such systems using notions of dynamical survival analysis (DSA). 2) The second approximation is a functional law of large numbers for an epidemic model on a configuration model random graph with interventions. No prior knowledge of epidemic models will be required.

Wednesday, November 8, 2023

Posted September 6, 2023
Last modified November 3, 2023

1:30 pm – 2:30 pm Lockett 233

Amit Kumar, Louisiana State University
Graph coloring via defect TFTs

This is the first talk in a series of two talks. I will begin by introducing how certain problems in mathematics can be interpreted as a local to global problem. First of these is the graph coloring problem where it is still less non-trivial to see. Second is the word problem in group theory, which has to be formulated as a local to global problem. The theory of bordism with defects and the corresponding TFT provide a common ground for both the problems. Next, I will review the concepts of TFT and Extended TFT. Finally, I will discuss the category of 2-Bordism with defects and its TFT. We will see in the second talk that both these problems have been approached by forming a bordism category for a given (finite) group together with a presentation.

Posted August 27, 2023
Last modified October 25, 2023

3:30 pm Lockett 233

Biji Wong, Duke University
Branched double covers of links in the 3-sphere, involutions, and bordered Floer theory

Branched double covers $\Sigma_2(L)$ of links $L$ in the 3-sphere are a nice tractable class of 3-manifolds that can be studied using Heegaard Floer theory. In this talk, we will discuss recent work to compute the Heegaard Floer d-invariants of $\Sigma_2(L)$ for L a 2-component plumbing link, using involutions and tools from bordered Floer theory. We will also give new families of links L where the d-invariants of $\Sigma_2(L)$ (in the spin structures) are determined by the signatures of L. This project is joint with J. Hanselman and M. Marengon.

Posted October 30, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Zoom

Gael Diebou, University of Toronto
Asymptotics and stability of global solutions to the Harmonic map heat flow

The harmonic map heat flow is the gradient flow of the standard energy of a given manifold-valued map. There are many existing well-posedness statements in the literature, all culminated in the (optimal) work by Wang who established local existence for initial data in $VMO$ (vanishing mean oscillations) and global existence for small data in $BMO$ (bounded mean oscillations). A natural question to ask is: What happens if the initial data has a large $BMO$-norm? More precisely, if there is an a priori global solution $u$, will $\nabla u$ ''grow'' at large times? In this talk, I will answer this question by showing that the gradient of an a priori global harmonic map arising from initial data in $VMO$ does not blow up at infinity; it decays. Moreover, this smallness at infinity implies a stability result for solutions constructed by Wang.

Friday, November 10, 2023

Posted January 18, 2023
Last modified August 12, 2024

10:30 am 233 Lockett Hall and Zoom (click here to join)

Maruthi Akella, University of Texas Fellow of AIAA, IEEE, and AAS
Sub-Modularity Measures for Learning and Robust Perception in Aerospace Autonomy

Onboard learning and robust perception can be generally viewed to characterize autonomy as overarching system-level properties. The complex interplay between autonomy and onboard decision support systems introduces new vulnerabilities that are extremely hard to predict with most existing guidance and control tools. In this seminar, we review some recent advances in learning-oriented and information-aware path- planning, and sub-modularity metrics for non-myopic sensor scheduling for “plug-and- play” systems. The concept of “learning-oriented” path-planning is realized through certain new classes of exploration inducing distance metrics. These technical foundations will be highlighted through aerospace applications with active learning inside dynamic and uncertain environments.

Posted November 7, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:30 pm Lockett Hall 239 (or email zhiyuw at lsu.edu for Zoom link)

James Anderson , Georgia Institute of Technology
Borel line graphs

We characterize Borel line graphs in terms of 10 forbidden induced subgraphs, namely the 9 finite graphs from the classical result of Beineke together with a 10th infinite graph associated to the equivalence relation $\E_0$ on the Cantor space. As a corollary, we prove a partial converse to the Feldman--Moore theorem, which allows us to characterize all locally countable Borel line graphs in terms of their Borel chromatic numbers. (We will give an overview of the necessary descriptive set theory background so that the talk is accessible to a general combinatorics audience).

Monday, November 13, 2023

Posted August 12, 2023
Last modified November 3, 2023

2:30 pm – 3:20 pm Lockett 233

Jonathan Gruber, University of York
Generic direct summands of tensor products for algebraic groups

Let G be a connected reductive algebraic group. The representation theory of G revolves around four important classes of G-modules: The simple modules, the Weyl modules, the induced modules and the indecomposable tilting modules. In this talk, I will explain how complexes of tilting modules can be used to study tensor products of G-modules, and show that this approach gives rise to a new class of G-modules, called generic direct summands of tensor products.

Posted September 6, 2023
Last modified November 11, 2023

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Zoom: https://lsu.zoom.us/j/96047132782

Ivan Veselić, Technical University of Dortmund
Spectral inequalities and parabolic observability for Schrodinger operators with unboundedly growing potentials

For the heat equation on $\mathbb R^d$ it is known that the heat equation is observable from a sensor set if and only if the set is thick. For (sufficiently regular) bounded domains, observability of the heat equation holds already if the sensor set has positive Lebesgue measure. We discuss these results and subsequently consider a third class of models lying between the two just mentioned and motivated by kinetic theory. The semigroup generator is a Schrodinger operator with a quadratic or some other regularly growing potential. We identify classes of sensors sets leading to observability and null controllability. In particular, in some cases finite volume sensor sets are allowed, even though the con figuration space is unbounded. This is joint work with Alexander Dicke and Albrecht Seelmann.

Tuesday, November 14, 2023

Posted September 4, 2023
Last modified November 10, 2023

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom

Jason Gaddis, Miami University
Ozone groups of noncommutative algebras

The ozone group of a noncommutative algebra is defined as the group of algebra automorphisms which fix every element of its center. This functions like a kind of Galois group for the algebra. In this talk, I will discuss the ozone group in the context of PI Artin–Schelter regular algebras and its applications to characterizing skew polynomial rings and their centers.

Posted November 8, 2023
Last modified November 13, 2023

3:30 pm Lockett 232

Nathan Glatt-Holtz, Tulane University
Statistical inference for high dimensional parameters from PDE constrained data: theoretical and computational developments

The Bayesian approach to inverse problems provides a principled and flexible methodology for the estimation of high dimensional unknown parameters appearing in partial differential equations. This methodology therefore represents an important frontier for statistical inference from sparse and noise corrupted data arising in physics informed settings. This talk will overview this emerging field and survey some of our recent and ongoing work in this domain. Specifically we will (i) Describe some new model PDE inference problems related to the measurement of fluid flow. (ii) Overview developments in Markov Chain Monte Carlo (MCMC) sampling methods which partially beat the curse of dimensionality and which are indispensable for resolving a wide variety of problems including the models in (i). (iii) Describe some results concerning consistency-namely the concentration of posterior measures around the true value of the unknown parameter-in the large data limit for `infinite dimensional' PDE-informed models. This is joint work with Jeff Borggaard (Virginia Tech), Christian Frederiksen (Tulane), Andrew Holbrook (UCLA), Justin Krometis (Virginia Tech), and Cecilia Mondaini (Drexel).

Posted October 27, 2023

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Digital Media Center 1034

Andrew Hicks, Louisiana State University
TBA

Wednesday, November 15, 2023

Posted September 6, 2023
Last modified November 13, 2023

1:30 pm – 2:30 pm Lockett 233

Amit Kumar, Louisiana State University
TFT with defects and applications

Even though this is the second talk in the series, the first talk is NOT a prerequisite. A QFT assigns a number to a closed n-manifold and a vector space to a codimension-1 submanifolds. An (1-)extended QFT assigns a number to a closed n-manifolds, a vector space to a codimension-1 submanifolds and a 1-category to a codimension 2 submanifolds. Defects arise when considering QFT with background fields, where it manifests itself as a stable singularity of certain functions (background fields.) On a physical level, defects allow existence of regions with different theories. A very good example of a defect is the phase-diagram of water: the three lines separates three phases each with its own (different) physics. We first formulate a TFT with defects as a field theory of manifolds with defects and then use these ideas to reformulate graph coloring problem and word problem.

Posted September 6, 2023
Last modified November 1, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Federico Salmoiraghi, Queen's University
Surgery on Anosov flows using bi-contact geometry

An example of the beautiful intertwine between hyperbolic dynamics, foliation theory, and contact geometry is given by an Anosov flow. Geometrically an Anosov flow is defined by two transverse invariant foliations with expanding and contracting behaviors. Much of our understanding of the structure of an Anosov flow relies on the study of the leaves space of the invariant foliations. Mitsumatsu first noticed that an Anosov vector field also belongs to the intersection of two transverse contact structures rotating towards each other. After giving the necessary background, I will show how to use this point of view to address questions in the theory of surgery on Anosov flows.

Friday, November 17, 2023

Posted September 2, 2023
Last modified August 12, 2024

10:30 am – 11:20 am Zoom (click here to join)

Sean Meyn, University of Florida Robert C. Pittman Eminent Scholar Chair, IEEE Fellow, IEEE CSS Distinguished Lecturer
Stochastic Approximation and Extremum Seeking Control

Stochastic approximation was introduced in the 1950s to solve root finding problems, of which optimization is a canonical application. It is argued in recent work that extremum seeking control (ESC), a particular approach to gradient-free optimization with an even longer history, can be cast as quasi-stochastic approximation (QSA). In this lecture, we will go through the basics of these (until now) disparate fields. Application of QSA theory to ESC leads to several significant conclusions, including that ESC is not globally stable, as examples show. Careful application of QSA theory leads to new algorithms that are stable without any loss of performance. Also, QSA theory immediately provides asymptotic and transient bounds, providing guidelines for algorithm design. In addition to surveying this general theory, the talk provides a tutorial on design principles through numerical studies.

Posted November 13, 2023

2:30 pm – 3:30 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)

Jagdeep Singh, Binghamton University, State University of New York
Apex Graphs and Cographs

A class of graphs is called hereditary if it is closed under taking induced subgraphs. Its apex class is defined as the class of graphs G that contain a vertex v such that G-v is in the hereditary class. In recent work, Vaidy Sivaraman, Tom Zaslavsky, and I showed that if a hereditary class has finitely many forbidden induced subgraphs, then so does its apex class. I will talk about this result and its matroid analogue.

Monday, November 20, 2023

Posted September 3, 2023
Last modified November 17, 2023

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Zoom: https://lsu.zoom.us/j/93252478608

Yannick Sire, Johns Hopkins University
Geometric variational problems: regularity vs singularity formation

I will describe in a very informal way some techniques to deal with the existence ( and more qualitatively regularity vs singularity formation) in different geometric problems and their heat flows motivated by (variations of) the harmonic map problem, the construction of Yang-Mills connections or nematic liquid crystals. I will emphasize in particular on recent results on the construction of very fine asymptotics of blow-up solutions via a new gluing method designed for parabolic flows. I’ll describe several open problems and many possible generalizations, since the techniques are rather flexible.

Tuesday, November 28, 2023

Posted September 24, 2023
Last modified November 26, 2023

2:30 pm – 3:20 pm Lockett 233 or click here to attend on Zoom
(Originally scheduled for 3:20 pm)

Hongdi Huang, Rice University
Twisting Manin's universal quantum groups and comodule algebras

Symmetry is an important concept that appears in mathematics and theoretical physics. While classical symmetries arise from group actions on polynomial rings, quantum symmetries are introduced to understand certain quantum objects (e.g., quantum groups) which appear in the theory of quantum mechanics and quantum field theory. In this talk, we will define Manin's universal quantum groups and its 2-cocycle twist. Moreover, we will talk about the invariants under the tensor equivalence of quantum symmetries.

Posted September 28, 2023
Last modified October 13, 2023

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm DMC 1034

Sara Pollock, University of Florida
Filtered Anderson Acceleration for Nonlinear PDE

Anderson acceleration (AA) has become increasingly popular in recent years due to its efficacy on a wide range of problems, including optimization, machine learning and complex multiphysics simulations. In this talk, we will discuss recent innovations in the theory and implementation of the algorithm. AA requires the storage of a (usually) small number of solution and update vectors, and the solution of an optimization problem that is generally posed as least-squares and solved efficiently by a thin QR decomposition. On any given problem, how successful it is depends on the details of its implementation, including how many and which of the solution and update vectors are used. We will introduce a filtered variant of the algorithm that improves both numerical stability and convergence by selectively removing columns from the least-squares matrix at each iteration. We will discuss the theory behind the introduced filtering strategy and connect it to one-step residual bounds for AA using standard tools and techniques from numerical linear algebra. We will demonstrate the method on discretized nonlinear PDE.

Wednesday, November 29, 2023

Posted September 6, 2023
Last modified November 28, 2023

1:30 pm – 2:30 pm Lockett 233

Gurleen Nanda, Louisiana State University
Moduli space of local systems and higher Teichmüller theory

Let G be a split semisimple algebraic group over $\mathbb{Q}$ and S be a compact oriented surface with or without boundary. In this talk we will introduce the $\mathcal{L}_{G,S}$ moduli space of G($\mathbb{C}$)-local systems on S. When S has holes we define a dual pair of local systems $\mathcal{X}_{G,S}$, $\mathcal{A}_{G,S}$, both carry positive atlas equivariant with respect to the action of mapping class group. In the remainder of the talk we will use positive configurations of flags to construct co-ordinate system on $\mathcal{X}_{G,S}$.

Posted October 12, 2023

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Basile Coron, Queen Mary University of London
Operadic structures and matroid invariants

We will begin with a general discussion on operadic structures, and then show that many well-known matroid invariants come naturally equipped with such structures. Applying the general tools of operadic theory such as Grobner bases and Koszul duality will shed new light on those invariants.

Friday, December 1, 2023

Posted September 29, 2023
Last modified August 12, 2024

10:30 am – 11:20 am Zoom (click here to join)

Hélène Frankowska, Sorbonne University
Differential Inclusions on Wasserstein Spaces

Optimal control in Wasserstein spaces addresses control of systems with large numbers of agents. It is well known that for optimal control of ODEs, the differential inclusions theory provides useful tools to investigate existence of optimal controls, necessary optimality conditions and Hamilton-Jacobi- Bellman equations. Recently, many models arising in social sciences used the framework of Wasserstein spaces, i.e. metric spaces of Borel probability measures endowed with the Wasserstein metric. This talk is devoted to a recent extension given in [1] of the theory of differential inclusions to the setting of general Wasserstein spaces. In the second part of the talk, necessary and sufficient conditions for the existence of solutions to state-constrained continuity inclusions in Wasserstein spaces, whose right-hand sides may be discontinuous in time, are provided; see [2]. These latter results are based on a fine investigation of the infinitesimal behavior of the underlying reachable sets, which heuristically amounts to showing that up to a negligible set, every admissible velocity can be realized as the metric derivative of a solution of the continuity inclusion, and vice versa. Building on these results, necessary and sufficient geometric conditions for the viability and invariance of stationary and time-dependent constraints, which involve a suitable notion of contingent cones in Wasserstein spaces, are established. Viability and invariance theorems in a more restrictive framework were already applied in [5], [6] to investigate stability of controlled continuity equations and uniqueness of solutions to HJB equations. The provided new tools allow us to get similar results in general Wasserstein spaces. References: [1] BONNET B. and FRANKOWSKA H., Caratheodory Theory and a Priori Estimates for Continuity Inclusions in the Space of Probability Measures, preprint https://arxiv.org/pdf/2302.00963.pdf, 2023. [2] BONNET B. and FRANKOWSKA H., On the Viability and Invariance of Proper Sets under Continuity Inclusions in Wasserstein Spaces, SIAM Journal on Mathematical Analysis, to appear. [3] BONNET B. and FRANKOWSKA H., Differential inclusions in Wasserstein spaces: the Cauchy-Lipschitz framework, Journal of Diff. Eqs. 271: 594-637, 2021. [4] BONNET B. and FRANKOWSKA H., Mean-field optimal control of continuity equations and differential inclusions, Proceedings of 59th IEEE Conference on Decision and Control, Republic of Korea, December 8-11, 2020: 470-475, 2020. [5] BONNET B. and FRANKOWSKA H., Viability and exponentially stable trajectories for differential inclusions in Wasserstein spaces, Proceedings of 61st IEEE Conference on Decision and Control, Mexico, December 6-9, 2022: 5086-5091, 2022. [6] BADREDDINE Z. and FRANKOWSKA H., Solutions to Hamilton-Jacobi equation on a Wasserstein space, Calculus of Variations and PDEs 81: 9, 2022.

Posted November 28, 2023

Control and Optimization Seminar Questions or comments?

2:30 pm – 3:30 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)

Ruth Luo, University of South Carolina
Long cycles in 2-connected hypergraphs

Dirac proved that every $n$-vertex, $2$-connected graph with minimum degree $\delta$ contains a cycle of length at least $\min\{n, 2\delta\}$. In this talk we present an analog for a long Berge cycles in uniform hypergraphs. In particular, the minimum degree condition required differs dramatically if the size of the edges is small or large. This is joint work with Alexandr Kostochka and Grace McCourt.

Friday, December 8, 2023

Posted September 8, 2023
Last modified August 12, 2024

10:30 am – 11:20 am Zoom (click here to join)

Meeko Oishi, University of New Mexico NSF BRITE Fellow
Human-Centered Probabilistic Planning and Control

Although human interaction with autonomous systems is becoming ubiquitous, few tools exist for planning and control of autonomous systems that account for human uncertainty and decision making. We seek methods for probabilistic verification and control that can help ensure compatibility of autonomous systems with human decision making and human uncertainty. This requires the development of theory and computational tools that can accommodate arbitrary, non-Gaussian uncertainty for both probabilistic verification and control, potentially without high confidence models. This talk will focus on our work in probabilistic verification of ReLU neural nets, data-driven stochastic optimal control and stochastic reachability. Our approaches to probabilistic verification are based in Fourier transforms and chance constrained optimization, and our approaches to data-driven stochastic planning and control are based in conditional distribution embeddings. Both of these approaches enable computation without gridding, sampling, or recursion. We also present recent work on data-driven tools for high fidelity modeling and characterization of human-in-the-loop trajectories, that accommodate dynamic processes with probabilistic human inputs.

Monday, December 11, 2023

Posted September 4, 2023
Last modified December 1, 2023

Joint control and optimization seminar and applied analysis seminar

3:30 pm – 4:30 pm https://lsu.zoom.us/j/98451981288

Piermarco Cannarsa, Università degli studi di Roma "Tor Vergata"
Generalised characteristics of Hamilton-Jacobi equations, propagation of singularities, and long-time behaviour

A generalised characteristic (GC) is a solution of certain differential inclusions that play a crucial role for propagation of singularities of solutions to Hamilton-Jacobi equations $H(x,u(x),Du(x))=0$. GC's were introduced in (D1977), in the context of hyperbolic conservation laws and then adapted to Hamilton-Jacobi equations in (AC2002) and (CY2009). In this talk, we will discuss several topics related to GC's including restricted classes of characteristics introduced in (KS2016), uniqueness issues, continuation properties in connection with propagation of singularities (CC2017). Then, for mechanical systems on the torus, that is, \begin{equation*} \frac 12|Du(x)|^2+V(x)=\alpha \\end{equation*} we will study the long time behaviour of GC's. By using limiting occupational measures, we will show that the critical set of $u$ is an approximate attractor for the GC flow. We will also give a criterion to decide whether, asymptotically, a GC is almost surely either singular or arbitrarily close to the regular critical set of $u$. \bigskip {\bf\large References} \medskip \begin{itemize} \item[(AC2002)] Albano, P., Cannarsa, P.: Propagation of singularities for solutions of nonlinear first order partial differential equations. Arch. Ration. Mech. Anal. 162(1), 1-23 (2002) \item[(CC2017)] Cannarsa, P., Cheng, W.: Generalized characteristics and Lax-Oleinik operators: global theory. Calc. Var. Partial Differ. Equ. 56(5), 31 (2017) \item[(CY2009)] Cannarsa, P., Yifeng, Yu.: Singular dynamics for semiconcave functions. J. Eur. Math. Soc. (JEMS) 11(5), 999-1024 (2009) \item[(D1977)] Dafermos, C.M.: Generalized characteristics and the structure of solutions of hyperbolic conservation laws. Indiana Univ. Math. J. 26(6), 1097-1119 (1977) \item[(KS2016)] Khanin, K., Sobolevski, A.: On dynamics of Lagrangian trajectories for Hamilton-Jacobi equations. Arch. Ration. Mech. Anal. 219(2), 861-885 (2016) \end{itemize}

Posted October 10, 2023
Last modified December 2, 2023

Joint Applied Analysis and Control and Optimization Seminar

3:30 pm Zoom Seminar at https://lsu.zoom.us/j/98451981288

Piermarco Cannarsa, Università degli studi di Roma "Tor Vergata"
Generalised Characteristics of Hamilton-Jacobi Equations, Propagation of Singularities, and Long-Time Behaviour

See https://lsu.box.com/s/8sw1vxst7xy7tw9hr6bk6jkvlqns8pqk for details.

Friday, January 5, 2024

Posted November 16, 2023

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Applied Math

Tuesday, January 9, 2024

Posted November 16, 2023
Last modified January 9, 2024

1:00 pm – 4:00 pm Monday, January 8, 2024 Lockett Hall 277
(Originally scheduled for Monday, January 8, 2024, 1:00 pm)

Written Qualifier Exam on Algebra

Wednesday, January 10, 2024

Posted November 16, 2023

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Analysis

Friday, January 12, 2024

Posted November 16, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Topology

Wednesday, January 17, 2024

Posted January 18, 2024

1:30 pm

Organizational

Posted January 13, 2024
Last modified January 15, 2024

3:30 pm Lockett 233

Justin Murray, Louisiana State University
The homotopy cardinality of the representation category for a Legendrian knot

Given a Legendrian knot in R^3 one can assign a combinatorial invariants called ruling polynomials. These invariants have been shown to recover not only a (normalized) count of augmentations, but are also closely related to a categorical count of augmentations in the form of the homotopy cardinality of the augmentation category. In this talk, we will introduce the homotopy cardinality of the n-dimensional representation category and establish its relation to the n-colored ruling polynomial. Along the way, we establish that two n-dimensional representations are equivalent in the representation category iff they are ''conjugate DGA homotopic''. We also provide some applications to Lagrangian concordance.

Friday, January 19, 2024

Posted January 17, 2024

11:00 am DMC 1014

Meet & Greet with the SCALA 2024 Invited Speakers

Posted October 13, 2023

Control and Optimization Seminar Questions or comments?

1:00 pm – 4:00 pm Saturday, January 20, 2024 Digital Media Center Theatre

Scientific Computing Around Louisiana (SCALA) 2024

https://www.cct.lsu.edu/SCALA2024

Monday, January 22, 2024

Posted January 11, 2024
Last modified August 12, 2024

11:30 am – 12:20 pm Zoom (click here to join)

Boris Mordukhovich, Wayne State University AMS Fellow, SIAM Fellow
Optimal Control of Sweeping Processes with Applications

This talk is devoted to a novel class of optimal control problems governed by sweeping (or Moreau) processes that are described by discontinuous dissipative differential inclusions. Although such dynamical processes, strongly motivated by applications, first appeared in the 1970s, optimal control problems for them have only been formulated quite recently and were found to be complicated from the viewpoint of developing control theory. Their study and applications require advanced tools of variational analysis and generalized differentiation, which will be presented in this talk. Combining this machinery with the method of discrete approximations leads us to deriving new necessary optimality conditions and their applications to practical models in elastoplasticity, traffic equilibria, and robotics. This talk is based on joint work with Giovanni Colombo (University of Padova), Dao Nguyen (San Diego State University), and Trang Nguyen (Wayne State University).

Posted October 15, 2023
Last modified January 10, 2024

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Robert Sims, University of Arizona
Stability of the Bulk Gap for Models with Frustration-Free Ground States

We prove that uniformly small short-range perturbations do not close the bulk gap above the ground state of frustration-free quantum spin systems that satisfy a local topological quantum order condition. In contrast with earlier results, we do not require a positive lower bound for finite-system Hamiltonians uniform in the system size. To obtain this result, we adapt the Bravyi-Hastings-Michalakis strategy to the GNS representation of the infinite-system ground state. This is joint work with Bruno Nachtergaele (University of California, Davis) and Amanda Young (University of Illinois, Urbana-Champaign).

Tuesday, January 23, 2024

Posted November 13, 2023
Last modified January 21, 2024

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom

Rena Chu, Duke University
Generalizations of the Schrödinger maximal operator: building arithmetic counterexamples

In 2016 Bourgain applied Gauss sums to construct a counterexample related to a decades-old question in PDEs. The story started in 1980 when Carleson asked about how "smooth" an initial data function must be to imply pointwise convergence for the solution of the linear Schrödinger equation. After progress by many authors, this was resolved by Bourgain, whose counterexample construction proved a necessary condition on the regularity, and Du and Zhang, who proved a sufficient condition. Bourgain's methods were number-theoretic, and this raised a natural question: could number-theoretic properties of other exponential sums have implications for other dispersive PDEs? We develop a flexible new method to construct counterexamples for analogues of Carleson's question. In particular, this applies the Weil bound for exponential sums, a consequence of the truth of the Riemann Hypothesis over finite fields.

Wednesday, January 24, 2024

Posted January 18, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233

Nilangshu Bhattacharyya, Louisiana State University
Characteristic Classes

Posted January 12, 2024
Last modified January 18, 2024

3:30 pm Lockett 233

Megan Fairchild, Louisiana State University
Non-orientable 4- genus of knots

The non-orientable 4-genus of a knot K in the three-sphere is defined to be the minimum first Betti number of a surface F so that K bounds F. We will survey the tools used to compute the non-orientable 4-genus and use various techniques to calculate this invariant for non-alternating 11 crossing knots. We also will view obstructions to a knot bounding a Mobius band given by the double branched cover of the three-sphere branched over K.

Friday, January 26, 2024

Posted January 19, 2024

2:00 pm – 3:00 pm Lockett Hall 233

Chun-Hung Liu, Texas A&M University
Assouad-Nagata dimension of minor-closed metrics

Assouad-Nagata dimension addresses both large-scale and small-scale behaviors of metric spaces and is a refinement of Gromov’s asymptotic dimension. A metric space is a minor-closed metric if it is defined by the distance function on the vertices of an edge-weighted graph that satisfies a fixed graph property preserved under vertex-deletion, edge-deletion, and edge-contraction. In this talk, we determine the Assouad-Nagata dimension of every minor-closed metric. It is a common generalization of known results about the asymptotic dimension of H-minor free unweighted graphs, about the Assouad-Nagata dimension of complete Riemannian surfaces of finite Euler genus, and about their corollaries on weak diameter coloring of minor-closed families of graphs and asymptotic dimension of minor-excluded groups.

Monday, January 29, 2024

Posted November 29, 2023
Last modified January 26, 2024

Algebra and Number Theory Seminar Questions or comments?

3:30 am – 4:30 pm https://lsu.zoom.us/j/92777480012

Blair Davey, Montana State University
On Landis' conjecture in the plane

In the late 1960s, E.M. Landis made the following conjecture: If $u$ and $V$ are bounded functions, and $u$ is a solution to the Schr\"odinger equation $\Delta u - V u = 0$ in $\mathbb{R}^n$ that decays like $|u(x)| \le c \exp(- C |x|^{1+})$, then $u$ must be identically zero. In 1992, V. Z. Meshkov disproved this conjecture by constructing bounded, complex-valued functions $u$ and $V$ that solve the Schr\"odinger equation in the plane and satisfy $|u(x)| \le c \exp(- C |x|^{4/3})$. The examples of Meshkov were accompanied by qualitative unique continuation estimates for solutions in any dimension. Meshkov's estimates were quantified in 2005 by J. Bourgain and C. Kenig. These results, and the generalizations that followed, have led to a fairly complete understanding of these unique continuation properties in the complex-valued setting. However, Landis' conjecture remains open in the real-valued setting. We will discuss a recent result of A. Logunov, E. Malinnikova, N. Nadirashvili, and F. Nazarov that resolves the real-valued version of Landis' conjecture in the plane.

Tuesday, January 30, 2024

Posted November 13, 2023
Last modified January 21, 2024

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom

Zhongkai Mi, Louisiana State University
The Lowest Discriminant Ideals of Cayley-Hamilton Hopf Algebras

Discriminant ideals for an algebra $A$ module finite over a central subring $C$ are indexed by positive integers. We study the lowest of them with nonempty zero set in Cayley Hamilton Hopf algebras whose identity fibers are basic algebras. Key results are obtained by considering actions of characters in the identity fiber on irreducible modules over maximal ideals of $C$ and actions of winding automorphisms. We apply these results to examples in group algebras of central extensions of abelian groups, big quantum Borel subalgebras at roots of unity and quantum coordinate rings at roots of unity. This is joint work with Quanshui Wu and Milen Yakimov.

Posted January 25, 2024

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 232

Changhong Mou, University of Wisconsin-Madison
Reduced Order Modeling in the Age of Data

Abstract: Data-driven modeling of complex dynamical systems is becoming increasingly popular across various domains of science and engineering. In this talk, I will introduce a systematic multiscale data-driven closure reduced order model (ROM) framework for complex systems with strong chaotic or turbulent behavior. I will utilize available data to construct novel ROM closure terms, thereby capturing the interaction between resolved and unresolved modes. Next, I will explain how the new data-driven closure ROM can be integrated with a conditional Gaussian data assimilation framework that employs cost-effective, conditionally linear functions to capture the statistical features of the closure terms. This leads to the stochastic data-driven closure ROM that facilitates an efficient and accurate scheme for nonlinear data assimilation (DA), the solution of which is provided by closed analytic formulae that do not require ensemble methods. It also allows the ROM to avoid many potential numerical and sampling issues in recovering the unobserved states from partial observations. Furthermore, I will introduce a hybrid DA algorithm for complex dynamical systems with partial observations. The method exploits cheap stochastic parameterized ROMs for filtering the observed state variables, significantly reducing the computational cost. It also uses machine learning to build a nonlinear map between observed and unobserved state variables, which enables the efficient computation of the ensemble members of the unobserved states. The hybrid DA algorithm is successfully applied to a precipitating quasi-geostrophic (PQG) model, which includes the effects of water vapor, clouds, and rainfall beyond the classical two-level QG model.

Wednesday, January 31, 2024

Posted January 18, 2024

1:30 pm Lockett 233

Adithyan Pandikkadan, Louisiana State University
Characteristic Classes

Posted January 24, 2024

3:30 pm – 4:30 pm Lockett 232

Phuc Nguyen, Louisiana State University
Poincar\'e-Sobolev's inequalities for the class of $\mathcal{A}$-superharmonic functions

I will discuss about (weighted) Poincar\'e-Sobolev's inequalities for the class of $\mathcal{A}$-superharmonic functions which are solutions, possibly singular, to a class of quasi-linear elliptic equations with nonnegative measure data. A feature of these inequalities is that they hold for a wide range of exponents and a large class of weights over Boman/John domains. This talk is based on joint work with Seng-Kee Chua.

Posted January 12, 2024
Last modified January 22, 2024

3:30 pm Lockett 233

Achinta Nandi, Oklahoma State University
On perturbations of singular complex analytic curves

Suppose $V$ is a singular complex analytic curve inside $\mathbb{C}^{2}$. We investigate when a singular or non-singular complex analytic curve $W$ inside $\mathbb{C}^{2}$ with sufficiently small Hausdorff distance $d_{H}(V, W)$ from $V$ must intersect $V$. We obtain a sufficient condition on $W$ which when satisfied gives an affirmative answer to our question. More precisely, we show the intersection is non-empty for any such $W$ that admits at most one non-normal crossing type discriminant point associated with some proper projection. As an application, we prove a special case of the higher-dimensional analog, and also a holomorphic multifunction analog of a result by Lyubich-Peters \cite{Lyubich-Peters14}. We shall also prove another special case of the higher dimensional analog of the result by Lyubich-Peters.

Thursday, February 1, 2024

Posted January 25, 2024

3:30 pm – 4:30 pm Lockett 232

Michael Novack, Carnegie Mellon
Soap films, Plateau's laws, and the Allen-Cahn equation

Abstract: Plateau's problem of minimizing area among surfaces with a common boundary is the basic model for soap films and leads to the theory of minimal surfaces. In this talk we will discuss a modification of Plateau's problem in which surfaces are replaced with regions of small but positive volume. The model captures features of real soap films that cannot be described by minimal surfaces, and the corresponding analysis requires the development of new ideas in geometric measure theory. We will also discuss the PDE approximation of this problem via the Allen-Cahn equation and its relation to Plateau's laws, which govern singularities in soap films.

Friday, February 2, 2024

Posted January 28, 2024

2:00 pm – 3:00 pm Lockett Hall 233

Yiwei Ge, Louisiana State University
Oriented diameter of near planar triangulations

The oriented diameter of an undirected graph $G$ is the smallest diameter over all the strongly connected orientations of $G$. A near planar triangulation is a planar graph such that every face except possibly the outer face is a triangle. In this talk, we will show that the oriented diameter of all $n$-vertex near planar triangulations(except seven small exceptions) is bounded by $\lceil \frac{n}{2}\rceil$, and the bound is tight. Joint work with Xiaonan Liu and Zhiyu Wang.

Posted January 31, 2024

Control and Optimization Seminar Questions or comments?

2:30 pm – 3:30 pm Zoom

Bruno Poggi, Universitat Autònoma de Barcelona
Two problems in the mathematical physics of the magnetic Schrödinger operator and their solutions via the landscape function.

Abstract. In two papers in the 90's, Zhongwei Shen studied non-asymptotic bounds for the eigenvalue counting function of the magnetic Schrödinger operator, as well as the localization of eigenfunctions. But in dimensions 3 or above, his methods required a strong scale-invariant quantitative assumption on the gradient of the magnetic field; in particular, this excludes many singular or irregular magnetic fields, and the questions of treating these later cases had remained open, giving rise to a problem and a conjecture. This strong assumption on the gradient of the magnetic field has appeared also in the harmonic analysis related to the magnetic Schrödinger operator. In this talk, we present our solutions to these questions, and other new results on the exponential decay of solutions (eigenfunctions, integral kernels, resolvents) to Schrödinger operators. We will introduce the Filoche-Mayboroda landcape function for the (non-magnetic) Schrödinger operator, present its pointwise equivalence to the classical Fefferman-Phong-Shen maximal function (also known as the critical radius function in harmonic analysis literature), and then show how one may use directionality assumptions on the magnetic field to construct a new landscape function in the magnetic case. We resolve the problem and the conjecture of Z. Shen (and recover other results in the irregular setting) by putting all these observations together.

Monday, February 5, 2024

Posted February 2, 2024
Last modified August 12, 2024

11:30 am – 12:20 pm Zoom (click here to join)

Ali Kara, University of Michigan
Stochastic Control with Partial Information: Optimality, Stability, Approximations and Learning

Partially observed stochastic control is an appropriate model for many applications involving optimal decision making and control. In this talk, we will first present a general introduction and then study optimality, approximation, and learning theoretic results. For such problems, existence of optimal policies have in general been established via reducing the original partially observed stochastic control problem to a fully observed one with probability measure valued states. However, computing a near-optimal policy for this fully observed model is challenging. We present an alternative reduction tailored to an approximation analysis via filter stability and arrive at an approximate finite model. Toward this end, we will present associated regularity and Feller continuity, and controlled filter stability conditions: Filter stability refers to the correction of an incorrectly initialized filter for a partially observed dynamical system with increasing measurements. We present explicit conditions for filter stability which are then utilized to arrive at approximately optimal solutions. Finally, we establish the convergence of a learning algorithm for control policies using a finite history of past observations and control actions (by viewing the finite window as a 'state') and establish near optimality of this approach. As a corollary, this analysis establishes near optimality of classical Q-learning for continuous state space stochastic control problems (by lifting them to partially observed models with approximating quantizers viewed as measurement kernels) under weak continuity conditions. Further implications and some open problems will also be discussed.

Posted September 22, 2023
Last modified January 25, 2024

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett 232

Eduard-Wilhelm Kirr, University of Illinois Urbana-Champagne
Can one find all coherent structures supported by a wave equation?

I will present a new mathematical technique aimed at discovering all coherent structures supported by a given nonlinear wave equation. It relies on global bifurcation analysis which shows that, inside the Fredholm domain, the coherent structures organize themselves into manifolds which either form closed surfaces or must reach the boundary of this domain. I will show how one can find all the limit points at the Fredholm boundary for the Nonlinear Schrodinger/Gross-Pitaevskii Equation. Then I will use these limit points to uncover all coherent structures and their bifurcation points.

Tuesday, February 6, 2024

Posted November 13, 2023
Last modified February 2, 2024

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom

Rajat Gupta, University of Texas at Tyler
On summation formulas attached to Hecke's functional equation and $p$-Herglotz functions

In this talk, we will review the work of Chandrasekharan and Narasimhan on the theory of Hecke’s functional equation (with one gamma factor) and the summation formulas of various kinds, such as the Voronoi summation formula, the Poisson summation formula, and the Abel-Plana summation formula. We will then give recent developments in this theory followed by some new results and summation formulas in the setting of Hecke’s functional equation analogous to the ones mentioned above. In particular, I will discuss these summation formulas in the case of cusp corms of weight $2k$ attached to the modular group ${\rm SL}_2(\mathbb{Z})$. Finally, I will also talk about on my recent work with Rahul Kumar on Herglotz functions and their analogues.

Posted February 1, 2024
Last modified February 2, 2024

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 232

Narek Hovsepyan, Rutgers University
On the lack of external response of a nonlinear medium in the second-harmonic generation process.

Abstract: Second Harmonic Generation (SHG) is a process in which the input wave (e.g. laser beam) interacts with a nonlinear medium and generates a new wave, called the second harmonic, at double the frequency of the original input wave. We investigate whether there are situations in which the generated second harmonic wave does not scatter and is localized inside the medium, i.e., the nonlinear interaction of the medium with the probing wave is invisible to an outside observer. This leads to the analysis of a semilinear elliptic system formulated inside the medium with non-standard boundary conditions. More generally, we set up a mathematical framework needed to investigate a multitude of questions related to the nonlinear scattering problem associated with SHG (or other similar multi-frequency optical phenomena). This is based on a joint work with F. Cakoni, M. Lassas and M. Vogelius.

Wednesday, February 7, 2024

Posted January 18, 2024

1:30 pm Lockett 233

Colton Sandvick, Louisiana State University
Characteristic Classes

Posted February 3, 2024

3:30 pm – 4:30 pm Zoom

Cody Stockdale, Clemson University
On the Calderón-Zygmund theory of singular integrals

Calderón and Zygmund's seminal work on singular integral operators has greatly influenced modern harmonic analysis. We begin our discussion with some classical aspects of CZ theory, including examples and applications, and then focus on the crucial weak-type (1,1) estimate for CZ operators. We investigate techniques for obtaining weak-type inequalities that use the CZ decomposition and ideas inspired by Nazarov, Treil, and Volberg. We end with an application of these methods to the study of the Riesz transforms in high dimensions.

Posted December 5, 2023
Last modified January 31, 2024

3:30 pm Lockett 233

Steven Sivek, Imperial College London
Rational homology 3-spheres and SL(2,C) representations

Building on non-vanishing theorems of Kronheimer and Mrowka in instanton Floer homology, Zentner proved that if Y is a homology 3-sphere other than S^3, then its fundamental group admits a homomorphism to SL(2,C) with non-abelian image. In this talk, I’ll explain how to generalize this to any Y whose first homology is 2-torsion or 3-torsion, other than #^n RP^3 for any n or lens spaces of order 3. This is joint work with LSU’s own Sudipta Ghosh and with Raphael Zentner.

Friday, February 9, 2024

Posted January 28, 2024

2:00 pm – 3:00 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)

Sam Spiro, Rutgers University
The Random Tur\'an Problem

Let $G_{n,p}$ denote the random $n$-vertex graph obtained by including each edge independently and with probability $p$. Given a graph $F$, let $\mathrm{ex}(G_{n,p},F)$ denote the size of a largest $F$-free subgraph of $G_{n,p}$. When $F$ is non-bipartite, the asymptotic behavior of $\mathrm{ex}(G_{n,p},F)$ was determined in breakthrough work done independently by Conlon-Gowers and by Schacht. In this talk we discuss some recent results for bipartite $F$ (where much less is known), as well as for the analogous problem for $r$-partite $r$-graphs.

Posted January 25, 2024
Last modified January 31, 2024

3:30 pm Lockett 232

Ali Kara, University of Michigan
Reinforcement Learning in Non-Markovian Environments under General Information Structures

Abstract: For decision-making under uncertainty, typically only an ideal model is assumed, and the control design is based on this given model. However, in reality, the assumed model may not perfectly reflect the underlying dynamics, or there might not be an available mathematical model. To overcome this issue, one approach is to use the past data of perceived state, cost and control trajectories to learn the model or the optimal control functions directly, a method also known as reinforcement learning. The majority of the existing literature has focused on methods structured for systems where the underlying state process is Markovian and the state is fully observed. However, there are many practical settings where one works with data and does not know the possibly very complex structure under which the data is generated and tries to respond to the environment. In this talk, I will present a convergence theorem for stochastic iterations, particularly focusing on Q-learning iterates, under a general, possibly non-Markovian, stochastic environment. I will then discuss applications of this result to the decision making problems where the agent's perceived state is a noisy version of some hidden Markov state process, i.e. partially observed MDPs, and when the agent keeps track of a finite memory of the perceived data. I will also discuss applications for a class of continuous-time controlled diffusion problems.

Friday, February 16, 2024

Posted February 11, 2024

2:00 pm – 3:00 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)

Youngho Yoo, Texas A&M University
Minimum degree conditions for apex-outerplanar minors

Motivated by Hadwiger's conjecture, we study graphs H for which every graph with minimum degree at least |V(H)|-1 contains H as a minor. We prove that a large class of apex-outerplanar graphs satisfies this property. Our result gives the first examples of such graphs whose vertex cover numbers are significantly larger than a half of its vertices, and recovers all known such graphs that have arbitrarily large maximum degree. If time permits, we discuss how our proof can be adapted to directed graphs to show that every directed graph with minimum out-degree at least t contains a certain orientation of the wheel and of every apex-tree on t+1 vertices as a subdivision and a butterfly minor respectively. Joint work with Chun-Hung Liu.

Posted February 15, 2024

3:30 pm – 4:30 pm Zoom

Meeting of the Professorial Faculty

Monday, February 19, 2024

Posted February 12, 2024

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm 232 Lockett Hall

Ke Chen, University of Maryland
Towards efficient deep operator learning for forward and inverse PDEs: theory and algorithms

Abstract: Deep neural networks (DNNs) have been a successful model across diverse machine learning tasks, increasingly capturing the interest for their potential in scientific computing. This talk delves into efficient training for PDE operator learning in both the forward and inverse PDE settings. Firstly, we address the curse of dimensionality in PDE operator learning, demonstrating that certain PDE structures require fewer training samples through an analysis of learning error estimates. Secondly, we introduce an innovative DNN, the pseudo-differential auto-encoder integral network (pd-IAE net), and compare its numerical performance with baseline models on several inverse problems, including optical tomography and inverse scattering. We will briefly mention some future works at the end, focusing on the regularization of inverse problems in the context of operator learning.

Tuesday, February 20, 2024

Posted February 5, 2024
Last modified February 14, 2024

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom

Hasan Saad, University of Virginia
Distributions of points on hypergeometric varieties

In the 1960's, Birch proved that the traces of Frobenius for elliptic curves taken at random over a large finite field is modeled by the semicircular distribution (i.e., $SU(2),$ the usual Sato-Tate for non-CM elliptic curves). In this talk, we show how the theory of harmonic Maass forms and modular forms allow us to determine the limiting distribution of normalized traces of Frobenius over families of varieties. For Legendre elliptic curves, the limiting distribution is $SU(2),$ whereas for a certain family of $K3$ surfaces, the limiting distribution is $O(3).$ Since the $O(3)$ distribution has vertical asymptotes, we show how to obtain an explicit result by bounding the error. Additionally, we show how to count "matrix" points on these varieties and therefore determine the limiting distributions for these "matrix points."

Wednesday, February 21, 2024

Posted February 20, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm – 2:00 pm Zoom

Meeting of the Professorial Faculty

Posted January 18, 2024

1:30 pm Lockett 233

Shea Vela-Vick, Louisiana State University
Characteristic Classes

Posted January 15, 2024
Last modified February 18, 2024

3:30 pm Lockett 233

Jake Murphy, LSU
Subgroups of Coxeter groups and Stallings folds

Stallings introduced a technique called a fold to study subgroups of free groups. These folds allow us to associate labeled graphs to subgroups of free groups, which in turn provide solutions to algorithmic questions about these subgroups, and Dani and Levcovitz generalized these techniques to the setting of right-angled Coxeter groups. In this talk, we will generalize these techniques to subgroups of general Coxeter groups by creating a labeled cell complex for a given subgroup. We will show that these complexes characterize the index of a subgroup and whether a subgroup is normal. Finally, we will construct a complex corresponding to the intersection of two subgroups and use this to determine whether subgroups of right-angled Coxeter groups are malnormal.

Friday, February 23, 2024

Posted February 17, 2024

Control and Optimization Seminar Questions or comments?

2:00 pm – 3:00 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)

Yixuan Huang, Vanderbilt University
Even and odd cycles through specified vertices

Cycles through specified vertices generalize Hamilton cycles. Given a vertex subset of a graph , we define the local connectivity on $\kappa_G(X)$ by $\min_{x,y \in X} \kappa_G(x,y)$, where $\kappa_G(x,y)$ is the minimum number of vertices or edges separating $x$ and $y$, and by Menger’s theorem, equal to the maximum number of internally disjoint $xy$-paths. We prove that if a vertex subset $X$ satisfies $\kappa_G(X) \ge k \ge3$ and $|X| > k$, then there is an even cycle through any $k$ vertices of $X$. In addition, if the block containing $X$ is non-bipartite, there is an odd cycle through any $k$ vertices of $X$. Our results extend the results based on ordinary connectivity due to Bondy and Lovász. As a corollary, we prove the existence of cycles through a particular subset in the prism graph.

Monday, February 26, 2024

Posted December 28, 2023
Last modified August 12, 2024

11:30 am – 12:20 pm Zoom (click here to join)

Huyên Pham Editor-in-Chief for SIAM Journal on Control and Optimization, 2024-
A Schrödinger Bridge Approach to Generative Modeling for Time Series

We propose a novel generative model for time series based on Schrödinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure consistent with the joint data distribution of the time series. The solution is characterized by a stochastic differential equation on finite horizon with a path-dependent drift function, hence respecting the temporal dynamics of the time series distribution. We estimate the drift function from data samples by nonparametric, e.g. kernel regression methods, and the simulation of the SB diffusion yields new synthetic data samples of the time series. The performance of our generative model is evaluated through a series of numerical experiments. First, we test with autoregressive models, a GARCH Model, and the example of fractional Brownian motion, and measure the accuracy of our algorithm with marginal, temporal dependencies metrics, and predictive scores. Next, we use our SB generated synthetic samples for the application to deep hedging on real-data sets.

Tuesday, February 27, 2024

Posted November 14, 2023
Last modified February 27, 2024

Algebra and Number Theory Seminar Questions or comments?

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom

Eleanor McSpirit, University of Virginia
Infinite Families of Quantum Modular 3-Manifold Invariants

In 1999, Lawrence and Zagier established a connection between modular forms and the Witten-Reshetikhin-Turaev invariants of 3-manifolds by constructing q-series whose radial limits at roots of unity recover these invariants for particular manifolds. These q-series gave rise to some of the first examples of quantum modular forms. Using a 3-manifold invariant recently developed Akhmechet, Johnson, and Krushkal, one can obtain infinite families of quantum modular invariants which realize the series of Lawrence and Zagier as a special case. This talk is based on joint work with Louisa Liles.

Wednesday, February 28, 2024

Posted February 26, 2024

3:30 pm – 4:30 pm Online Zoom

Yaghoub Rahimi, Georgia Institute of Technology
AVERAGES OVER THE GAUSSIAN PRIMES: GOLDBACH’S CONJECTURE AND IMPROVING ESTIMATES

In this discussion we will establish a density version of the strong Goldbach conjecture for Gaussian integers, restricted to sectors in the complex plane.

Posted January 12, 2024
Last modified February 21, 2024

3:30 pm Lockett 233

Maddalena Pismataro, University of Bologna
Cohomology rings of abelian arrangements

Abelian arrangements are generalizations of hyperplane and toric arrangements, whose complements cohomology rings have been studied since the 70’s. We introduce the complex hyperplane case, proved by Orlik and Solomon (1980), and the real case, Gelfand-Varchenko (1987). Then, we describe toric arrangements, showing results due to De Concini and Procesi (2005) and to Callegaro, D ’Adderio, Delucchi, Migliorini, and Pagaria (2020). Finally, we discuss a new technique to prove the Orlik-Solomon and De Concini-Procesi relations from the Gelfand-Varchenko ring and to provide a presentation of the cohomology ring of the complements of all abelian arrangements. This is a join work with Evienia Bazzocchi and Roberto Pagaria.

Friday, March 1, 2024

Posted February 25, 2024

Mathematical Physics and Representation Theory Seminar

2:00 pm – 3:00 pm Lockett Hall 233

Scott Baldridge, Louisiana State University
Using quantum states to understand the four-color theorem

The four-color theorem states that a bridgeless plane graph is four-colorable, that is, its faces can be colored with four colors so that no two adjacent faces share the same color. This was a notoriously difficult theorem that took over a century to prove. In this talk, we generate vector spaces from certain diagrams of a graph with a map between them and show that the dimension of the kernel of this map is equal to the number of ways to four-color the graph. We then generalize this calculation to a homology theory and in doing so make an interesting discovery: the four-color theorem is really about all of the smooth closed surfaces a graph embeds into and the relationships between those surfaces. The homology theory is based upon a topological quantum field theory. The diagrams generated from the graph represent the possible quantum states of the graph and the homology is, in some sense, the vacuum expectation value of this system. It gets wonderfully complicated from this point on, but we will suppress this aspect from the talk and instead show a fun application of how to link the Euler characteristic of the homology to the famous Penrose polynomial of a plane graph. This talk will be hands-on and the ideas will be explained through the calculation of easy examples! My goal is to attract students and mathematicians to this area by making the ideas as intuitive as possible. Topologists and representation theorists are encouraged to attend also—these homologies sit at the intersection of topology, representation theory, and graph theory. This is joint work with Ben McCarty.

Monday, March 4, 2024

Posted January 16, 2024
Last modified February 28, 2024

2:30 pm – 3:20 pm 233 Lockett

Ben McCarty, University of Memphis
A new approach to the four color theorem

The Penrose polynomial of a graph, originally defined by Roger Penrose in an important 1971 paper, shares many similarities with Kauffman’s bracket and the Jones polynomial. In order to capitalize on these similarities, we first modify the definition of the Penrose polynomial to obtain a related family of polynomials, called the n-color polynomials. Each of the n-color polynomials may be thought of as an analog of the Jones polynomial, and is the graded Euler characteristic of a bigraded homology theory (analogous to Khovanov homology). We then show how to define a spectral sequence leading to a filtered homology theory (analogous to Lee homology) where coloring information becomes apparent. We will then discuss several applications of the theory to graph coloring and the four color problem. This is joint work with Scott Baldridge.

Posted February 20, 2024
Last modified March 2, 2024

Pasquale Porcelli Lecture Series Special Lecture Series

3:30 pm – 4:30 pm Atchafalaya Room, LSU Student Union or Zoom (click here to join)

R. Tyrrell Rockafellar, University of Washington
Risk and Uncertainty in Optimization

Abstract: New mathematics is on the forefront in many emerging areas of technology, and its methods for sorting out ideas and testing for truth and shortcomings are as vital as ever. This talk aims to explain how that has worked in confronting “risk”. Problems of optimization are concerned with deciding things “optimally”. In many situations in management, finance, and engineering design, however, plans have to be fixed in the present without knowing fully how they will play out in the future. A future cost or hazard may depend on random variables with probability distributions that a present decision can only influence in a limited way. Should optimization then rely on average outcomes? Worst-case outcomes? High-probability avoidance of dangerous outcomes? Or what? This is a subject with a history of competing approaches that reached a turning point with the axiomatic development of a powerful theory of risk. The mathematical concepts and results from that have been overturning tradition in one important area of application after another.

Tuesday, March 5, 2024

Posted February 20, 2024
Last modified March 2, 2024

Pasquale Porcelli Lecture Series Special Lecture Series

2:30 pm – 3:30 pm Hill Memorial Library or Zoom (click here to join)

R. Tyrrell Rockafellar, University of Washington
Variational Analysis and Geometry

The theory needed for problems of optimization has required vast developments of a kind of alternative calculus in which, for instance, discontinuous functions that might take on infinite values nonetheless have “subgradients” which are highly useful. In maximizing and minimizing, variables are often required to be nonnegative, or to have values not too high or too low. This leads to a fascinatingly different nonclassical kind of geometry.

Posted November 13, 2023
Last modified March 3, 2024

Algebra and Number Theory Seminar Questions or comments?

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom

Edmund Yik-Man Chiang, The Hong Kong University of Science and Technology
Discrete special functions: a D-modulus approach to special functions

We show that there is a holonomic D-modules (PDEs) approach to classical special functions, as such both the classical special functions and their difference analogues, some have only been found recently, can be efficiently computed by Weyl-algebraic framework. According to Truesdell, rudiments of algebraic approaches to special functions were already observed by some nineteenth century mathematicians. This algebraic method does not use well-known Lie algebra theory explicity apart from basic knowledge of solving linear PDEs. We illustrate our method with Bessel functions in this talk. We shall also explain the connection with this D-modules approach with recent advances in Nevanlinna theories for difference operators, which have its roots from discrete Painleve equations.

Posted January 18, 2024

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:20 pm Digital Media Center: Room 1034

Soeren Bartels, University of Freiburg, Germany
Babuska's paradox in linear and nonlinear bending theories

The plate bending or Babuska paradox refers to the failure of convergence when a linear bending problem with simple support boundary conditions is approximated using polygonal domain approximations. We provide an explanation based on a variational viewpoint and identify sufficient conditions that avoid the paradox and which show that boundary conditions have to be suitably modified. We show that the paradox also matters in nonlinear thin-sheet folding problems and devise approximations that correctly converge to the original problem.

Wednesday, March 6, 2024

Posted January 18, 2024
Last modified March 3, 2024

1:30 pm Lockett 233

Justin Murray, Louisiana State University
Singularities of Legendrian manifolds, isotopies, and applications to cellular contact homology.

In this talk, I will review the work of Arnold on singularities and caustics. Along the way, we will review when these 3-dimensional singularities give rise to 2-dimensional Legendrian isotopies and when they do not. After this, we will provide a complete list of base projections for these resolved singularities. This list will exclude various bifurcations of the base projection that are whose sheets are "far enough" apart. Time permitting, I will discuss how one can apply these to cellular Legendrian contact homology.

Posted February 20, 2024
Last modified March 2, 2024

Pasquale Porcelli Lecture Series Special Lecture Series

2:30 pm – 3:30 pm Hill Memorial Library or Zoom (click here to join)

R. Tyrrell Rockafellar, University of Washington
Variational Convexity and Local Optimality

For necessary and sufficient conditions for local optimality, the inherited ideal has been for them to be as close to each other as possible. In optimization, however, what’s more important is sufficient conditions that identify key common features in a problem which support algorithmic developments. Variational convexity, although only recently identified as such a condition, appears to be fundamentally important.

Posted January 9, 2024
Last modified February 27, 2024

3:30 pm Lockett 233

Jone Lopez de Gamiz Zearra, Vanderbilt University
On subgroups of right-angled Artin groups

In this talk we will discuss subgroups of right-angled Artin groups (RAAGs for short). Although, in general, subgroups of RAAGs are known to have a wild structure and bad algorithmic behaviour, we will show that under certain conditions they have a tame structure. Firstly, we will discuss finitely generated normal subgroups of RAAGs and show that they are co-(virtually abelian). As a consequence, we deduce that they have decidable algorithmic problems. Secondly, we will recall results of Baumslag-Roseblade and Bridson-Howie-Miller-Short on subgroups of direct products of free groups and explain how they generalize to other classes of RAAGs.

Thursday, March 7, 2024

Posted September 29, 2023
Last modified January 29, 2024

3:30 pm – 4:20 pm Lockett 232

Jacob Rasmussen, University of Illinois Urbana-Champaign
The L-space conjecture for 3-manifolds

The L-space conjecture of Boyer-Gordon-Watson and Juhasz relates three very different properties that a closed 3-manifold M can possess. One of these properties is algebraic: is \pi_1(M) left orderable? The second is geometric: does the M admit a coorientable taut foliation? The third is analytic: is the Heegaard Floer homology M as simple as it can be, given the size of H_1(M). If the conjecture is true, it would reveal the existence of a striking dichotomy for rational homology 3-spheres. In this talk, I'll explain what each of the three conditions appearing in the L-space conjecture mean, and then discuss efforts to prove and disprove it, and why we should care.

Friday, March 8, 2024

Posted March 3, 2024

2:00 pm – 3:00 pm Lockett Hall 233 (simulcasted via Zoom)

Hailun Zheng, University of Houston-Downtown
Polytope and spheres: the enumeration and reconstruction problems

Consider a simplicial d-polytope P or a simplicial (d-1)-sphere P with n vertices. What are the possible numbers of faces in each dimension? What partial information about P is enough to reconstruct P up to certain equivalences? In this talk, I will introduce the theory of stress spaces developed by Lee. I will report on recent progress on conjectures of Kalai asserting that under certain conditions one can reconstruct P from the space of affine stresses of P ---- a higher-dimensional analog of the set of affine dependencies of vertices of P. This in turn leads to new results in the face enumeration of polytopes and spheres; in particular, a strengthening of (the numerical part of) the g-theorem. Joint work with Satoshi Murai and Isabella Novik.

Saturday, March 9, 2024

Posted March 3, 2024

Control and Optimization Seminar Questions or comments?

until Monday, March 11, 2024

Southern Regional Number Theory Conference : Celebrating 10 Years!

https://www.math.lsu.edu/~srntc/nt2024/

Monday, March 18, 2024

Posted January 22, 2024
Last modified March 4, 2024

11:30 am – 12:20 pm Zoom (click here to join)

Dante Kalise, Imperial College
Feedback Control Synthesis for Interacting Particle Systems across Scales

This talk focuses on the computational synthesis of optimal feedback controllers for interacting particle systems operating at different scales. In the first part, we discuss the construction of control laws for large-scale microscopic dynamics by supervised learning methods, tackling the curse of dimensionality inherent in such systems. Moving forward, we integrate the microscopic feedback law into a Boltzmann-type equation, bridging controls at microscopic and mesoscopic scales, allowing for near-optimal control of high-dimensional densities. Finally, in the framework of mean field optimal control, we discuss the stabilization of nonlinear Fokker-Planck equations towards unstable steady states via model predictive control.

Posted March 5, 2024

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:20 pm 233 Lockett

Pablo Boixeda Alvarez, Yale University
Microlocal sheaves and affine Springer fibers

The resolutions of Slodowy slices $\tilde{\mathcal{S}}_e$ are symplectic varieties that contain the Springer fiber $(G/B)_e$ as a Lagrangian subvariety. In joint work with R. Bezrukavnikov, M. McBreen, and Z. Yun, we construct analogues of these spaces for homogeneous affine Springer fibers. We further understand the categories of microlocal sheaves in these symplectic spaces supported on the affine Springer fiber as some categories of coherent sheaves. In this talk, I will mostly focus on the case of the homogeneous element $ts$ for $s$, a regular semisimple element, and will discuss some relations of these categories with the small quantum group providing a categorification of joint work with R.Bezrukavnikov, P. Shan and E. Vasserot. If I have time, I will then mention some recent application of this result to the Breuil-Mezard conjecture by T. Feng and B. Le Hung.

Wednesday, March 20, 2024

Posted January 18, 2024
Last modified April 2, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Jake Murphy, LSU
Incoherent Coxeter groups

A group is coherent if every finitely generated subgroup is also finitely presented. In this talk, we will cover results of Jankiewicz and Wise showing that many Coxeter groups are incoherent using Bestvina-Brady Morse theory.

Posted November 29, 2023
Last modified March 20, 2024

3:30 pm – 4:30 pm Lockett 233

Katherine Raoux, University of Arkansas
A 4-dimensional rational genus bound

The minimal genus question asks: “What is the minimum genus of a surface representing a particular 2-dimensional homology class?” Historically, minimal genus questions have focused on 2-dimensional homology with integer coefficients. In this talk, we consider a minimal genus question for homology classes with Q mod Z coefficients. We define the rational 4-genus of knots and present a lower bound in terms of Heegaard Floer tau invariants. Our bound also leads to PL slice genus bounds. This is joint work with Matthew Hedden.

Posted January 24, 2024
Last modified March 13, 2024

3:30 pm – 4:30 pm Lockett 232

Alan Chang, Washington University in St. Louis
Venetian blinds, digital sundials, and efficient coverings

Davies's efficient covering theorem states that we can cover any measurable set in the plane by lines without increasing the total measure. This result has a dual formulation, known as Falconer's digital sundial theorem, which states that we can construct a set in the plane to have any desired projections, up to null sets. The argument relies on a Venetian blind construction, a classical method in geometric measure theory. In joint work with Alex McDonald and Krystal Taylor, we study a variant of Davies's efficient covering theorem in which we replace lines with curves. This has a dual formulation in terms of nonlinear projections.

Thursday, March 21, 2024

Posted January 20, 2024
Last modified February 5, 2024

3:30 pm – 4:20 pm Lockett 232

Chongying Dong, UC Santa Cruz
Monstrous moonshine and orbifold theory

This introductory talk will survey the recent development of the monstrous moonshine. Conjectured by McKay-Thompson-Conway-Norton and proved by Borcherds, the moonshine conjecture reveals a deep connection between the largest sporadic finite simple group Monster and genus zero functions. From the point of view of vertex operator algebra, moonshine is a connection among finite groups, vertex operator algebras and modular forms. This talk will explain how the moonshine phenomenon can be understood in terms of orbifold theory.

Friday, March 22, 2024

Posted March 20, 2024

Control and Optimization Seminar Questions or comments?

2:00 pm – 3:00 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)

Enrique Gomez-Leos , Iowa State University
On a problem of Erdős and Gyárfás

Given positive integers n,p,q, where p≤n, 1≤q≤(p choose 2), a (p,q)-coloring of the complete graph Kn is an edge coloring of Kn in which every clique on p vertices has at least q colors appearing in its edges. Let f(n,p,q) be the minimum number of colors needed for a (p,q)-coloring on Kn. Erdős and Gyárfás originally posed the question in 1997 and determined a general upper bound. In addition to determining the linear and quadratic threshold, they also showed that 5/6(n-1) ≤ f(n,4,5) ≤ n. Recently, Mubayi and Joos introduced a new method for proving upper bounds on these generalized Ramsey numbers; by finding a “conflict-free" matching in an appropriate auxiliary hypergraph, they determined the value of f(n,4,5) to be 5/6n + o(n). In this talk, we will introduce recent improvements to f(n,5,8). Indeed, we show that f(n,5,8) ≥ 6/7(n-1) and discuss how to use the conflict-free hypergraph matching method to show that f(n,5,8) ≤ n + o(n). This is joint work with Emily Heath, Coy Schwieder, Alex Parker, and Shira Zerbib.

Monday, March 25, 2024

Posted February 12, 2024
Last modified March 4, 2024

10:30 am – 11:20 am Note the Special Earlier Seminar Time For Only This Week. This is a Zoom Seminar. Zoom (click here to join)

Antoine Girard, Laboratoire des Signaux et Systèmes CNRS Bronze Medalist, IEEE Fellow, and George S. Axelby Outstanding Paper Awardee
Switched Systems with Omega-Regular Switching Sequences: Application to Switched Observer Design

In this talk, I will present recent results on discrete-time switched linear systems. We consider systems with constrained switching signals where the constraint is given by an omega-regular language. Omega-regular languages allow us to specify fairness properties (e.g., all modes have to be activated an infinite number of times) that cannot be captured by usual switching constraints given by dwell-times or graph constraints. By combining automata theoretic techniques and Lyapunov theory, we provide necessary and sufficient conditions for the stability of such switched systems. In the second part of the talk, I will present an application of our framework to observer design of switched systems that are unobservable for arbitrary switching. We establish a systematic and "almost universal" procedure to design observers for discrete-time switched linear systems. This is joint work with Georges Aazan, Luca Greco and Paolo Mason.

Posted February 17, 2024
Last modified March 18, 2024

3:30 pm Lockett 232

Samuel Punshon-Smith, Tulane University
Annealed mixing and spectral gap for advection by stochastic velocity fields

We consider the long-time behavior of a passive scalar advected by an incompressible velocity field. In the dynamical systems literature, if the velocity field is autonomous or time periodic, long-time behavior follows by studying the spectral properties of the transfer operator associated with the finite time flow map. When the flow is uniformly hyperbolic, it is well known that it is possible to construct certain anisotropic Sobolev spaces where the transfer operator becomes quasi-compact with a spectral gap, yielding exponential decay in these spaces. In the non-autonomous and non-uniformly hyperbolic case this approach breaks down. In this talk, I will discuss how in the stochastic velocity setting one can recover analogous results under expectation using pseudo differential operators to obtain exponential decay of solutions to the transport equation from $H^{-\delta}$ to $H^{-\delta}$ -- a property we call annealed mixing. As a result, we show that the Markov process obtained by considering the advection diffusion equation with a source term has an $H^{-\delta}$ Wasserstein spectral gap, uniform in diffusivity, and that the stationary measure has a unique limit in the zero diffusivity limit. This is a joint work with Jacob Bedrossian and Patrick Flynn.

Tuesday, March 26, 2024

Posted January 29, 2024

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:20 pm Digital Media Center: Room 1034

Henrik Schumacher, University of Georgia
Repulsive Curves and Surfaces

Repulsive energies were originally constructed to simplify knots in $\mathbb{R}^3$. The driving idea was to design energies that blow up to infinity when a time-dependent family of knots develops a self-intersection. Thus, downward gradient flows should simplify a given knot without escaping its knot class. In this talk I will focus on a particular energy, the so-called \emph{tangent-point energy}. It can be defined for curves as well as for surfaces. After outlining its geometric motivation and some of the theoretical results (existence, regularity), I will discuss several hardships that one has to face if one attempts to numerically optimize this energy, in particular in the surface case. As we will see, a suitable choice of Riemannian metric on the infinite-dimensional space of embeddings can greatly help to deal with the ill-conditioning that arises in high-dimensional discretizations. I will also sketch briefly how techniques like the Barnes-Hut method can help to reduce the algorithmic complexity to an extent that allows for running nontrivial numerical experiments on consumer hardware. Finally (and most importantly), I will present a couple of videos that employ the gradient flows of the tangent-point energy to visualize some stunning facts from the field of topology. Although some high tier technicalities will be mentioned (e.g., fractional Sobolev spaces and fractional differential operators), the talk should be broadly accessible, also to undergrad students of mathematics and related fields.

Wednesday, March 27, 2024

Posted January 18, 2024
Last modified March 31, 2024

1:30 pm Lockett 233

Neal Stoltzfus, Mathematics Department, LSU
The Free Differential Calculus tool to study Braid Automorphisms

This talk will survey applications of the Jacobian and Hessian in the free differential calculus to the study of automorphisms in low dimensions, particularly braids. This is a central technical tool in my talk next Wed. We will develop the homology of covering spaces of surfaces with boundary (ribbon graphs), study braid automorphisms using the Jacobian of the Artin map image of a braid in the free differential calculus following Birman and Cohen-Suciu. The Burau representation will be developed (with the Lawrence-Krammer-Bigelow representation explored next week). The second part of the talk will cover (Lefschetz-Poincare) duality from the free differential calculus perspective using an analog of the Hessian.

Posted December 1, 2023
Last modified March 22, 2024

3:30 pm Lockett 233

Katherine Goldman, Ohio State University
CAT(0) and cubulated Shephard groups

Shephard groups are common generalizations of Coxeter groups, Artin groups, graph products of cyclic groups, and (certain) complex reflection groups. We extend a well-known result that Coxeter groups are CAT(0) to a class of Shephard groups that have “enough” finite parabolic subgroups. We also show that in this setting, if the underlying Coxeter diagram is type FC, then the Shephard group is cubulated (i.e., acts properly and cocompactly on a CAT(0) cube complex). Our method of proof combines the works of Charney-Davis on the Deligne complex for an Artin group and of Coxeter on the classification and properties of the regular complex polytopes. Along the way we introduce a new criteria (based on work of Charney) for a simplicial complex made of simplices of shape A_3 to be CAT(1).

Thursday, March 28, 2024

Posted March 19, 2024

Control and Optimization Seminar Questions or comments?

3:30 pm Digital Media Center 1034

Yue Yu, Lehigh University
Nonlocal operator is all you need

During the last 20 years there has been a lot of progress in applying neural networks (NNs) to many machine learning tasks. However, their employment in scientific machine learning with the purpose of learning physics of complex system is less explored. Differs from the other machine learning tasks such as the computer vision and natural language processing problems where a large amount of unstructured data are available, physics-based machine learning tasks often feature scarce and structured measurements. In this talk, we will take the learning of heterogeneous material responses as an exemplar problem, to investigate the design of neural networks for physics-based machine learning. In particular, we propose to parameterize the mapping between loading conditions and the corresponding system responses in the form of nonlocal neural operators, and infer the neural network parameters from high-fidelity simulation or experimental measurements. As such, the model is built as mappings between infinite-dimensional function spaces, and the learnt network parameters are resolution-agnostic: no further modification or tuning will be required for different resolutions in order to achieve the same level of prediction accuracy. Moreover, the nonlocal operator architecture also allows the incorporation of intrinsic mathematical and physics knowledge, which improves the learning efficacy and robustness from scarce measurements. To demonstrate the applicability of our nonlocal operator learning framework, three typical scenarios in physics-based machine learning will be discussed: the learning of a material-specific constitutive law, the learning of an efficient PDE solution operator, and the development of a foundational constitutive law across multiple materials. As an application, we learn material models directly from digital image correlation (DIC) displacement tracking measurements on a porcine tricuspid valve leaflet tissue, and show that the learnt model substantially outperforms conventional constitutive models.

Monday, April 1, 2024

Posted January 22, 2024
Last modified March 4, 2024

11:30 am – 12:20 pm Zoom (click here to join)

Boris Kramer, University of California San Diego
Scalable Computations for Nonlinear Balanced Truncation Model Reduction

Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems on nonlinear manifolds and preserves either open- or closed-loop observability and controllability aspects of the nonlinear system. Two computational challenges have so far prevented its deployment on large-scale systems: (a) the computation of Hamilton-Jacobi-(Bellman) equations that are needed for characterization of controllability and observability aspects, and (b) efficient model reduction and reduced-order model (ROM) simulation on the resulting nonlinear balanced manifolds. We present a novel unifying and scalable approach to balanced truncation for large-scale control-affine nonlinear systems that consider a Taylor-series based approach to solve a class of parametrized Hamilton-Jacobi-Bellman equations that are at the core of balancing. The specific tensor structure for the coefficients of the Taylor series (tensors themselves) allows for scalability up to thousands of states. Moreover, we will present a nonlinear balance-and-reduce approach that finds a reduced nonlinear state transformation that balances the system properties. The talk will illustrate the strength and scalability of the algorithm on several semi-discretized nonlinear partial differential equations, including a nonlinear heat equation, vibrating beams, Burgers' equation and the Kuramoto-Sivashinsky equation.

Posted March 26, 2024
Last modified March 31, 2024

3:30 pm Lockett Hall 233

Wei Li, DePaul University
Edge States on Sharply Joined Photonic Crystals

Edge states are important in transmitting information and transporting energy. We investigate edge states in continuous models of photonic crystals with piecewise constant coefficients, which are more realistic and controllable for manufacturing optical devices. First, we show the existence of Dirac points on honeycomb structures with suitable symmetries. Then we show that when perturbed in two appropriate ways, the perturbed honeycomb structures have a common band gap, and when joined along suitable interfaces, there exist edge states which propagate along the interfaces and exponentially decay away from the interfaces. The main tools used are layer potentials, asymptotic analysis, the Gohberg-Sigal theory and Lyapunov-Schmidt reductions. This is joint work with Junshan Lin, Jiayu Qiu, Hai Zhang.

Tuesday, April 2, 2024

Posted March 28, 2024

Algebra and Number Theory Seminar Questions or comments?

2:30 pm – 3:20 pm Zoom

Meeting of Tenured Faculty

Posted November 14, 2023
Last modified March 26, 2024

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom

Micah Milinovich, University of Mississippi
Biases in the gaps between zeros of Dirichlet L-functions

We describe a family of Dirichlet L-functions that provably have unusual value distribution and experimentally have a significant and previously undetected bias in the distribution of gaps between their zeros. This has an arithmetic explanation that corresponds to the nonvanishing of a certain Gauss-type sum. We give a complete classification of the characters for when these sums are nonzero and count the number of corresponding characters. It turns out that this Gauss-type sum vanishes for 100% of primitive Dirichlet characters, so L-functions in our newly discovered family are rare (zero density set amongst primitive characters). If time allows, I will also describe some newly discovered experimental results concerning a "Chebyshev-type" bias in the gaps between the zeros of the Riemann zeta-function. This is joint work with Jonathan Bober (Bristol) and Zhenchao Ge (Waterloo).

Wednesday, April 3, 2024

Posted January 18, 2024
Last modified April 2, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Huong Vo, Louisiana State University
The Solomon-Tits theorem

The Solomon-Tits theorem states that a spherical Tits building over a field is homotopy equivalent to a wedge of spheres of the appropriate dimension. In this talk, we will go over some specific examples that show the theorem using PL Morse Theory.

Posted December 1, 2023
Last modified April 1, 2024

3:30 pm Lockett 233

Neal Stoltzfus, Mathematics Department, LSU
The Heart of the Braid Group

The ubiquitous braid group can be approached from many perspectives (algebraic geometrically, combinatorially, geometric group theoretically). This talk will concentrate on developing a description of the image of the known injective (finite dimensional faithful) representation of Lawrence/Krammer/Bigelow. Recalling Artin's faithful infinite dimensional representation and his "combing of pure braids", we first develop an analog for the (unfaithful) Burau representation case using covering spaces, local coefficients and the Reidemeister homotopical intersection theory for the braid action on one-point configurations. Next we introduce the braid action on the (unordered) two-point configuration space utilized by Krammer and Bigelow. For an easier description and computation, we will utilize the two-fold covering space of ordered pair configurations. The complements of these (discriminantal) arrangements are fibrations whose fundamental groups are semi-direct products from pure braid combing. Computing Blanchfield duality of the complements of open tubular neighborhood of the hyperplane arrangements we determine the first restriction on the image of the LKB representation: Hermitian form invariance under the intersection form discovered by Budney and Song. Additional conditions are determined by arithmetic monoidal conditions arising from matrix invariants over polynomial monoids, N[q, 1-q, t] related to (Dehornoy-Paris-Garside) group structures within the braid group. We conclude with a discussion of potential applications.

Thursday, April 4, 2024

Posted March 28, 2024

LSU AWM Student Chapter LSU AWM Student Chapter Website

2:00 pm – 3:00 pm Lockett 233 (Simulcasted via Zoom)

Laszlo Szekely, University of South Carolina
Tanglegrams with the largest crossing number

A tanglegram consists of two binary trees with the same number of leaves, a left binary tree and a right binary tree, and a perfect matching between the leaves of the two trees. The size of a tanglegram is the number of matching edges. Tanglegrams are drawn in a special way. Leaves of the left tree must be on the line $x=0$, leaves of the right tree must be on the line $x=1$, the left binary tree is a plane tree in the halfplane $x\leq 0$, the right binary tree is a plane tree in the halfplane $x\geq 1$, and the perfect matching must be drawn in straight line segments. Such a drawing is called a layout of the tanglegram. The crossing number of a layout is the number of unordered pairs of matching edges that cross, while The crossing number of a tanglegram is the least number of crossings in layouts of this tanglegram. It is easy to see that the crossing number of a size $n$ tanglegram is at most $\binom{n}{2}$. Anderson, Bai, Barrera-Cruz, Czabarka, Da Lozzo, Hobson, Lin, Mohr, Smith, Sz\'ekely, and Whitlatch [Electronic J. Comb. {25}(4) (2018) \#P4.24] observed that the crossing number of any tanglegram is strictly less than $\frac{1}{2}\binom{n}{2}$, but some $n$, some tanglegrams have crossing number at least $\frac{1}{2}\binom{n}{2}-\frac{n^{3/2}-n}{2}$. In the current work we show on the one hand that the crossing number of any tanglegram is at most $\frac{1}{2}\binom{n}{2} -\Omega(n)$, and on the other hand that for some $n$, some tanglegrams have crossing number at least $\frac{1}{2}\binom{n}{2}-O(n\log n)$.

Friday, April 5, 2024

Posted April 2, 2024
Last modified April 3, 2024

11:30 am – 12:30 pm Lockett -Keisler Lounge

Dr. Lisa Kuhn, Southeastern LA University
AWM-Ask me Anything - Dr Lisa Kuhn

This is an informal event where you can ask any questions you might have about her work, career, what it's like to be a woman in math, etc. Food will be provided in the Keisler lounge, and the event will start at 11:30. All are welcome!

Posted March 27, 2024
Last modified January 7, 2025

12:30 pm – 1:30 pm Lockett 284

Dr. Lisa Kuhn, Southeastern LA University
PDE Structures: Finite Elements, Data Science and the Search for Efficient Solutions

Recent advancements in smart materials have significantly influenced the complexity of partial differential equation (PDE) structures, which frequently exhibit material discontinuities and intricate boundary conditions, especially with PDE systems. As we transition further into the age of artificial intelligence, researchers are increasingly exploring machine and deep learning methodologies to derive PDE solutions. However, success has been limited when considering control of distributed parameter systems which is supported by finite element theory. This presentation will present recent findings in generating PDE solutions utilizing both finite elements with adapted bases and hybrid techniques while striving to uphold infinite-dimensional distributed parameter control theory. The discussion will include results of one and two-dimensional clamped structures employing Euler-Bernoulli beams and isotropic plates. Computational methodologies such as modified higher-order bases and neural finite elements will be elaborated upon.

Posted March 28, 2024

2:00 pm – 3:00 pm Lockett Hall 233 (Simulcasted via Zoom)

Eva Czabarka, University of South Carolina
Maximum diameter of $k$-colorable graphs

Between 1965 and 1989 several people showed that the diameter of an $n$-vertex connected graph $G$ with minimum degree $\delta$ is at most $\frac{3n}{\delta+1}-1$. In 1989 Erd\H{o}s, Pach, Pollack and Tuza posed the following conjecture: For fixed integers $r,\delta\geq 2$, for any connected graph $G$ with minimum degree $\delta$ and order $n$ we have (1) If $G$ is $K_{2r}$-free and $\delta$ is a multiple of $(r-1)(3r+2)$ then, as $n\rightarrow \infty$, $$ \operatorname{diam}(G) \leq \frac{2(r-1)(3r+2)}{(2r^2-1)}\cdot \frac{n}{\delta} + O(1)=\left(3-\frac{2}{2r-1}-\frac{1}{(2r-1)(2r^2-1)}\right)\frac{n}{\delta}+O(1). $$ (2) If $G$ is $K_{2r+1}$-free and $\delta$ is a multiple of $3r-1$, then, as $n\rightarrow \infty$, $$\operatorname{diam}(G) \leq \frac{3r-1}{r}\cdot \frac{n}{\delta} + O(1)=\left(3-\frac{2}{2r}\right)\frac{n}{\delta}+O(1). $$ Erd\H{o}s, Pach, Pollack and Tuza also created examples that show that the above conjecture, if true, is tight. Not much progress was made till 2009, when Czabarka, Dankelman and Sz\'ekely showed that for $r=2$ a weaker version of (2) holds: For every connected $4$-colorable graph $G$ of order $n$ and minimum degree $\delta\ge 1$, $ \operatorname{diam}(G) \leq \frac{5n}{2\delta}-1.$ This suggests a weakening of the conjecture by replacing the condition $K_{k+1}$-free with $k$-colorability. With Inne Singgih and L\'aszl\'o A. Sz\'ekely we provided conterexamples of part (1) of the conjecture in both versions (forbidden clique size or colorability) for every $r\ge 2$ for large enough $\delta$. These examples give that, if we are to bound the diameter of a $K_{k+1}$-free $n$-vertex graph with minimum degree $\delta$ by $C_k\cdot\frac{n}{\delta}$, then $C\ge 3-\frac{2}{k}$ regardless of the parity of $k$. With Stephen Smith and L\'aszl\'o A. Sz\'ekely we showed that this modified conjecture holds for both $3$- and $4$-colorable graphs (the latter result is an alternative and shorter proof to the 2009 result).

Monday, April 8, 2024

Posted February 21, 2024
Last modified April 8, 2024

3:30 pm

Jessica Lin, McGill University
Generalized Front Propagation for Stochastic Spatial Models

In this talk, I will present a general framework which can be used to analyze the scaling limits of various stochastic spatial "population" models. Such models include ternary Branching Brownian motion subject to majority voting and several examples of interacting particle systems motivated by biology. The approach is based on moment duality and a PDE methodology introduced by Barles and Souganidis, which can be used to study the asymptotic behaviour of rescaled reaction-diffusion equations. In the limit, the models exhibit phase separation with an evolving interface which is governed by a global-in-time, generalized notion of mean-curvature flow. This talk is based on joint work with Thomas Hughes (Bath).

Posted February 19, 2024

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm Lockett 232

Jessica Lin, McGill University
TBA

Wednesday, April 10, 2024

Posted January 18, 2024
Last modified April 5, 2024

1:30 pm Lockett 233, Zoom

Agniva Roy, Louisiana State University
Legendrian Rainbow Closures, Sheaf Moduli, and Grassmanians

Recent advancements in computing invariants of Legendrian knots in the 3-sphere, based on seminal work of Kashiwara-Schapira and continued by Shende- Treumann-Zaslow-Casals-Williams-Gao-Shen-Weng-Hughes-Gorsky-Gorsky-Simental and many others, have uncovered deep connections between contact and symplectic geometry and various properties of algebraic varieties. In this talk, I will try to explore the simplest examples of (k,n) torus links, and show how the sheaf moduli of these links give rise to Grassmanian varieties. Also, we will see how exact Lagrangian fillings give a geometric understanding of Plucker coordinates in the (2,n) case. The talk will focus largely on pictures and examples, with a view towards conveying the fascinating interplay of ideas that happens here.

Posted December 6, 2023
Last modified April 1, 2024

LSU AWM Student Chapter LSU AWM Student Chapter Website

3:30 pm Lockett 233

Joseph Breen, University of Iowa
The Giroux correspondence in arbitrary dimensions

The Giroux correspondence between contact structures and open book decompositions is a cornerstone of 3-dimensional contact topology. While a partial correspondence was previously known in higher dimensions, the underlying technology available at the time was completely different from that of the 3-dimensional theory. In this talk, I will discuss recent joint work with Ko Honda and Yang Huang on extending the statement and technology of the 3-dimensional correspondence to all dimensions.

Thursday, April 11, 2024

Posted April 3, 2024
Last modified April 4, 2024

3:30 pm – 4:30 pm Lockett Keisler Lounge

Nadejda Drenska, Louisiana State University
Dr. Nadia Drenska's Journey in Machine Learning.

In this talk, Dr.Nadia Drenska will speak about her journey in machine learning. The talk will consist of both an overview of the area of machine learning and a discussion of various problems. The speaker will focus on two types of problems, originating in `prediction with expert advice’, and in `semi-supervised learning’. The talk is a part of the 2024 AWM workshop on Machine Learning.

Friday, April 12, 2024

Posted April 8, 2024

LSU AWM Student Chapter LSU AWM Student Chapter Website

2:00 pm – 3:00 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)

Jonathan Tidor, Stanford University
Ramsey and Turán numbers of sparse hypergraphs

The degeneracy of a graph is a measure of sparseness that plays an important role in extremal graph theory. To give one example, a 1966 conjecture of Erdős states that $d$-degenerate bipartite graphs have Turán number $O(n^{2-1/d})$. Though this is still far from solved, the bound $O(n^{2-1/4d})$ was proved by Alon, Krivelevich, and Sudakov in 2003. As another example, the Burr--Erdős conjecture states that graphs of bounded degeneracy have Ramsey number linear in their number of vertices. (This is in contrast to general graphs whose Ramsey number can be as large as exponential in the number of vertices.) This conjecture was resolved by Lee in 2017. I will talk about the hypergraph analogues of these two questions. Though the typical notion of hypergraph degeneracy does not give any information about either the Ramsey or Turán numbers of hypergraphs, I will define a new notion called skeletal degeneracy that is better-suited for these problems. We prove the hypergraph analogue of the Burr--Erdős conjecture: hypergraphs of bounded skeletal degeneracy have Ramsey number linear in their number of vertices. Furthermore, we give good bounds on the Turán number of partite hypergraphs in terms of their skeletal degeneracy. Both of these results use the technique of dependent random choice. Joint work with Jacob Fox, Maya Sankar, Michael Simkin, and Yunkun Zhou.

Posted April 3, 2024
Last modified April 8, 2024

3:30 pm – 3:30 pm

Machine Learning Workshop

Join us for an interactive workshop in Machine Learning designed for both Undergraduate and Graduate students. This event is a part of the AWM student chapter event on Machine Learning. Participants can engage in hands-on experience on their computers during the workshop.

Monday, April 15, 2024

Posted January 27, 2024
Last modified March 4, 2024

Control and Optimization Seminar Questions or comments?

11:30 am – 12:20 pm Zoom (click here to join)

Sergey Dashkovskiy , Julius-Maximilians-Universität Würzburg
Stability Properties of Dynamical Systems Subjected to Impulsive Actions

We consider several approaches to study stability and instability properties of infinite dimensional impulsive systems. The approaches are of Lyapunov type and provide conditions under which an impulsive system is stable. In particular we will cover the case, when discrete and continuous dynamics are not stable simultaneously. Also we will handle the case when both the flow and jumps are stable, but the overall system is not. We will illustrate these approaches by means of several examples.

Tuesday, April 16, 2024

Posted March 19, 2024

Informal Geometry and Topology Seminar Questions or comments?

until 3:30 pm Digital Media Center 1034

Quoc Tran-Dinh, UNC Chapel Hill
Boosting Convergence Rates for Fixed-Point and Root-Finding Algorithms

Approximating a fixed-point of a nonexpansive operator or a root of a nonlinear equation is a fundamental problem in computational mathematics, which has various applications in different fields. Most classical methods for fixed-point and root-finding problems such as fixed-point or gradient iteration, Halpern's iteration, and extragradient methods have a convergence rate of at most O(1/square root k) on the norm of the residual, where k is the iteration counter. This convergence rate is often obtained via appropriate constant stepsizes. In this talk, we aim at presenting some recent development to boost the theoretical convergence rates of many root-finding algorithms up to O(1/k). We first discuss a connection between the Halpern fixed-point iteration in fixed-point theory and Nesterov's accelerated schemes in convex optimization for solving monotone equations involving a co-coercive operator (or equivalently, fixed-point problems of a nonexpansive operator). We also study such a connection for different recent schemes, including extra anchored gradient method to obtain new algorithms. We show how a faster convergence rate result from one scheme can be transferred to another and vice versa. Next, we discuss various variants of the proposed methods, including randomized block-coordinate algorithms for root-finding problems,which are different from existing randomized coordinate methods in optimization. Finally, we consider the applications of these randomized coordinate schemes to monotone inclusions and finite-sum monotone inclusions. The algorithms for the latter problem can be applied to many applications in federated learning.

Wednesday, April 17, 2024

Posted January 18, 2024
Last modified April 15, 2024

1:30 pm Lockett 233, Zoom

Krishnendu Kar, Louisiana State University
An Introduction to ‘Spetra’cular category

We define higher homotopy groups of a topological space $X$ by taking homotopy classes of the maps from higher dimensional spheres. These higher-homotopy groups are exponentially more difficult to compute than homology or cohomology groups due to the failure of some robust computational tools such as excision. Excision holds for these groups up to connectivity, and so does the Mayer-Vietoris sequence. The suspension map $\Sigma:X\rightarrow \Sigma X$ induces a map on higher homotopy groups $\Sigma:\pi_n(X)\rightarrow \pi_{n+1}(\Sigma X)$. A theorem by Freudenthal states that after taking enough suspensions, these homotopy groups will stabilize eventually. We call the colimit of these homotopy groups as the stable homotopy group. In the modern treatment of stable homotopy theory, spaces are replaced by spectra. In this talk, we will see some important facts, examples, and, more importantly, justification for the title.

Posted April 1, 2024
Last modified April 15, 2024

3:30 pm Lockett 233

Kevin Schreve, Louisiana State University
Homology growth and aspherical manifolds

Suppose we have a space X and a tower of finite covers that are increasingly better approximations to the universal cover. In this talk, we will be interested in how classical homological invariants grow as we go up the tower. In particular, I will survey various conjectures about the rational/F_p-homology growth and integral torsion growth in these towers. We'll discuss constructions of closed aspherical manifolds that have F_p-homology growth outside of the middle dimension, and give some applications to (non)-fibering of high-dimensional manifolds. This is joint work with Grigori Avramidi and Boris Okun.

Friday, April 19, 2024

Posted April 14, 2024

Control and Optimization Seminar Questions or comments?

2:00 pm – 3:00 pm Lockett Hall 233

Xingxing Yu, Georgia Institute of Technology
Planar Turan Number of Cycles

The planar Turan number of a graph $H$, $ex_P(n,H)$, is the maximum number of edges in an $n$-vertex planar graph without $H$ as a subgraph. We discuss recent work on $ex_P(n,H)$, in particular when $H=C_k$ (cycle of length $k$), including our work on $ex_P(n,C_7)$. We prove an upper bound on $ex_P(n, C_k)$ for $k, n\ge 4$, establishing a conjecture of Cranston, Lidicky, Liu, and Shantanam. The discharging method and previous work on circumference of planar graphs are used.

Monday, April 22, 2024

Posted January 6, 2024
Last modified March 4, 2024

11:30 am – 12:20 pm Zoom (click here to join)

Madalena Chaves, Centre Inria d'Université Côte d'Azur
Coupling, Synchronization Dynamics, and Emergent Behavior in a Network of Biological Oscillators

Biological oscillators often involve a complex network of interactions, such as in the case of circadian rhythms or cell cycle. Mathematical modeling and especially model reduction help to understand the main mechanisms behind oscillatory behavior. In this context, we first study a two-gene oscillator using piecewise linear approximations to improve the performance and robustness of the oscillatory dynamics. Next, motivated by the synchronization of biological rhythms in a group of cells in an organ such as the liver, we then study a network of identical oscillators under diffusive coupling, interconnected according to different topologies. The piecewise linear formalism enables us to characterize the emergent dynamics of the network and show that a number of new steady states is generated in the network of oscillators. Finally, given two distinct oscillators mimicking the circadian clock and cell cycle, we analyze their interconnection to study the capacity for mutual period regulation and control between the two reduced oscillators. We are interested in characterizing the coupling parameter range for which the two systems play the roles "controller-follower".

Posted January 28, 2024
Last modified April 1, 2024

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:20 pm Lockett 233

Greg Parker, Stanford University
$\mathbb Z_2$-harmonic spinors as limiting objects in geometry and topology

$\mathbb Z_2$-harmonic spinors are singular solutions of Dirac-type equations that allow topological twisting around a submanifold of codimension 2. These objects arise as limits at the boundary of various moduli spaces in several distinct areas of low-dimensional topology, gauge/Floer theory, and enumerative geometry. The first part of this talk will introduce these objects, and discuss the various contexts in which they arise and the relationship between them. The second part of the talk will focus on the deformations of $\mathbb Z_2$-harmonic spinors when varying background parameters as a model for the novel analytic problems presented by these objects. In particular, the deformations of the singular submanifold play a role, giving the problem some characteristics similar to a free-boundary-value problem and leading to a hidden elliptic pseudo-differential operator that governs the geometry of the moduli spaces.

Posted April 21, 2024

3:30 pm – 4:30 pm Lockett 232

Ben Seeger, The University of Texas at Austin
Equations on Wasserstein space and applications

The purpose of this talk is to give an overview of recent work involving differential equations posed on spaces of probability measures and their use in analyzing mean field limits of controlled multi-agent systems, which arise in applications coming from macroeconomics, social behavior, and telecommunications. Justifying this continuum description is often nontrivial and is sensitive to the type of stochastic noise influencing the population. We will describe settings for which the convergence to mean field stochastic control problems can be resolved through the analysis of the well-posedness for a certain Hamilton-Jacobi-Bellman equation posed on Wasserstein spaces, and how this well-posedness allows for new convergence results for more general problems, for example, zero-sum stochastic differential games of mean-field type.

Posted February 21, 2024
Last modified April 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm Lockett 232

Ben Seeger, The University of Texas at Austin
Equations on Wasserstein space and applications

Wednesday, April 24, 2024

Posted January 18, 2024
Last modified April 22, 2024

1:30 pm Lockett 233, Zoom

Megan Fairchild, Louisiana State University
The Double Branched Cover of the Three-Sphere Over a Knot.

In this talk, we will examine how the double branched cover of the three-sphere over a knot is constructed and the linking form defined on its first homology. We will discuss how to calculate first homology, defining the linking form, and calculating the linking form given a knot diagram. The main goal of the talk is to better understand this object and examine its connection to non-orientable 4-genus of knots.

Posted January 31, 2024
Last modified April 23, 2024

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm Lockett 233

Morgan Weiler, Cornell University
TBA

Friday, April 26, 2024

Posted April 19, 2024

Control and Optimization Seminar Questions or comments?

2:00 pm – 3:00 pm Lockett 233

Ryan Martin, Iowa State University
Counting cycles in planar graphs

Basic Tur\'an theory asks how many edges a graph can have, given certain restrictions such as not having a large clique. A more generalized Tur\'an question asks how many copies of a fixed subgraph $H$ the graph can have, given certain restrictions. There has been a great deal of recent interest in the case where the restriction is planarity. In this talk, we will discuss some of the general results in the field, primarily the asymptotic value of ${\bf N}_{\mathcal P}(n,H)$, which denotes the maximum number of copies of $H$ in an $n$-vertex planar graph. In particular, we will focus on the case where $H$ is a cycle. It was determined that ${\bf N}_{\mathcal P}(n,C_{2m})=(n/m)^m+o(n^m)$ for small values of $m$ by Cox and Martin and resolved for all $m$ by Lv, Gy\H{o}ri, He, Salia, Tompkins, and Zhu. The case of $H=C_{2m+1}$ is more difficult and it is conjectured that ${\bf N}_{\mathcal P}(n,C_{2m+1})=2m(n/m)^m+o(n^m)$. We will discuss recent progress on this problem, including verification of the conjecture in the case where $m=3$ and $m=4$ and a lemma which reduces the solution of this problem for any $m$ to a so-called ``maximum likelihood'' problem. The maximum likelihood problem is, in and of itself, an interesting question in random graph theory. This is joint work with Emily Heath and Chris (Cox) Wells.

Monday, April 29, 2024

Posted January 17, 2024
Last modified March 4, 2024

11:30 am – 12:20 pm Zoom (click here to join)

Tobias Breiten, Technical University of Berlin
On the Approximability of Koopman-Based Operator Lyapunov Equations

Computing the Lyapunov function of a system plays a crucial role in optimal feedback control, for example when the policy iteration is used. This talk will focus on the Lyapunov function of a nonlinear autonomous finite-dimensional dynamical system which will be rewritten as an infinite-dimensional linear system using the Koopman operator. Since this infinite-dimensional system has the structure of a weak-* continuous semigroup in a specially weighted Lp-space one can establish a connection between the solution of an operator Lyapunov equation and the desired Lyapunov function. It will be shown that the solution to this operator equation attains a rapid eigenvalue decay, which justifies finite rank approximations with numerical methods. The usefulness for numerical computations will also be demonstrated with two short examples. This is joint work with Bernhard Höveler (TU Berlin).

Wednesday, May 1, 2024

Posted February 1, 2024
Last modified April 30, 2024

3:30 pm Lockett 233

Jean-François Lafont, The Ohio State University
Strict hyperbolizations produce linear groups

Strict hyperbolization is a process developed by Charney--Davis, which inputs a simplicial complex, and outputs a negatively curved piecewise hyperbolic space. By applying this process to interesting triangulations of manifolds, one can create negatively curved manifolds with various types of pathological large scale behavior. I will give a gentle introduction to strict hyperbolization, and will explain why the fundamental groups of the resulting spaces are always linear over Z. This is joint work with Lorenzo Ruffoni (Tufts University).

Thursday, May 2, 2024

Posted April 16, 2024
Last modified April 29, 2024

3:00 pm – 4:00 pm Lockett 232

Meeting with Dean Cynthia Peterson

Friday, May 3, 2024

Posted April 19, 2024

Control and Optimization Seminar Questions or comments?

2:00 pm – 3:00 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)

Peter Nelson, University of Waterloo
Infinite matroids on lattices

There are at least well-studied ways to extend matroids to more general objects - one can allow the ground set to be infinite, or instead define the concept of independence on a lattice other than a set lattice. I will discuss some nice ideas that arise when combining these two generalizations. This is joint work with Andrew Fulcher.

Monday, May 6, 2024

Posted January 16, 2024
Last modified March 4, 2024

11:30 am – 12:20 pm Zoom (click here to join)

Jorge Poveda, University of California, San Diego Donald P. Eckman, NSF CAREER, and AFOSR Young Investigator Program Awardee
Multi-Time Scale Hybrid Dynamical Systems for Model-Free Control and Optimization

Hybrid dynamical systems, which combine continuous-time and discrete-time dynamics, are prevalent in various engineering applications such as robotics, manufacturing systems, power grids, and transportation networks. Effectively analyzing and controlling these systems is crucial for developing autonomous and efficient engineering systems capable of real-time adaptation and self-optimization. This talk will delve into recent advancements in controlling and optimizing hybrid dynamical systems using multi-time scale techniques. These methods facilitate the systematic incorporation and analysis of both "exploration and exploitation" behaviors within complex control systems through singular perturbation and averaging theory, resulting in a range of provably stable and robust algorithms suitable for model-free control and optimization. Practical engineering system examples will be used to illustrate these theoretical tools.

Wednesday, May 8, 2024

Posted May 3, 2024
Last modified May 8, 2024

11:00 am – 12:00 pm Zoom

Olga Iziumtseva, University of Nottingham
Asymptotic and geometric properties of Volterra Gaussian processes

In this talk we discuss asymptotic and geometric properties of Gaussian processes defined as $U(t) = \int_0^t K(t, s)dW(s),\ t \geq 0$, where $W$ is a Wiener process and $K$ is a continuous kernel. Such processes are called Volterra Gaussian processes. It forms an important class of stochastic processes with a wide range of applications in turbulence, cancer tumours, energy markets and epidemic models. Le Gall’s asymptotic expansion for the volume of Wiener Sausage shows that local times and self-intersection local times can be considered as the geometric characteristics of stochastic processes that look like a Wiener process. In this talk we discuss the law of the iterated logarithm, existence of local times and construct Rosen renormalized self-intersection local times for Volterra Gaussian processes.

Thursday, May 9, 2024

Posted March 21, 2024
Last modified May 3, 2024

https://www.math.lsu.edu/OAL-RAG2024

8:30 am – 4:40 pm 232 Lockett Hall

Order, Algebra, Logic, and Real Algebraic Geometry (Day 1 of 3)

Friday, May 10, 2024

Posted March 21, 2024
Last modified May 3, 2024

https://www.math.lsu.edu/OAL-RAG2024

8:30 am – 4:40 pm 232 Lockett Hall

Order, Algebra, Logic, and Real Algebraic Geometry (Day 2 of 3)

Saturday, May 11, 2024

Posted March 21, 2024
Last modified May 3, 2024

https://www.math.lsu.edu/OAL-RAG2024

8:30 am – 12:00 pm 232 Lockett Hall

Order, Algebra, Logic, and Real Algebraic Geometry (Day 3 of 3)

Monday, May 13, 2024

Posted April 29, 2024

Control and Optimization Seminar Questions or comments?

11:30 am – 12:20 pm Zoom (click here to join)

Giovanni Fusco, Università degli Studi di Padova
A Lie-Bracket-Based Notion of Stabilizing Feedback in Optimal Control

With reference to an optimal control problem where the state has to asymptotically approach a closed target while paying a non-negative integral cost, we propose a generalization of the classical dissipative relation that defines a control Lyapunov function by a weaker differential inequality. The latter involves both the cost and the iterated Lie brackets of the vector fields in the dynamics up to a certain degree $k\ge 1$, and we call any of its (suitably defined) solutions a degree-k minimum restraint function. We prove that the existence of a degree-k minimum restraint function allows us to build a Lie-bracket-based feedback which sample stabilizes the system to the target while regulating (i.e., uniformly bounding) the cost.

Thursday, June 6, 2024

Posted June 4, 2024

Mathematical Physics and Representation Theory Seminar

3:30 pm – 4:30 pm Lockett 233

Mikhail Khovanov, Johns Hopkins University
Foams in algebraic K-theory and dynamics

We'll discuss a recent paper where algebraic K-theory is related to foams with a flat connection.

Monday, June 17, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Shea Vela-Vick, Louisiana State University
Classical Knot Concordance

Monday, June 24, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Adithyan Pandikkadan, Louisiana State University
Classical Knot Concordance

Wednesday, June 26, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Tristan Reynoso, Louisiana State University
Classical Knot Concordance

Monday, July 1, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Nilangshu Bhattacharyya, Louisiana State University
Classical Knot Concordance

Wednesday, July 3, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Megan Fairchild, Louisiana State University
Classical Knot Concordance

Monday, July 8, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Shea Vela-Vick, Louisiana State University
Classical Knot Concordance

Wednesday, July 10, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Adithyan Pandikkadan, Louisiana State University
Classical Knot Concordance

Monday, July 15, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Colton Sandvik, Louisiana State University
Classical Knot Concordance

Wednesday, July 17, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Tristan Reynoso, Louisiana State University
Classical Knot Concordance

Monday, July 22, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Nilangshu Bhattacharyya, Louisiana State University
Classical Knot Concordance

Wednesday, July 24, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Adithyan Pandikkadan, Louisiana State University
Classical Knot Concordance

Monday, July 29, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Colton Sandvik, Louisiana State University
Classical Knot Concordance

Wednesday, July 31, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Shea Vela-Vick, Louisiana State University
Classical Knot Concordance

Monday, August 5, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Megan Fairchild, Louisiana State University
Classical Knot Concordance

Wednesday, August 7, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Nilangshu Bhattacharyya, Louisiana State University
Classical Knot Concordance

Posted August 30, 2024
Last modified September 16, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Locket 233

TBD

Monday, August 12, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Tristan Reynoso, Louisiana State University
Classical Knot Concordance

Wednesday, August 14, 2024

Posted June 12, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233, Zoom

Nilangshu Bhattacharyya, Louisiana State University
Classical Knot Concordance

Friday, August 16, 2024

Posted January 22, 2024

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Applied Mathematics

Monday, August 19, 2024

Posted January 22, 2024

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Topology

Wednesday, August 21, 2024

Posted January 22, 2024

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Analysis

Friday, August 23, 2024

Posted January 22, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Algebra

Wednesday, August 28, 2024

Posted August 27, 2024

1:30 pm Lockett 233

Organizational meeting

Tuesday, September 3, 2024

Posted August 21, 2024
Last modified August 28, 2024

Algebra and Number Theory Seminar Questions or comments?

2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom

Rahul Kumar, Pennsylvania State University
Period function from Ramanujan's Lost Notebook and Kronecker limit formulas

The Lost Notebook of Ramanujan contains a number of beautiful formulas, one of which can be found on page 220. It involves an interesting function, which we denote as $\mathcal{F}_1(x)$. In this talk, we show that $\mathcal{F}_1(x)$ belongs to the category of period functions as it satisfies the period relations of Maass forms in the sense of Lewis and Zagier. Hence, we refer to $\mathcal{F}_1(x)$ as the Ramanujan period function. The Kronecker limit formulas are concerned with the constant term in the Laurent series expansion of certain Dirichlet series at $s=1$. We will also discuss that $\mathcal{F}_1(x)$ naturally appears in a Kronecker limit-type formula of a certain zeta function.

Wednesday, September 4, 2024

Posted August 30, 2024
Last modified September 3, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Locket 233

Huong Vo, Louisiana State University
Quasi-isometry and Milnor Schwarz theorem

In this talk, we will go over the proof of Milnor-Schwarz theorem, which states that a group G is quasi-isometric to a metric space X if it acts nicely on X. The definition of a quasi-isometry will be covered and so will other definitions relevant to the theorem.

Posted August 27, 2024

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Nilangshu Bhattacharyya, Louisiana State University
Transverse invariant as Khovanov skein spectrum at its extreme Alexander grading

Olga Plamenevskaya described a transverse link invariant as an element of Khovanov homology. Lawrence Roberts gave a link surgery spectral sequence whose $E^2$ page is the reduced Khovanov skein homology (with $\mathbb{Z}_{2}$ coefficient) of a closed braid $L$ with odd number of strands and $E^{\infty}$ page is the knot Floer homology of the lift of the braid axis in the double branch cover, and the spectral sequence splits with respect to the Alexander grading. The transverse invariant does not vanish in the Khovanov skein homology, and under the above spectral sequence and upon mapping the knot Floer homology to the Heegard Floer homology, the transverse invariant corresponds to the contact invariant. Lipshitz-Sarkar gave a stable homotopy type invariant of links in $S^3$. Subsequently, Lipshitz-Ng-Sarkar found a cohomotopy element in the Khovanov spectrum associated to the Plamenevskaya invariant. We can think of this element as a map from Khovanov spectra at its extreme quantum grading to the sphere spectrum. We gave a stable homotopy type for Khovanov skein homology and showed that we can think of the cohomotopy transverse element as a map from the Khovanov spectra at its extreme quantum grading to the Khovanov skein spectra at its extreme Alexander grading. This is a joint work with Adithyan Pandikkadan, which will be presented in this talk.

Friday, September 6, 2024

Posted August 31, 2024

10:30 am – 11:20 am Zoom (click here to join)

Ugo Boscain, Sorbonne University, France
3D Optimal Control Problems Constrained on Surfaces

In this talk I consider a surface embedded in a 3D contact sub-Riemannian manifold (i.e., an optimal control problem in dimension 3 with 2 controls which is linear with respect to the controls and with quadratic cost; we will also make a natural controllability assumption). Such a surface inherits a field of direction (with norm) from the ambient space. This field of directions is singular at characteristic points (i.e., where the surface is tangent to the set of admissible directions). In this talk we will study when the problem restricted to the surface is controllable, in other words when the normed field of directions permits to give to the surface the structure of metric space (of SNCF type). We will also study how to define the heat and the Schroedinger equation on such a structure and if the singular points are “accessible” or not by the evolution.

Posted August 28, 2024

Algebra and Number Theory Seminar Questions or comments?

2:30 pm – 3:30 pm Lockett Hall 233 (Simulcasted via Zoom)

Yiwei Ge, Louisiana State University
Reconstructing induced-$C_4$-free graphs from digitally convex sets

A set $S$ of vertices is {\it digitally convex} if for every vertex $v$, $N[v]\subseteq N[S]$ implies $v\in S$. In 2014, Lafrance, Oellermann, and Pressey showed that trees are reconstructable from their digitally convex sets. We improved upon that result by showing that all induced-$C_4$-free graphs are reconstructable from their digitally convex sets, and we provide an algorithm for the reconstruction. This is based on a project with a group from the Graduate Research Workshop in Combinatorics (GRWC).

Tuesday, September 10, 2024

Posted August 14, 2024
Last modified September 5, 2024

2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom

Heidi Goodson, Brooklyn College, CUNY
An Exploration of Sato-Tate Groups of Curves

The focus of this talk is on families of curves and their associated Sato-Tate groups -- compact groups predicted to determine the limiting distributions of coefficients of the normalized L-polynomials of the curves. Complete classifications of Sato-Tate groups for abelian varieties in low dimension have been given in recent years, but there are obstacles to providing classifications in higher dimension. In this talk I will give an overview of the techniques we can use for some nice families of curves and discuss the ways in which these techniques fall apart when there are degeneracies in the algebraic structure of the associated Jacobian varieties. I will include examples throughout the talk in order to make the results more concrete to those new to this area of research.

Friday, September 13, 2024

Posted September 10, 2024

Informal Geometry and Topology Seminar Questions or comments?

2:30 pm – 3:30 pm Zoom Link

Anton Dochtermann, Texas State University
Cycle systems, parking functions, and h-vectors of matroids

The h-vector of a matroid M is an important invariant related to the independence complex of M, which can also be covered as an evaluation of its Tutte polynomial. A well-known conjecture of Stanley posits that the h-vector of a matroid is a "pure O-sequence", meaning that it can be recovered by counting faces of a pure multicomplex. Merino has established Stanley's conjecture for the case of cographic matroids via a connection to chip-firing on graphs and the concept of a G-parking function. Inspired by these constructions, we introduce the notion of a cycle system for a matroid M . This leads to a collection of integer sequences that we call (co)parking functions for M, which we show are in bijection with the set of bases of M. We study maximal coparking functions, and also how cycle systems behave under deletion and contraction. This leads to a proof of Stanley’s conjecture for the case of matroids that admit cycle systems. This is joint work with Scott Cory, Solis McClain, and David Perkinson.

Wednesday, September 18, 2024

Posted August 30, 2024
Last modified September 16, 2024

1:30 pm Locket 233

Saumya Jain, Louisiana State University
Quasi-isometric invariance of hyperbolicity

In this talk, we will define $\delta$-hyperbolic spaces and show that geodesics and quasi-geodesics stay close in a hyperbolic space. We will then prove that hyperbolicity is a quasi-isometric invariant.

Posted August 28, 2024
Last modified September 9, 2024

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Tristan Wells Filbert, Louisiana State University
Whitehead doubles of dual knots are deeply slice

In collaboration with McConkey, St. Clair, and Zhang, we show that the Whitehead double of the dual knot to $1/n$ surgery on the knot $6_1$ in the 3-sphere is deeply slice in a contractible 4-manifold. That is, it bounds a smoothly embedded disc in the manifold, but not in a collar neighborhood of its boundary, the surgered manifold. This is partial progress in answering one of the Kirby questions regarding nullhomotopic deeply slice knots, mentioned in earlier work of Klug and Ruppik. To prove our theorem, we make use of the immersed curves perspective of bordered Floer homology and knot Floer homology.

Friday, September 20, 2024

Posted September 3, 2024

10:30 am – 11:20 am Zoom (click here to join)

Denis Efimov, University of Lille
Homogeneity with Respect to a Part of Variables and Accelerated Stabilization

The presentation addresses the problem of transforming a locally asymptotically stabilizing time-varying control law to a global one with accelerated finite/fixed-time convergence rates. The approach relies on an extension of the theory of homogeneous systems to homogeneity only with respect to a part of the state variables and on the associated partial stability properties. The proposed control design builds upon the kind of approaches first studied in [MCloskey and Murray,1997] and uses the implicit Lyapunov function framework. A sampled-time implementation scheme of the control law is also presented and its properties are characterized. The method is illustrated by finite-time and nearly fixed-time stabilization of a nonholonomic integrator.

Posted September 13, 2024

2:30 pm – 3:30 pm Friday, September 13, 2024 Zoom Link

Bryce Frederickson, Emory
Turán and Ramsey problems in vector spaces over finite fields

Abstract: Turán-type problems ask for the densest-possible structure which avoids a fixed substructure H. Ramsey-type problems ask for the largest possible "complete" structure which can be decomposed into a fixed number of H-free parts. We discuss some of these problems in the context of vector spaces over finite fields. In the Turán setting, Furstenberg and Katznelson showed that any constant-density subset of the affine space $AG(n,q)$ must contain a $k$-dimensional affine subspace if n is large enough. On the Ramsey side of things, a classical result of Graham, Leeb, and Rothschild implies that any red-blue coloring of the projective space $PG(n-1,q)$ must contain a monochromatic k-dimensional projective subspace, for n large. We highlight the connection between these results and show how to obtain new bounds in the latter (projective Ramsey) problem from bounds in the former (affine Turán) problem. This is joint work with Liana Yepremyan.

Monday, September 23, 2024

Posted September 19, 2024

Informal Geometry and Topology Seminar Questions or comments?

5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial Student Association Meeting

We will have a guest visitor Aimee Milam from CareSource. Pizza will be served.

Wednesday, September 25, 2024

Posted August 30, 2024
Last modified September 23, 2024

1:30 pm Locket 233

Rachel Meyers, Louisiana State University
Quasi-isometries and Boundaries of $\delta$-Hyperbolic Spaces

In this talk, we define the boundary of a $\delta$-hyperbolic space as a set of rays and describe the topology of X with this boundary. Further, we will prove if two spaces are quasi-isometric then the boundaries are homeomorphic.

Thursday, September 26, 2024

Posted September 15, 2024

Control and Optimization Seminar Questions or comments?

7:50 am – 2:00 pm Virtually via Zoom, Click here to join Zoom, Meeting ID: 894 8105 1822, Passcode: SIIT-LSU24

SIIT-LSU Conference on Analysis and PDE In Honor of Igor E. Verbitsky’s Retirement

This is an Analysis and PDE international joint conference between LSU and Sirindhorn International Institute of Technology (SIIT), Thailand, in honor of Professor Igor E. Verbitsky’s Retirement. The conference will take place virtually via Zoom and everyone is invited to participate. All the conference materials are now available on the conference website: https://sites.google.com/view/siit-lsu/

Friday, September 27, 2024

Posted August 27, 2024

10:30 am – 11:20 am Zoom (click here to join)

Jean Auriol, CNRS Researcher, L2S, CentraleSupélec
Robust Stabilization of Networks of Hyperbolic Systems with Chain Structure

In this talk, we focus on recent developments for the stabilization of networks of elementary hyperbolic systems with a chain structure. Such a structure arises in multiple industrial processes such as electric power transmission systems, traffic networks, or torsional vibrations in drilling devices. The objective is to design feedback control laws that stabilize the chain using the available actuators and sensors. The different systems composing the network are called elementary in the sense that when taken alone, we know how to design stabilizing output-feedback control laws. We will first consider the case where the actuators and sensors are available at one end of the chain. Using appropriate state predictors, we will present a recursive approach to stabilize the whole chain. Then, we will focus on the case where the actuators and sensors are only available at the junction between two subsystems composing the chain. We will show that such a configuration does not always guarantee the controllability of the chain. Under appropriate controllability/observability conditions, we will design simple stabilizing control laws. Our approach will be based on rewriting the system as Integral Delay Equations (IDEs) with pointwise and distributed control terms. Finally, we will show how the proposed techniques can be used to develop output feedback control laws for traffic flow on two cascaded freeway segments connected by a junction.

Posted September 21, 2024

LSU AWM Student Chapter LSU AWM Student Chapter Website

12:00 pm – 1:00 pm Keisler Lounge, Lockett Hall

Association of Women in Mathematics- Student chapter- Lunch and INFO SESSION

Join us to discuss upcoming events and opportunities to get involved in LSU’s Association for Women in Mathematics. Refreshments will be provided! Hope to see you there!

Posted September 19, 2024

1:30 pm – 2:30 pm Keisler Lounge

Meet & Greet with Jon Loftin (MathWorks)

Pizza will be served. Jon Loftin will present on "Deep Learning with MATLAB: A Visual Approach" after the lunch.

Posted September 19, 2024

2:30 pm – 3:30 pm Lockett 284

Deep Learning with MATLAB: A Visual Approach

Deep learning is quickly becoming embedded in everyday applications. It’s becoming essential for students and educators to adopt this technology to solve complex real-world problems. MATLAB and Simulink provide a flexible and powerful platform to develop and automate data analysis, deep learning, AI, and simulation workflows in a wide range of domains and industries. In this workshop we will introduce deep learning with MATLAB. We will utilize a previously trained network and modify it, using the MATLAB Deep Network Designer. The Deep Network Designer allows you to interactively build, visualize, and train neural networks. Individuals can generate the code for the neural network and finetune parameters. Users can use popular pre-trained networks or construct their own. We will also look at the MATLAB Classification Learner to run several models on a single data set. These visual approaches create a more efficient workflow.

Posted September 17, 2024

Informal Geometry and Topology Seminar Questions or comments?

2:30 pm – 3:30 pm Zoom Link

Matthew Kroeker, Waterloo
Unavoidable flats in matroids representable over a finite field

For a positive integer k and finite field F, we prove that every simple F-representable matroid with sufficiently high rank has a rank-k flat which either is independent, or is a projective or affine geometry over a subfield of F. As a corollary, we obtain the following Ramsey theorem: given an F-representable matroid of sufficiently high rank and any 2-colouring of its points, there is a monochromatic rank-k flat. This is joint work with Jim Geelen and Peter Nelson.

Wednesday, October 2, 2024

Posted August 30, 2024
Last modified September 30, 2024

1:30 pm Locket 233

Nilangshu Bhattacharyya, Louisiana State University
Some basic hyperbolic geometry

We will first discuss hyperboloid model for hyperbolic space and then discuss ball model and upper half space model. Furthermore, we will define the boundary at infinity and implicitly identify with spheres. We move on to talk about isometry group of hyperbolic spaces and classifying them (elliptic, parabolic and hyperbolic), with some examples. If time permits, I may state the Mostow's rigidity theorem.

Posted September 18, 2024
Last modified January 7, 2025

3:30 pm Lockett 237

Ian Tobasco, Rutgers University
Rigidity and Elasticity

This talk will introduce elasticity theory from the geometric point of view for students from mathematics and related disciplines. Our basic objects of study will be (nearly) length preserving maps that arise from (nearly) minimizing an energy functional having to do with the amount of work required to deform a body. After defining the basic quantities of interest, we will discuss Fritz John's seminal study of small strain maps, along with his counterexample to rigidity and its ultimate resolution in the early 2000s by Friesecke, James, and Müller. Time permitting, we will discuss a bit about elastic patterns --- fine structures that occur in naturally wrinkled or crumpled sheets that show us what we do not yet understand about the rigidity of thin elastic domains.

Posted September 27, 2024

3:30 pm Lockett 381

Padmanabhan Sundar, Mathematics Department, LSU
Uniqueness and stability for the Boltzmann-Enskog equation

The time-evolution of a moderately dense gas in a vacuum is described in classical mechanics by a particle density function obtained from the Boltzmann–Enskog equation. By the introduction of a shifted distance, an inequality is proven on the Wasserstein distance for any two measure-valued solutions to the Boltzmann–Enskog equation. Using it, we find sufficient conditions for the uniqueness and continuous-dependence on initial data for solutions of the equation. This is a joint work with Martin Friesen and Barbara Ruediger.

Thursday, October 3, 2024

Posted July 13, 2024
Last modified September 16, 2024

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 232

Ian Tobasco, Rutgers University
Homogenization of Kirigami and Origami-Based Mechanical Metamaterials

Mechanical metamaterials are many-body elastic systems that deform in unusual ways, due to the interactions of nearly rigid building blocks. Examples include origami patterns with many folds, or kirigami patterns made by cutting material from an elastic sheet. In either case, the local deformations of the pattern involve internal degrees of freedom which must be matched with the usual global Euclidean invariances --- e.g., groups of origami panels move by rotations and translations while the whole pattern bends into a curved shape. This talk will introduce the homogenization problem for kirigami and origami metamaterials to a broad audience, and describe our recent results. Our goal is to explain the link between the design of the individual cuts/folds and the bulk deformations they produce. This is joint work with Paul Plucinsky (U. Southern California, Aerospace and Mechanical Engineering) and Paolo Celli (Stony Brook U., Civil Engineering). This talk will be mathematically self-contained, not assuming a background in elasticity.

Friday, October 4, 2024

Posted August 11, 2024
Last modified September 22, 2024

10:30 am – 11:20 am Zoom (click here to join)

Panagiotis Tsiotras, Georgia Institute of Technology AIAA and IEEE Fellow
From Covariance Control to Covariance Steering: The First 40 Years

Uncertainty propagation and mitigation is at the core of all robotic and control systems. The standard approach so far has followed the spirit of control of a system “with uncertainties,” as opposed to the direct control “of uncertainties.” Covariance control, developed by Bob Skelton and his colleagues in the early 80’s, was introduced as a principled approach to handle uncertainty with guarantees in the asymptotic case. The finite-time case has only been recently addressed, and borrowing ideas from the classical optimal mass transport and the Schrödinger Bridge problems, provides a new tool to control stochastic systems with strict performance guarantees that go beyond classical controllability results that only hold for deterministic systems. In this talk, I will review recent results on covariance and distribution control for discrete stochastic systems, subject to probabilistic (chance) constraints, and will demonstrate the application of the approach on control and robot motion planning problems under uncertainty. I will also discuss current trends and potential directions for future work.

Posted August 28, 2024

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:30 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)

Ce Chen, University of Illinois Urbana-Champaign
On the maximum $F$-free induced subgraphs in $K_t$-free graphs

For graphs $F$ and $H$, let $f_{F,H}(n)$ be the minimum possible size of a maximum $F$-free induced subgraph in an $n$-vertex $H$-free graph, which is a generalization of both the Ramsey function and the Erd\H{o}s--Rogers function. Assuming the existence of certain locally dense $H$-free graphs, we give a general upper bound on $f_{F,H}(n)$ by establishing a container lemma for the $F$-free subgraphs. In particular, we improve the upper bounds on $f_{F,H}(n)$ when H is $K_3$ and $K_4$. This is joint work with J\'{o}zsef Balogh and Haoran Luo.

Monday, October 7, 2024

Posted September 27, 2024
Last modified October 1, 2024

2:30 pm – 3:20 pm Lockett 233

Tom Gannon, UCLA
Quantization of the universal centralizer and central D-modules

We will discuss joint work with Victor Ginzburg that proves a conjecture of Nadler on the existence of a quantization, or non-commutative deformation, of the Knop-Ngô morphism—a morphism of group schemes used in particular by Ngô in his proof of the fundamental lemma in the Langlands program. We will first explain the representation-theoretic background, give an extended example of this morphism for the group GL_n(C), and then present a precise statement of our theorem. Time permitting, we will also discuss how the tools used to construct this quantization can also be used to prove conjectures of Ben-Zvi and Gunningham, which predict a relationship between the quantization of the Knop-Ngô morphism and the parabolic induction functor.

Posted October 4, 2024

Algebra and Number Theory Seminar Questions or comments?

5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial Student Association Meeting

We will have guest speaker Morgan Ascanio from Symetra. We will also vote on bylaws for the club. Pizza will be served.

Tuesday, October 8, 2024

Posted August 21, 2024
Last modified October 7, 2024

2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom

Wanlin Li, Washington University in St. Louis
Non-vanishing of Ceresa and Gross–Kudla–Schoen cycles

The Ceresa cycle and the Gross–Kudla–Schoen modified diagonal cycle are algebraic $1$-cycles associated to a smooth algebraic curve with a chosen base point. They are algebraically trivial for a hyperelliptic curve and non-trivial for a very general complex curve of genus $\ge 3$. Given a pointed algebraic curve, there is no general method to determine whether the Ceresa and GKS cycles associated to it are rationally or algebraically trivial. In this talk, I will discuss some methods and tools to study this problem.

Wednesday, October 9, 2024

Posted August 30, 2024
Last modified October 7, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Locket 233

Krishnendu Kar, Louisiana State University
Goodwillie-ingly Exploring Taylor Towers: Unravelling Functor Calculus

The study of the calculus of a function is the study of local behaviour of the function. One of the biggest features of calculus is approximation, i.e. given an unknown function; we may approximate to known functions to tell its property. A key example is Taylor series approximation, for a $n$ times differentiable function we can approximate to a polynomial of degree $n$. Goodwillie unlocked these deceptively simple yet so useful features of functions for functors, mostly to study K-theories. We may approximate a functor by suitable polynomial functors, and analogously, we get something called a Taylor tower. A key question here is how one might define the derivative of a functor in such a way it is commensurate with the original theory of calculus. Then, given a Taylor tower, we ask similar questions as we ask a Taylor series, how does Taylor tower converge in some analogous way? In this talk, we will explore some notions of Goodwillie’s calculus and answer some of the questions imposed.

Posted October 3, 2024

1:30 pm – 2:30 pm Zoom

Faculty Meeting with the Dean

Thursday, October 10, 2024

Posted July 11, 2024

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm tba

College of Science Fall Convocation

Friday, October 11, 2024

Posted October 8, 2024

10:30 am – 11:20 am Zoom (click here to join)

Karl Worthmann, Institute of Mathematics, Technische Universität Ilmenau
Koopman-Based Control with Guarantees

Extended dynamic mode decomposition (EDMD), embedded in the Koopman framework, is a widely-applied technique to predict the evolution of an observable along the flow of a dynamical control system. However, despite its popularity, the error analysis is still fragmentary. We provide a complete and rigorous analysis for control-affine systems by splitting up the approximation error into the projection and estimation error resulting from the finite dictionary size and the finite amount of i.i.d. data used to generate the surrogate model. Further, we indicate extensions towards reproducible kernel Hilbert spaces to establish L∞-error bounds using kernel EDMD. Then, we demonstrate the applicability of the EDMD surrogate models for the control of nonlinear systems.

Posted October 4, 2024

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:30 pm Lockett Hall 233 (simulcasted via Zoom)

Zilin Jiang, Arizona State University
Beyond the classification theorem of Cameron, Goethals, Seidel, and Shult

The classification of graphs with smallest eigenvalues at least −2 culminated in a beautiful theorem of Cameron, Goethals, Seidel and Shult, who related such graphs to root systems from the representation theory of semisimple Lie algebras. In this talk, I will explore graphs with smallest eigenvalues between −2 and −λ*, where λ* is about 2.0198, and I will explain why the mysterious number λ* is a barrier for classification. Joint work with Alexander Polyanskii and Hricha Acharya.

Monday, October 14, 2024

Posted October 9, 2024

2:30 pm – 3:20 pm Lockett 233

Tobias Simon, University of Erlangen, Germany
Realizations of irreducible unitary representations of the Lorentz group in spaces of distributional sections over de Sitter space

In Algebraic Quantum Field Theory, one is interested in constructing nets of local von Neumann algebras satisfying the Haag Kastler axioms. Every such net defines a local net of standard subspaces in the corresponding Hilbert space by letting the selfadjoint elements in the local algebras act on a common cyclic and separating vector. In this talk, we discuss work by Frahm, Neeb and Olafsson which constructs nets standard subspaces on de Sitter space satisfying the corresponding axioms. Here the main tool is "realizing" irreducible unitary representations of the Lorentz group SO(1,d) in spaces of distributional sections over de Sitter space. These can be constructed from SO(1,d-1)-finite distribution vectors obtained as distributional boundary values of holomorphically extended orbit maps of SO(d)-finite vectors. Our main contribution is the proof of polynomial growth rates of these orbit maps, which guarantees the existence of the boundary values in the space of distribution vectors.

Tuesday, October 15, 2024

Posted October 9, 2024

11:00 am – 12:00 pm TBD

"What to do in Summer"

Join us for the "Summer Opportunities Event," organized by the SIAM Student Chapter! This session will provide valuable insights on building effective CVs and resumes, as well as exploring a variety of summer opportunities such as internships, summer schools, and workshops. The event will help you enhance your academic profile, gain professional experience, and guide you in finding the right opportunities and preparing the necessary materials.

Posted October 14, 2024

Informal Geometry and Topology Seminar Questions or comments?

3:00 pm – 3:45 pm Thursday, October 10, 2024 Zoom

Meeting of the Tenured Faculty

Wednesday, October 16, 2024

Posted August 30, 2024
Last modified October 17, 2024

1:30 pm Locket 233

Adithyan Pandikkadan, Louisiana State University
Construction of Hyperbolic Manifolds

In this talk, we will discuss two ways for constructing hyperbolic manifolds. We will begin by introducing hyperbolic surfaces, focusing on how to equip a hyperbolic structure on higher genus surfaces. Following this, we will discuss the construction of arithmetic hyperbolic manifolds which is a more general approach.

Posted October 14, 2024

3:30 pm Lockett 381

Benjamin Fehrman, Louisiana State University
Lectures on Homogenization

In these lectures, we will develop a fully rigorous theory of stochastic homogenization for linear elliptic equations, beginning with the periodic case. Applications of homogenization are diverse, and include modeling the conductivity of composites with small-scale defects and the large-scale behavior of passive advected quantities like temperature in turbulent fluid flows. These systems are effectively random, to our eyes, and their study is essentially equivalent to the asymptotic behavior of a diffusion process in a random environment. Our aim is to derive an effective model that provides a good approximation of the original system with high probability.

Posted August 29, 2024
Last modified October 7, 2024

Mathematical Physics and Representation Theory Seminar

3:30 pm

Bin Sun, Michigan State University
$L^2$-Betti numbers of Dehn fillings

I will talk about a recent joint work with Nansen Petrosyan where we obtain conditions under which $L^2$-Betti numbers are preserved by group-theoretic Dehn fillings. As an application, we verify the Singer Conjecture for certain Einstein manifolds and provide new examples of hyperbolic groups with exotic subgroups. We also establish a virtual fibering criterion and obtain bounds on deficiency of Dehn fillings. A key step in our approach of computations of $L^2$-Betti numbers is the construction of a tailored classifying space, which is of independent interest.

Monday, October 21, 2024

Posted September 27, 2024
Last modified October 16, 2024

2:30 pm – 3:20 pm Lockett 233

Xinchun Ma, University of Chicago
Cherednik algebras, Torus knots and flag commuting varieties

In this talk, we will explore how the Khovanov-Rozansky homology of the (m,n)-torus knot can be extracted from the finite-dimensional representation of the rational Cherednik algebra at slope m/n, equipped with the Hodge filtration. Our approach involves constructing a family of coherent sheaves on the Hilbert scheme of points on the plane, arising from cuspidal character D-modules. In describing this family of coherent sheaves, the geometry of nilpotent flag commuting varieties naturally emerges, closely related to the compactified regular centralizer in type A.

Posted October 4, 2024

Algebra and Number Theory Seminar Questions or comments?

5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial Student Association Meeting

We will have guest speaker Jordan Hayes from AETNA (CVS Health). Pizza will be served.

Tuesday, October 22, 2024

Posted August 14, 2024
Last modified October 17, 2024

2:30 pm Lockett 233 or click here to attend on Zoom

Brian Grove, LSU
The Explicit Hypergeometric Modularity Method

The existence of hypergeometric motives predicts that hypergeometric Galois representations are modular. More precisely, explicit identities between special values of hypergeometric character sums and coefficients of certain modular forms on appropriate arithmetic progressions of primes are expected. A few such identities have been established in the literature using various ad-hoc techniques. I will discuss a general method to prove these hypergeometric modularity results in dimensions two and three. This is joint work with Michael Allen, Ling Long, and Fang-Ting Tu.

Posted October 18, 2024

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm DMC 1034

Xili Wang, Peking University
DL for PDEs: towards parametric, high-dimensional and PDE-constrained optimization

Despite advances in simulating multiphysics problems through numerical discretization of PDEs, mesh-based approximation remains challenging, especially for high-dimensional problems governed by parameterized PDEs. Moreover, other PDE-related problems, such as PDE-constrained shape optimization, introduce additional difficulties including mesh deformation and correction. While Physics-Informed Neural Networks (PINNs) offer an alternative, they often lack the accuracy of traditional methods like finite element methods. Relying solely on a 'black-box' approach may not be the best choice for scientific computing. Inspired by adaptive finite element methods, we propose a deep adaptive sampling approach to solve low-regularity parametric PDEs and high-dimensional committor functions in rare event simulations. Additionally, by integrating the mesh-free nature of neural networks into the direct-adjoint looping (DAL), we achieve fully mesh-independent solutions for PDE-constrained shape optimization problems.

Wednesday, October 23, 2024

Posted August 30, 2024
Last modified October 17, 2024

1:30 pm Locket 233

Megan Fairchild, Louisiana State University
Slicing Obstructions from 4-Manifold Theory

The orientable 4 genus of a knot is defined to be the minimum genus amongst all smoothly embedded surfaces in the 4-ball with boundary the knot. A knot is called slice if it bounds a smoothly embedded disk in the 4-ball. Invariants of knots, either classical or Heegaard Floer, are commonly used as lower bounds for the orientable 4 genus of knots. We will examine a different approach to showing knots are not smoothly slice, coming from 4-manifold theory.

Posted October 22, 2024

3:30 pm Lockett 237

Benjamin Fehrman, Louisiana State University
Lectures on Homogenization - Part 2

Posted October 15, 2024
Last modified October 22, 2024

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm 232 Lockett

Nathan Mehlhop, Louisiana State University
Ergodic averaging operators

Certain quantitative estimates such as oscillation inequalities are often used in the study of pointwise convergence problems. Here, we study these for discrete ergodic averaging operators and discrete singular integrals along polynomial orbits in multidimensional subsets of integers or primes. Because of its relevance to multiparameter averaging operators, we also consider the vector-valued setting. Several tools including the Hardy-Littlewood circle method, Weyl's inequality, the Ionescu-Wainger multiplier theorem, the Magyar-Stein-Wainger sampling principle, the Marcinciewicz-Zygmund inequality, and others, are important in this field. The talk will introduce the problem and many of these ideas, and then give some outline of how the various estimates can be put together to give the conclusion.

Friday, October 25, 2024

Posted August 19, 2024
Last modified September 27, 2024

10:30 am – 11:20 am Zoom (click here to join)

Andrii Mironchenko, University of Klagenfurt IEEE CSS George S. Axelby Outstanding Paper Awardee
Superposition Theorems for Input-to-State Stability of Time-Delay Systems

We characterize input-to-state stability (ISS) for nonlinear time-delay systems (TDS) in terms of stability and attractivity properties for systems with inputs. Using the specific structure of TDS, we obtain much tighter results than those possible for general infinite-dimensional systems. The subtle difference between forward completeness and boundedness of reachability sets (BRS) is essential for the understanding of the ISS characterizations. As BRS is important in numerous other contexts, we discuss this topic in detail as well. We shed light on the differences between the ISS theories for TDS, generic infinite-dimensional systems, and ODEs.

Posted October 1, 2024

2:30 pm – 3:30 pm Friday, October 4, 2024 Zoom Link

Andrew Fulcher, University College Dublin
The cyclic flats of L-polymatroids

In recent years, $q$-polymatroids have drawn interest because of their connection with rank-metric codes. For a special class of $q$-polymatroids called $q$-matroids, the fundamental notion of a cyclic flat has been developed as a way to identify the key structural features of a $q$-matroid. In this talk, we will see a generalization of the definition of a cyclic flat that can apply to $q$-polymatroids, as well as a further generalization, $L$-polymatroids. The cyclic flats of an $L$-polymatroid is essentially a reduction of the data of an $L$-polymatroid such that the $L$-polymatroid can be retrieved from its cyclic flats. As such, in matroid theory, cyclic flats have been used to characterize numerous invariants.

Monday, October 28, 2024

Posted September 25, 2024
Last modified October 7, 2024

Mathematical Physics and Representation Theory Seminar

11:00 am – 12:00 pm TBD
(Originally scheduled for Tuesday, October 8, 2024)

Summer Opportunities

TBA DATE is still to be determined!

Posted September 27, 2024
Last modified October 24, 2024

2:30 pm – 3:20 pm Lockett 233

Nikolay Grantcharov, University of Chicago
Infinitesimal structure of BunG

Given a semisimple group G and a smooth projective curve X over an algebraically closed field of arbitrary characteristic, let Bun_G(X) denote the moduli space of principal G-bundles over X. For a bundle P without infinitesimal symmetries, we describe the n^th order divided-power infinitesimal jet spaces of Bun_G(X) at P for each n. The description is in terms of differential forms on the Fulton-Macpherson compactification of the configuration space, with logarithmic singularities along the diagonal divisor. We also briefly discuss applications into constructing Hitchin's flat connection on the vector bundle of conformal blocks.

Posted September 26, 2024
Last modified October 25, 2024

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett 233

Matias Delgadino, University of Texas at Austin
Generative Adversarial Networks: Dynamics

Generative Adversarial Networks (GANs) was one of the first Machine Learning algorithms to be able to generate remarkably realistic synthetic images. In this presentation, we delve into the mechanics of the GAN algorithm and its profound relationship with optimal transport theory. Through a detailed exploration, we illuminate how GAN approximates a system of PDE, particularly evident in shallow network architectures. Furthermore, we investigate known pathological behaviors such as mode collapse and failure to converge, and elucidate their connections to the underlying PDE framework through an illustrative example.

Tuesday, October 29, 2024

Posted August 21, 2024
Last modified October 25, 2024

2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom

Brett Tangedal, University of North Carolina, Greensboro
Real Quadratic Fields and Partial Zeta-Functions

We focus on real quadratic number fields and explain an approach to the partial zeta-functions associated with the various ideal class groups of such fields dating back to the original work of Zagier, Stark, Shintani, David Hayes, and others. Along the way, we will give a brief introduction to Stark's famous first order zero conjecture.

Wednesday, October 30, 2024

Posted August 30, 2024
Last modified October 27, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Locket 233

Matthew Lemoine, Louisiana State University
A Brief Introduction to Khovanov Homology through an example

In this talk, we will discuss Khovanov Homology and how to compute this homology using an example with the trefoil knot. We will also discuss the relations between Khovanov Homology and the Jones Polynomial.

Posted October 29, 2024

3:30 pm Lockett 237

Benjamin Fehrman, Louisiana State University
Lectures on Homogenization - Part 3

Posted October 7, 2024
Last modified October 28, 2024

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Monika Kudlinska, University of Cambridge
Solving equations in free-by-cyclic groups

A group G is said to be free-by-cyclic if it maps onto the infinite cyclic group with free kernel of finite rank. Free-by-cyclic groups form a large and widely-studied class with close links to 3-manifold topology. A group G is said to be equationally Noetherian if any system of equations over G is equivalent to a finite subsystem. In joint work with Motiejus Valiunas we show that all free-by-cyclic groups are equationally Noetherian. As an application, we deduce that the set of exponential growth rates of a free-by-cyclic group is well ordered.

Friday, November 1, 2024

Posted August 26, 2024
Last modified October 24, 2024

10:30 am – 11:20 am Zoom (click here to join)

Angelia Nedich, Arizona State University
Resilient Distributed Optimization for Cyber-physical Systems

This talk considers the problem of resilient distributed multi-agent optimization for cyber-physical systems in the presence of malicious or non-cooperative agents. It is assumed that stochastic values of trust between agents are available which allows agents to learn their trustworthy neighbors simultaneously with performing updates to minimize their own local objective functions. The development of this trustworthy computational model combines the tools from statistical learning and distributed consensus-based optimization. Specifically, we derive a unified mathematical framework to characterize convergence, deviation of the consensus from the true consensus value, and expected convergence rate, when there exists additional information of trust between agents. We show that under certain conditions on the stochastic trust values and consensus protocol: 1) almost sure convergence to a common limit value is possible even when malicious agents constitute more than half of the network, 2) the deviation of the converged limit, from the nominal no attack case, i.e., the true consensus value, can be bounded with probability that approaches 1 exponentially, and 3) correct classification of malicious and legitimate agents can be attained in finite time almost surely. Further, the expected convergence rate decays exponentially with the quality of the trust observations between agents. We then combine this trust-learning model within a distributed gradient-based method for solving a multi-agent optimization problem and characterize its performance.

Posted October 29, 2024

LSU AWM Student Chapter LSU AWM Student Chapter Website

12:30 pm – 1:20 pm

AWM Student Chapter Q & A Session with Prof. Angelia Nedich

Join us for a QA session hosted by the Association for Women in Mathematics (AWM) Student Chapter. We are honored to have Prof. Angelia Nedich from Arizona State University, a leading convex analysis and optimization researcher. Prof. Nedich will share insights from her research and discuss her academic experiences.

Monday, November 4, 2024

Posted November 1, 2024

Algebra and Number Theory Seminar Questions or comments?

5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial Student Association Meeting

Guest speaker Jack Berry from Cigna health will speak. Pizza will be served.

Tuesday, November 5, 2024

Posted October 8, 2024
Last modified October 30, 2024

2:30 pm – 3:30 pm Virtual talk: click here to attend on Zoom

Linli Shi, University of Connecticut
On higher regulators of Picard modular surfaces

The Birch and Swinnerton-Dyer conjecture relates the leading coefficient of the L-function of an elliptic curve at its central critical point to global arithmetic invariants of the elliptic curve. Beilinson’s conjectures generalize the BSD conjecture to formulas for values of motivic L-functions at non-critical points. In this talk, I will relate motivic cohomology classes, with non-trivial coefficients, of Picard modular surfaces to a non-critical value of the motivic L-function of certain automorphic representations of the group GU(2,1).

Wednesday, November 6, 2024

Posted August 30, 2024
Last modified November 4, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Locket 233

Nilangshu Bhattacharyya, Louisiana State University
Gromov norm of a compact manifold and straightening

We will define the Gromov norm of a compact manifold and straightening (every singular chain is naturally homotopic to a straight one).

Posted October 12, 2024
Last modified October 30, 2024

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm 232 Lockett

Vishwa Dewage, Clemson University
The Laplacian of an operator and applications to Toeplitz operators

Werner's quantum harmonic analysis (QHA) provides a set of tools that are applicable in many areas of analysis, including operator theory. As noted by Fulsche, QHA is particularly suitable to study Toeplitz operators on the Fock space. We explore the Laplacian of an operator and a heat equation for operators on the Fock space using QHA. Then we discuss some applications to Toeplitz operators. This talk is based on joint work with Mishko Mitkovski.

Friday, November 8, 2024

Posted September 6, 2024
Last modified October 11, 2024

10:30 am – 11:20 am Zoom (click here to join)

Laura Menini, Università degli Studi di Roma Tor Vergata
Distance to Instability for LTI Systems under Structured Perturbations

The talk will present a procedure to compute the distance to instability for linear systems subject to structured perturbations, in particular perturbations that affect polynomially the dynamics of the system. The procedure is based on classical notions from stability of linear systems, optimization and algebraic geometry, some of which will be reviewed briefly. The application to the design of fixed-structure controllers to deal with robust control problems will also be outlined, with the goal of choosing the controller which obtains the best conservative estimate of the region of stability. The results will be illustrated on some academic examples.

Posted November 5, 2024

Algebra and Number Theory Seminar Questions or comments?

2:30 pm – 3:30 pm Lockett Hall 233 (simulcasted via Zoom)

Matthew Mizell, LSU
Structures That Arise From Nested Sequences of Flats in Projective and Affine Geometries

In a vector space $V$, take a sequence of subspaces $V_1,V_2,\dots,V_n$ such that $V_1 \subseteq V_2 \subseteq \ldots \subseteq V_n = V$. Color the non-zero elements of $V_1$ green, the elements of $V_2 \backslash V_1$ red, the elements of $V_3 \backslash V_2$ green and so on. We call the resulting set of green elements a target. The study of targets was initiated by Nelson and Nomoto in 2018 for vector spaces over the $2$-element field. In this talk, we will discuss targets over arbitrary finite fields. We will also consider the graph analogue of targets as well as targets over affine geometries. Our main results will characterize each type of target in terms of its forbidden substructures. This is joint work with James Oxley.

Tuesday, November 12, 2024

Posted October 8, 2024
Last modified November 4, 2024

2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom

Michael Allen, Louisiana State University
An infinite family of hypergeometric supercongruences

In a recent series of papers with Brian Grove, Ling Long, and Fang-Ting Tu, we explore the relationship between modular forms and hypergeometric functions in the particular settings of complex, finite, and $p$-adic fields, and unify these perspectives through Galois representations. In this talk, we focus primarily on the $p$-adic aspects, where this relationship arises in the form of congruences between truncated hypergeometric sums and Fourier coefficients of modular forms. Such congruences are predicted to hold modulo $p$ by formal commutative group law, we refer to a congruence modulo a higher power of $p$ as a supercongruence. In this talk, we briefly survey results and methods in the area of supercongruences before establishing an infinite family of supercongruences which hold modulo $p^2$ for all primes in certain arithmetic progressions depending on the parameters of the corresponding hypergeometric functions.

Posted October 22, 2024

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm DMC 1034

Jeremy Shahan, Louisiana State University
Shape Optimization with Unfitted Finite Element Methods

We present a formulation of a PDE-constrained shape optimization problem that uses an unfitted finite element method (FEM). The geometry is represented (and optimized) using a level set approach and we consider objective functionals that are defined over bulk domains. For a discrete objective functional (i.e. one defined in the unfitted FEM framework), we derive the exact Frechet, shape derivative in terms of perturbing the level set function directly. In other words, no domain velocity is needed. We also show that the derivative is (essentially) the same as the shape derivative at the continuous level, so is rather easy to compute. In other words, one gains the benefits of both the optimize-then-discretize and discretize-then-optimize approaches.

Wednesday, November 13, 2024

Posted August 30, 2024
Last modified November 11, 2024

1:30 pm Locket 233

Saumya Jain, Louisiana State University
Gromov norm is directly proportional to the volume

We will prove that the Gromov norm of a compact oriented hyperbolic manifold is directly proportional to its volume.

Posted November 12, 2024

3:30 pm Lockett 237

Benjamin Fehrman, Louisiana State University
Lectures on Homogenization - Part 4

Posted November 12, 2024

3:30 pm Lockett 237

Benjamin Fehrman, Louisiana State University
Lectures on Homogenization - Part 4

Posted October 12, 2024
Last modified October 22, 2024

3:30 pm – 4:30 pm 232 Lockett

Robert Fulsche, University of Hannover, Germany
Harmonic analysis on phase space and operator theory

In his paper \emph{Quantum harmonic analysis on phase space} from 1984 (J. Math. Phys.), Reinhard Werner developed a new phase space formalism which allowed for a joint harmonic analysis of functions and operators. Since his reasoning was mostly guided by motivations from the physical side of quantum mechanics, mathematicians ignored this highly interesting contribution for almost 35 years. Only in the last few years, interest in Werner's approach grew and actually yielded a number of interesting and relevant results in time-frequency analysis as well as in operator theory. The speaker, who has been working mostly on the operator theory side of quantum harmonic analysis (QHA), will try to describe the basic features of QHA and how they relate to problems in operator theory. After presenting some basics of the formalism of QHA, we will discuss one application of the audience's choice: Either a result in Fredholm theory, results in commutative operator algebras or a characterization problem of a certain important algebra appearing in QHA.

Posted September 17, 2024
Last modified November 11, 2024

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Arka Banerjee, Auburn University
Urysohn 1-width and covers

A metric space has small Urysohn 1-width if it admits a continuous map to a 1-dimensional complex where the preimage of each point has small diameter. An open problem is, if a space's universal cover has small Urysohn 1-width, must the original space also have small Urysohn 1-width? While one might intuitively expect this to be true, there are strange examples that suggest otherwise. In this talk, I will explore the motivations behind this question and discuss some partial progress we have made in understanding it. This is a joint work with H. Alpert and P. Papasoglu.

Friday, November 15, 2024

Posted August 29, 2024
Last modified October 22, 2024

10:30 am – 11:20 am Zoom (click here to join)

Piernicola Bettiol, Université de Bretagne Occidentale, France
Average Cost Minimization Problems Subject to State Constraints

Optimal control problems involving parameters appear to be a natural framework for some models arising in applications such as aerospace engineering, machine learning, and biology, among many others. According to the nature of the problem (or the model), we may have different minimization criteria; in some circumstances it is more convenient to provide the performance criterion in terms of an average cost, providing a paradigm which differs from the more traditional minimax or robust optimization criteria. In this talk, we shall consider pathwise state constraint optimal control problems in which unknown parameters intervene in the dynamics, the cost, the endpoint constraint, and the state constraint. The cost criteria to minimize take the integral form of a given endpoint cost function with respect to a reference probability measure that is defined on the set of unknown parameters. For this class of problems, we shall present the necessary optimality conditions.

Monday, November 18, 2024

Posted September 11, 2024
Last modified October 25, 2024

3:30 pm Lockett 233

Michael Novack, Louisiana State University
TBA

Posted November 1, 2024

Algebra and Number Theory Seminar Questions or comments?

5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial Student Association Meeting

Last meeting of the semester. Pizza will be served.

Tuesday, November 19, 2024

Posted October 8, 2024
Last modified November 18, 2024

2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom

David Lowry-Duda, ICERM
Murmuration phenomena in number theory

Approximately 2 years ago, a group of number theorists experimenting with machine learning observed unexpected biases in data from elliptic curves. When plotted, these biases loosely resemble gatherings of starlings, leading to the name "murmurations." This now seems to be a very general phenomenon in number theory. Many different families of arithmetic objects exhibit consistent biases. But proving these behaviors has been challenging. In this talk, we'll give several examples of murmuration phenomena, connect these biases to distributions of zeros of L-functions, and describe recent success proving murmurations (especially for modular forms).

Posted October 18, 2024

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm DMC 1034

Suhan Zhong, Texas A&M University
Two-stage stochastic programs with polynomial loss function

Two-stage stochastic programs (SPs) with polynomial loss functions serve as a powerful framework for modeling decision-making problems under uncertainty. In this talk, we introduce a two-phase approach to find global optimal solutions for two-stage SPs with continuous decision variables and nonconvex recourse functions. Our method does not only generate global lower bounds for the nonconvex stochastic program, but also yields an explicit polynomial approximation for the recourse function. It is particularly suitable for the case where the random vector follows a continuous distribution or when dealing with a large number of scenarios. Numerical experiments are conducted to demonstrate the effectiveness of our proposed approach.

Wednesday, November 20, 2024

Posted August 30, 2024
Last modified November 18, 2024

1:30 pm Locket 233

Samuel Weiner, Louisiana State University
A Survey of Topological Graph Theory

Although graphs are often thought of as strictly combinatorial objects, many substantial developments in graph theory have come by considering their topological properties. For instance, we may define the genus of a graph G to be the minimum integer n such that G embeds into an orientable surface of genus n. Kuratowski's Theorem is a seminal result that precisely determines the class of all genus-2 graphs; a recent result due to Robertson and Seymour characterizes the much broader class of all graphs of bounded genus. We will explore these and other results that lie at the intersection of topology and graph theory. The speaker will assume no prior graph theory knowledge.

Posted November 19, 2024

3:30 pm Lockett 237

Benjamin Fehrman, Louisiana State University
Lectures on Homogenization - Part 5

Thursday, November 21, 2024

Posted November 11, 2024

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 232

Benjamin Dodson, Johns Hopkins University
Global well-posedness and scattering for the radial, conformal wave equation

In this talk we prove global well-posedness and scattering for the radially symmetric nonlinear wave equation with conformally invariant nonlinearity. We prove this result for sharp initial data.

Friday, November 22, 2024

Posted August 21, 2024
Last modified November 10, 2024

10:30 am – 11:20 am Zoom (click here to join)

Benedetto Piccoli, Rutgers University, Camden AMS Fellow, SIAM W. T. and Idalia Reid Prize Awardee
Control Theory in Traffic Applications: 100 Years of Traffic Models

In 1924, in The Quarterly Journal of Economics, Frank H. Knight debated on social costs using an example of two roads, which was the basis of Wardrop’s principle. The author suggested the use of road tolls, and it was probably the first traffic model ever. A few other milestones of a long history include the traffic measurements by Greenshields in 1934, the Lighthill-Whitham-Richards model in the late 1950s, and follow-the-leader microscopic models. After describing some of these milestones, we will turn to the modern theory of conservation laws on topological graphs with applications to traffic monitoring. The theory requires advanced mathematics, such as BV spaces and Finsler-type metrics on L1. In the late 2000s, this theory was combined with Kalman filtering to deal with traffic monitoring using data from cell phones and other devices. Then we will turn to measure-theoretic approaches for multi-agent systems, which encompass follow-the-leader-type models. Tools from optimal transport allow us to deal with the mean-field limit of controlled equations, representing the action of autonomous vehicles. We will conclude by discussing how autonomy can dissipate traffic waves and reduce fuel consumption, and we will illustrate results of a 2022 experiment with 100 autonomous vehicles on an open highway in Nashville.

Posted November 21, 2024

2:30 pm – 3:30 pm Zoom Link

Dillon Mayhew, University of Leeds
Excluded minors for Z3-gainable biased graphs

A biased graph is a graph along with a collection of distinguished cycles, which are said to be balanced. The only rule is that a theta subgraph cannot contain exactly two balanced cycles.Minors of biased graphs work more or less as one would expect: we can delete or contract edges (and delete isolated vertices), and the balanced cycles of the minor are inherited from the larger biased graph.Sometimes the balanced cycles are determined by a gaining function which applies elements of a group to (oriented) edges. We calculate the product of edge labels around a cycle (taking the inverse of a label if that edge is oriented against our direction of travel), and declare a cycle to be balanced if this product is the group identity. If the balanced cycles can be produced in this way via some labeling with elements from the group H, then the biased graph is said to be H-gainable.H-gainable biased graphs form a minor-closed class within the universe of biased graphs, so we naturally ask for a characterisation via excluded minors. This characterisation was completed for the group Z2 by Zaslavsky. We have now completed the characterisation when the group is Z3.More generally, we can postulate a version of Rota's conjecture: when H is a finite group, there are only finitely many excluded-minor biased graphs for the class of H-gainable biased graphs. One might think that this is exactly the same problem as Rota's conjecture for the class of frame matroids or lift matroids arising from H-gainable biased graphs. However, there is no reason to be believe that solving one of these problems will solve the other.This is joint work with Nick Brettell, Rutger Campbell, and Daryl Funk.

Monday, November 25, 2024

Posted November 23, 2024

Algebra and Number Theory Seminar Questions or comments?

2:30 pm Lockett 240

Wasiur KhudaBukhsh, University of Nottingham
Enzyme kinetic reactions as interacting particle systems: Stochastic averaging and parameter inference

We consider a stochastic model of multistage Michaelis--Menten (MM) type enzyme kinetic reactions describing the conversion of substrate molecules to a product through several intermediate species. The high-dimensional, multiscale nature of these reaction networks presents significant computational challenges, especially in statistical estimation of reaction rates. This difficulty is amplified when direct data on system states are unavailable, and one only has access to a random sample of product formation times. To address this, we proceed in two stages. First, under certain technical assumptions akin to those made in the Quasi-steady-state approximation (QSSA) literature, we prove two asymptotic results: a stochastic averaging principle that yields a lower-dimensional model, and a functional central limit theorem that quantifies the associated fluctuations. Next, for statistical inference of the parameters of the original MM reaction network, we develop a mathematical framework involving an interacting particle system (IPS) and prove a propagation of chaos result that allows us to write a product-form likelihood function. The novelty of the IPS-based inference method is that it does not require information about the state of the system and works with only a random sample of product formation times. We provide numerical examples to illustrate the efficacy of the theoretical results. Preprint: https://arxiv.org/abs/2409.06565

Tuesday, December 3, 2024

Posted August 29, 2024
Last modified December 2, 2024

2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom

Jiuya Wang, University of Georgia
Counterexamples for Turkelli's Modification of Malle's Conjecture

Malle's conjecture gives a conjectural distribution of number fields with bounded discriminant. Klueners gives counterexamples of Malle's conjecture, due to the presence of roots of unity in intermediate fields. These types of counterexamples exists in both global function fields and number fields. Turkelli proposes a modification of Malle's conjecture inspired by a function field analogue. We give counterexamples for Turkelli's modified conjecture. We will also talk about the difference of Malle's conjecture on function fields and number fields.

Wednesday, December 4, 2024

Posted August 30, 2024
Last modified December 2, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Locket 233

Huong Vo, Louisiana State University
Mostow's Rigidity Theorem

Mostow's Rigidity Theorem states that two connected, compact, oriented hyperbolic manifolds of dimension at least 3 that are homotopy equivalent are isometric. In this talk, we will review key steps and finish the proof of this theorem.

Friday, December 6, 2024

Posted August 13, 2024
Last modified November 24, 2024

Control and Optimization Seminar Questions or comments?

10:30 am – 11:20 am Zoom (click here to join)

Karl Johansson, KTH Royal Institute of Technology, Sweden Fellow of IEEE, IEEE CSS Hendrik W. Bode Lecture Prize Awardee
Machine Learning Components in Cyber-Physical Transport Systems

Advances in sensing, connectivity, computing, and electrification are reshaping the infrastructure for moving people and goods. Research in optimizing and enhancing the resilience of transport systems highlights the broader impact of control technology on mobility. This talk will explore the emerging field of learning-enabled cyber-physical-human systems and discuss some specific examples in intelligent transport. We will show how connected vehicles acting as mobile sensors and actuators can enable traffic predictions and control at a scale never before possible, by learning traffic models using physics-informed machine learning techniques. The complexities of safe interactions between automated and human-driven vehicles will be discussed, emphasizing the integration of formal reasoning methods and the use of tele-operation. The presentation highlights joint work with students, postdocs, and collaborators in academia and industry.

Friday, December 13, 2024

Posted September 4, 2024
Last modified December 10, 2024

Control and Optimization Seminar Questions or comments?

11:30 am – 12:20 pm Note the new seminar time. Zoom (click here to join)

María Soledad Aronna, Escola de Matematica Aplicada, Brazil
Control of Pest and Disease Dynamics

In this talk, we will discuss some models related to disease control. These models include the optimization of vaccination and testing strategies, as well as systems for biological control of insects and pests. We will demonstrate how optimal control theory and other associated tools aid in analyzing the systems and provide answers to practical questions.

Friday, January 3, 2025

Posted November 8, 2024

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Applied Math

Monday, January 6, 2025

Posted November 8, 2024

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Algebra

Wednesday, January 8, 2025

Posted November 8, 2024

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Analysis

Friday, January 10, 2025

Posted November 8, 2024

Algebra and Number Theory Seminar Questions or comments?

1:00 pm – 4:00 pm Lockett Hall 232

Written Qualifier Exam on Topology

Tuesday, January 14, 2025

Posted January 11, 2025

2:30 pm – 3:20 pm Virtual talk: click here to attend on Zoom

Walter Bridges, University of North Texas.
The proportion of coprime fractions in number fields

The ring $\mathbb{Z}[\sqrt{-5}]$ is often one of the first examples students encounter of a ring that is not unique factorization domain. Relatedly, in the number field $\mathbb{Q}(\sqrt{-5})$, we have $$ \frac{1+\sqrt{-5}}{2}=\frac{3}{1-\sqrt{-5}}. $$ Both fractions are reduced, meaning that numerator and denominator do not share any (non-unit) factors in $\mathbb{Z}[\sqrt{-5}]$. However, neither fraction is coprime, in the sense that the numerator and denominator pair do not generate $\mathbb{Z}[\sqrt{-5}]$. In this talk, we will answer the question of how often this phenomenon occurs. That is, we compute the density, suitably defined, of the set of coprime fractions in the set of all reduced fractions in a generic number field. Our answer for $\mathbb{Q}(\sqrt{-5})$ is 80%. We will begin with a review of algebraic number theory, then discuss our notion of density in number fields. Finally, we will show that the density in question may be computed using well-known properties of Hecke L-functions. We intend this talk to be accessible to beginning graduate students.

Friday, January 17, 2025

Posted January 13, 2025

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 232

Trinh Tien Nguyen, University of Wisconsin Madison
Boundary Layers in Fluid Dynamics and Kinetic Theory

Abstract: In this talk, I will discuss recent results on Prandtl boundary layer theory in fluid dynamics. We demonstrate that the Prandtl expansion holds for initial data that is analytic near the boundary under the no-slip boundary condition. I will then present a recent result on the validity of the Prandtl expansion from Boltzmann theory, marking an important step toward justifying other types of approximate solutions (arising from fluid dynamics) as macroscopic limits of the kinetic Boltzmann equations.

Tuesday, January 21, 2025

Posted January 19, 2025

2:30 pm – 3:30 pm Virtual talk: click here to attend on Zoom

Asimina Hamakiotes, University of Connecticut
Abelian extensions arising from elliptic curves with complex multiplication

Let $K$ be an imaginary quadratic field, and let $\mathcal{O}_{K,f}$ be an order in $K$ of conductor $f \geq 1$. Let $E$ be an elliptic curve with complex multiplication by $\mathcal{O}_{K,f}$, such that $E$ is defined by a model over $\mathbb{Q}(j(E))$, where $j(E)$ is the $j$-invariant of $E$. Let $N\geq 2$ be an integer. The extension $\mathbb{Q}(j(E), E[N])/\mathbb{Q}(j(E))$ is usually not abelian; it is only abelian for $N=2,3$, and $4$. Let $p$ be a prime and let $n\geq 1$ be an integer. In this talk, we will classify the maximal abelian extension contained in $\mathbb{Q}(E[p^n])/\mathbb{Q}$.

Friday, January 24, 2025

Posted November 10, 2024

Control and Optimization Seminar Questions or comments?

11:30 am – 12:20 pm Zoom (click here to join)

Rushikesh Kamalapurkar, University of Florida
Operator Theoretic Methods for System Identification

Operator representations of dynamical systems on Banach spaces provide a wide array of modeling and analysis tools. In this talk, I will focus on dynamic mode decomposition (DMD). In particular, new results on provably convergent singular value decomposition (SVD) of total derivative operators corresponding to dynamic systems will be presented. In the SVD approach, dynamic systems are modeled as total derivative operators that operate on reproducing kernel Hilbert spaces (RKHSs). The resulting total derivative operators are shown to be compact provided the domain and the range RKHSs are selected carefully. Compactness is used to construct a novel sequence of finite rank operators that converges, in norm, to the total derivative operator. The finite rank operators are shown to admit SVDs that are easily computed given sample trajectories of the underlying dynamical system. Compactness is further exploited to show convergence of the singular values and the right and left singular functions of the finite rank operators to those of the total derivative operator. Finally, the convergent SVDs are utilized to construct estimates of the vector field that models the system. The estimated vector fields are shown to be provably convergent, uniformly on compact sets. Extensions to systems with control and to partially unknown systems are also discussed. This talk is based in part on joint works [RK23], [RK24], and [RRKJ24] with J.A. Rosenfeld.

Posted January 10, 2025
Last modified January 17, 2025

3:30 pm – 4:30 pm Lockett 232

Suhan Zhong, Texas A&M University
Polynomial Optimization in Data Science

Abstract: Optimization plays a pivotal role in data science. Recent advances in polynomial optimization have introduced innovative methods to solve many challenging problems in this field. In this talk, I will showcase the application of polynomial optimization through the lens of two-stage stochastic models. Additionally, I will provide a brief overview of the underlying theory and discuss potential future research directions.

Monday, January 27, 2025

Posted January 15, 2025
Last modified January 21, 2025

3:30 pm – 4:30 pm Lockett 232

Saber Jafarpour, University of Colorado Boulder
Safety and Resilience of Learning-enabled Autonomous Systems: A Monotone Contracting System Perspective.

Abstract: Learning-enabled autonomous systems are increasingly deployed for decision-making in safety-critical environments. Despite their substantial computational advantages, ensuring the safety and reliability of these systems remains a significant challenge due to their high dimensionality and inherent nonlinearity. In this talk, we leverage tools and techniques from control theory to develop theoretical and algorithmic methods for certifying the safety and robustness of learning-enabled autonomous systems. Our approach investigates safety and resilience from a reachability perspective. We employ contraction and monotone systems theories to develop computationally efficient frameworks for approximating reachable sets of autonomous systems. We demonstrate how these frameworks can be applied to verify and train robust standalone neural networks and to provide run-time safety assurance in systems with learning-based controllers.

Wednesday, January 29, 2025

Posted December 11, 2024
Last modified January 27, 2025

3:30 pm Lockett 233

Akram Alishahi, University of Georgia
Contact invariants in Heegaard Floer homology

Over the past two decades multiple invariants of contact structures have been defined in different variations of Heegaard Floer homology. We will start with an overview of these invariants and their connections. Then, we will discuss one of these invariants that is defined for a contact 3-manifold with a foliated boundary and lives in bordered sutured Floer homology in more details. This is a joint work with Földvári, Hendricks, Licata, Petkova and Vertesi.

Thursday, January 30, 2025

Posted December 5, 2024
Last modified January 22, 2025

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 232

Ken Ono, University of Virginia
Partitions detect primes

This talk presents “partition theoretic” analogs of the classical work of Matiyasevich that resolved Hilbert’s Tenth Problem in the negative. The Diophantine equations we consider involve equations of MacMahon’s partition functions and their natural generalizations. Here we explicitly construct infinitely many Diophantine equations in partition functions whose solutions are precisely the prime numbers. To this end, we produce explicit additive bases of all graded weights of quasimodular forms, which is of independent interest with many further applications. This is joint work with Will Craig and Jan-Willem van Ittersum.

Friday, January 31, 2025

Posted December 6, 2024
Last modified January 2, 2025

11:30 am – 12:20 pm Zoom (click here to join)

Harbir Antil, George Mason University
Optimization and Digital Twins

With recent advancements in computing resources and interdisciplinary collaborations, a new research field called Digital Twins (DTs) is starting to emerge. Data from sensors located on a physical system is fed into its DT, the DT in turn help make decisions about the physical system. This cycle then continues for the life-time of the physical system. A typical example is for instance a bridge. In many cases, these problems can be cast as optimization problems with finite or infinite dimensional (partial differential equations) constraints. This talk will provide an introduction to this topic. Special attention will be given to: 1) Optimization algorithms that are adaptive and can handle inexactness, e.g., Trust- Regions and ALESQP; 2) Optimization under uncertainty and tensor train decomposition to overcome the curse of dimensionality; 3) Reduced order modeling for dynamic optimization using randomized compression. Additionally, the DT framework may require coupling mutiphysics / systems / data with very different time scales. Keeping this in mind, a newly introduced notion of barely coupled problems will be discussed. Realistic examples of DTs to identify weakness in structures such as bridges, wind turbines, electric motors, and neuromorphic imaging will be considered.

Posted January 21, 2025

1:30 pm – 2:30 pm Lockett Hall 233

Avin Sunuwar, LSU
Chain theorems on 3-connected graphs

Chain theorems provide a pathway in constructing and analyzing families of graphs. In this seminar, we explore improvements in chain theorems for 3-connected graphs and their subclasses. We discuss an improved version of Tutte’s Wheel Theorem, which enhances algorithmic efficiency by limiting the construction process to extensions of the wheel W4 with restricted operations. Then, we discuss a chain theorem for smoothly 3-connected graphs. Additionally, we present a chain theorem for rooted graphs. These results not only refine classical theorems but also pave the way for further advancements in graph theory and its applications.

Posted January 28, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 232

Federico Glaudo, Institute for Advanced Study, Princeton
A Journey through PDEs and Geometry

This talk will explore a range of intriguing questions that lie at the crossroads of partial differential equations and geometry. Topics include the stability of near-solutions to PDEs, the isoperimetric inequalities on curved spaces, as well as the random matching problem. The aim is to make the ideas accessible and engaging for a broad mathematical audience.

Wednesday, February 5, 2025

Posted February 3, 2025

1:30 pm

Megan Fairchild, Louisiana State University
Rachel Meyers, Louisiana State University
Introduction to the h-Cobordism Theorem

We state the h-Cobordism theorem and go over the motivation and background to understand the statement of the theorem. Additionally, we discuss its relevance and impact to the generalized Poincarè conjecture in dimensions 5 and higher.

Posted January 23, 2025
Last modified January 27, 2025

3:30 pm Lockett 233

Matthew Stoffregen, Michigan State University
Pin(2) Floer homology and the Rokhlin invariant

In this talk, we describe a family of homology cobordism invariants that can be extracted from Pin(2)-equivariant monopole Floer homology (using either Manolescu or Lin's definitions), that have some properties in common with both the epsilon and upsilon invariants in knot Floer homology. We'll show a relationship of this family to questions about torsion in the homology cobordism group, and to triangulation of higher-dimensional manifolds. This is joint work in progress with Irving Dai, Jen Hom, and Linh Truong.

Thursday, February 6, 2025

Posted February 5, 2025

Control and Optimization Seminar Questions or comments?

2:30 pm – 3:30 pm Zoom

Ajay Chandra, Imperial College London
An Invitation to Singular Stochastic Partial Differential Equations

Abstract: In this talk I will start by motivating the fundamental importance of singular stochastic partial differential equations in (i) our understanding of the large-scale behaviour of dynamic random systems and (ii) developing a rigorous approach to quantum field theory. I will describe the key mathematical difficulties these equations pose, and sketch how combining analytic, probabilistic, and algebraic arguments have allowed mathematicians to overcome these difficulties and develop a powerful new PDE theory. I’ll also discuss some more recent developments in this area, namely applications to gauge theory and non-commutative probability theory.

Friday, February 7, 2025

Posted November 1, 2024
Last modified January 8, 2025

11:30 am – 12:20 pm Zoom (click here to join)

Ali Zemouche, University of Lorraine, France
Advanced Robust Moving Horizon Estimation Schemes for Nonlinear Systems

This presentation deals with robust stability analysis of moving horizon estimation (MHE) for a class of nonlinear systems. New mathematical tools are introduced, enabling the development of new design conditions to optimize the parameters of the MHE scheme's cost function. These conditions are closely tied to the size of the MHE window and the system's incremental exponential input/output-to-state stability (i-EIOSS) coefficients. To enhance the robustness of the MHE while minimizing the window size, advanced prediction techniques are proposed. Additionally, innovative linear LMI-based methods are presented for synthesizing the i-EIOSS coefficients and prediction gains. The effectiveness of the proposed prediction methods is validated through numerical examples, highlighting their performance improvements.

Posted February 5, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Zoom

Meeting of the Professorial Faculty

Wednesday, February 12, 2025

Posted February 3, 2025
Last modified February 10, 2025

12:30 pm

Porter Morgan, University of Massachusetts Amherst
Obtaining exotic 4-manifolds through torus surgery

Let M be a closed, smooth, oriented 4-manifold. In this talk, we’ll explore how to construct an irreducible copy of M using torus surgery; this means that we construct a 4-manifold X that’s homeomorphic to M, but not diffeomorphic to it, and also that X is irreducible in the sense that it can’t be expressed as a non-trivial connect sum. We’ll first describe a general strategy for finding irreducible copies. Then we’ll define torus surgery, and go through an example of building an irreducible copy with this tool. If time permits, we’ll talk about some other surgery techniques that can be used to build irreducible copies.

Posted November 12, 2024
Last modified February 10, 2025

2:30 pm

Porter Morgan, University of Massachusetts Amherst
Irreducible 4-manifolds with order two fundamental group

Let R be a closed, smooth, oriented 4–manifold with order two fundamental group. The works of Freedman and Hambleton-Kreck show that R is determined up to homeomorphism by just a few basic properties. That said, there are often many different manifolds that are homeomorphic to R, but not diffeomorphic to it or each other. In this talk, we’ll describe how to construct irreducible copies of R; roughly speaking, these are smooth manifolds that are homeomorphic to R, and don’t decompose into non-trivial connected sums. We’ll show that if R has odd intersection form and non-negative first Chern number, then in all but seven cases, it has an irreducible copy. We’ll describe some of the techniques used to realize these irreducible smooth structures, including torus surgeries, symplectic fiber sums, and a novel approach to constructing Lefschetz fibrations equipped with free involutions. This is joint work with Mihail Arabadji.

Posted December 2, 2024
Last modified February 7, 2025

2:30 pm – 3:20 pm Lockett 381

Chian Yeong Chuah, Ohio State University
Marcinkiewicz Schur Multiplier Theory for Schatten-p class

The boundedness of Schur Multipliers plays an important role in the study of non-commutative harmonic analysis. In this talk, we provide a Marcinkiewicz type multiplier theory for the Schur multipliers on the Schatten p-classes. This generalizes a previous result of Bourgain for Toeplitz type Schur multipliers and complements a recent result by Conde-Alonso, Gonzalez-Perez, Parcet and Tablate. As a corollary, we obtain a new unconditional decomposition for the Schatten p-classes for p>1. Similar results can also be extended to the case of R^d and Z^d, where d>=2.

Friday, February 14, 2025

Posted February 10, 2025

3:30 pm – 4:30 pm Lockett 233 (Simulcasted via Zoom)

Christine Cho, Louisiana State University
Weak maps and the Tutte polynomial

Let M and N be distinct matroids such that N is the image of M under a rank-preserving weak map. Generalizing results of Dean Lucas, we prove that, for x and y positive, T(M;x,y) \geq T(N;x,y) if and only if x+y \geq xy. We give several consequences of this result related to relative freedom of elements of a matroid.

Monday, February 17, 2025

Posted February 10, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm Lockett 232

Hongki Jung, Louisiana State University
$\Lambda(p)$--subsets of manifolds

In 1989, Bourgain proved the existence of maximal $\Lambda(p)$--subsets within the collection of mutual orthogonal functions. We shall explore the Euclidean analogue of $\Lambda(p)$—sets through localization. As a result, we construct maximal $\Lambda(p)$--subsets on a large class of curved manifolds, in an optimal range of Lebesgue exponents $p$. This is joint work with C. Demeter and D. Ryou.

Wednesday, February 19, 2025

Posted February 3, 2025

1:30 pm

Krishnendu Kar, Louisiana State University
TBD

Posted February 6, 2025
Last modified February 12, 2025

3:30 pm Lockett 233

Neal Stoltzfus, Mathematics Department, LSU
Discrete Laplacians, Ribbon Graphs, and Link Polynomials

The Whitney homology of the independence lattices of the state space of a ribbon graphs supports three independent anti-commuting discrete Laplacians. They relate to the three fundamental combinatorial invariants of independent subsets: rank, nullify and genus. We explore the combinations that give link invariants.

Posted January 20, 2025
Last modified February 10, 2025

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm 232 Lockett Hall

Kabe Moen, University of Alabama
New perspectives on the subrepresentation formula

The classical subrepresentation formula establishes that a smooth function is bounded pointwise by the Riesz potential applied to its gradient. This fundamental inequality, combined with the mapping properties of the Riesz potential, leads to the celebrated Gagliardo-Nirenberg-Sobolev inequality, which plays a crucial role in analysis and partial differential equations. In this talk, we show a powerful extension of the subrepresentation formula to several prominent operators in harmonic analysis, including exotic cases such as rough singular integrals and spherical maximal functions. Additionally, we uncover some new structural properties of subrepresentation formulas, including an openness property and an equivalence with weighted Sobolev inequalities and isoperimetric inequalities.

Friday, February 21, 2025

Posted December 23, 2024
Last modified January 10, 2025

11:30 am – 12:20 pm Zoom (click here to join)

Carsten Scherer, University of Stuttgart, Germany IEEE Fellow
Robust Control and the Design of Controllers for Optimization

Recent years have witnessed a renewed interest in considering optimization algorithms as feedback systems. This viewpoint turns, for example, the analysis of the convergence properties of a first order algorithm into a problem of stability analysis of a Lure system. In this talk we highlight why advanced methods in robust control play a key role for developing unprecedented tools to analyze the convergence properties of first order algorithms for solving strongly convex programs. In contrast to alternative approaches, we reveal that the proposed avenue permits not only the analysis but also the systematic design of optimization algorithms using convex semi-definite programming.

Posted October 18, 2024

1:00 pm – 4:00 pm Saturday, February 22, 2025 Digital Media Center Theatre

Finite Element Rodeo

https://www.cct.lsu.edu/finite_element2025

Posted February 17, 2025

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:30 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)

Yixuan Huang, Vanderbilt University
Hierarchy of trees, walks, and Hamiltonicity of products

A spanning t-tree is a spanning tree of maximum degree at most t. A spanning t-walk is a spanning closed walk visiting every vertex at most t times. Spanning t-trees and spanning t-walks are generalizations of Hamiltonian paths and Hamiltonian cycles. Jackson and Wormald (1990) showed that the existence of spanning t-walks implies the existence of spanning t-trees, which again implies the existence of spanning (t+1)-walks. In this talk, we go through results on the existence of these two objects and introduce some results on Hamiltonicity of products of graphs that can be added to this hierarchy.

Tuesday, February 25, 2025

Posted January 26, 2025
Last modified February 24, 2025

2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom

Akio Nakagawa, Kanazawa University
Hypergeometric functions over finite fields

In this talk, I will explain about Otsubo’s definition of hypergeometric functions over finite fields, and I will introduce how the confluent hypergeometric functions over finite fields are useful by showing a transformation formula for Appell–Lauricella functions over finite fields. If time allows, I will introduce my recent work on relations between hypergeometric functions and algebraic varieties.

Wednesday, February 26, 2025

Posted November 12, 2024
Last modified February 26, 2025

1:30 pm Lockett 241

Dave Auckly, Kansas State University
Die on a grid — a twisted story

We will begin by presenting an infinite collection of puzzles with dice. We will see that solutions to these puzzles lead one to explore geometry on interesting spaces where things get twisted.

Posted January 14, 2025
Last modified February 18, 2025

3:30 pm

Dave Auckly, Kansas State University
Restrictions on the genus of trivial families of surfaces in twisted families of 4-manifolds

Several notions of equivalence in topology may be expressed via the existence of families. Thus, asking when an untwisted family of surfaces can be placed in a twisted family of manifolds in a natural question. This talk will describe a generalized adjunction inequality for families.

Posted February 23, 2025
Last modified February 24, 2025

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Vitually via Zoom (click here!)

Hamed Musavi, King's College London
An overview on the recent progress on quantitative Szemeredi Theorems

In this talk, we will start with introducing the classical (qualitative) Ramsey-type Theorems in Additive Combinatorics such as Roth, Sarkozy and Szemeredi Theorems. Then we propose the quantitative problems and a motivation behind their importance. Next, we mention a few recent results on these problems. Finally if time permits, we will talk about ideas in the proofs. This is a joint work with Ben Krause, Terence Tao, and Joni Teravainen.

Friday, February 28, 2025

Posted December 8, 2024
Last modified February 24, 2025

11:30 am – 12:20 pm Zoom (click here to join)

John Baras, University of Maryland Fellow of AAAS, AMS, IEEE, and SIAM
Robust Machine Learning, Reinforcement Learning and Autonomy

Robustness is a fundamental concept in systems science and engineering. It is a critical consideration in inference and decision-making problems. It has recently surfaced again in the context of machine learning (ML), reinforcement learning (RL) and artificial intelligence (AI). We describe a novel and unifying theory of robustness for ML/RL/AI emanating from our much earlier fundamental results on robust output feedback control for general systems. We briefly summarize this theory and the universal solution it provides consisting of two coupled HJB equations. These earlier results rigorously established the equivalence of three seemingly unrelated problems: the robust output feedback control problem, a partially observed differential game, and a partially observed risk sensitive stochastic control problem. We first show that the “four block” view of the above results leads naturally to a similar formulation of the robust ML problem, and to a rigorous path to analyze robustness and attack resiliency in ML. Then we describe a recent risk-sensitive approach, using an exponential criterion in deep learning, that explains the convergence of stochastic gradients despite over-parametrization. Finally, we describe our most recent results on robust and risk sensitive RL for control, using exponential rewards, that emerge from our earlier theory, with the important new extension that the models are now unknown. We show how all forms of regularized RL can be derived from our theory, including KL and entropy regularization, a relation to probabilistic graphical models, and distributional robustness. The deeper reason for this unification emerges: it is the fundamental tradeoff between performance and risk measures in decision making, via rigorous duality. We close with open problems and future research directions.

Posted February 24, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Zoom (email zhiyuw at lsu.edu for Zoom link)

Tung Nguyen, Princeton University
Induced subdivisions and polylogarithmic chromatic number

We discuss a proof that for every graph H, every n-vertex graph with no induced subdivision of H and with bounded clique number has chromatic number at most polylog(n). This extends a result of Fox and Pach that similar polylogarithmic bounds hold for all string graphs, and is close to optimal as there are triangle-free n-vertex string graphs with chromatic number at least loglog n. Joint work with Alex Scott and Paul Seymour.

Wednesday, March 5, 2025

Posted February 3, 2025

1:30 pm

Huong Vo, Louisiana State University
TBD

Thursday, March 6, 2025

Posted November 21, 2024
Last modified March 5, 2025

3:30 pm Lockett 233

Christoph Fischbacher, Baylor University
Non-selfadjoint operators with non-local point interactions

In this talk, I will discuss non-selfadjoint differential operators of the form $i\frac{d}{dx}+V+k\langle \delta,\cdot\rangle$ and $-\frac{d^2}{dx^2}+V+k\langle \delta,\cdot\rangle$, where $V$ is a bounded complex potential. The additional term, formally given by $k\langle \delta,\cdot\rangle$, is referred to as ``non-local point interaction" and has been studied in the selfadjoint context by Albeverio, Cojuhari, Debowska, I.L. Nizhnik, and L.P. Nizhnik. I will begin with a discussion of the spectrum of the first-order operators on the interval and give precise estimates on the location of the eigenvalues. Moreover, we will show that the root vectors of these operators form a Riesz basis. If the initial operator is dissipative (all eigenvalues have nonnegative imaginary part), I will discuss the possibility of choosing the non-local point interaction in such a way that it generates a real eigenvalue even if the potential is very dissipative. After this, I will focus on the dissipative second order-case and show similar results on constructing realizations with a real eigenvalue. Based on previous and ongoing collaborations with Matthias Hofmann, Andrés Lopez Patiño, Sergey Naboko, Danie Paraiso, Chloe Povey-Rowe, Monika Winklmeier, Ian Wood, and Brady Zimmerman.

Friday, March 7, 2025

Posted February 24, 2025

10:30 am Lockett Hall 233

James "Dylan" Douthitt, Louisiana State University
Induced-minor-closed classes of matroids (dissertation defense)

Abstract: A graph is chordal if every cycle of length at least four has a chord. In 1961, Dirac characterized chordal graphs as those graphs that can be built from complete graphs by repeated clique-sums. Generalizing this, we consider the class of simple $GF(q)$-representable matroids that can be built from projective geometries over $GF(q)$ by repeated generalized parallel connections across projective geometries. We show that this class of matroids is closed under induced minors and characterize the class by its forbidden induced minors, noting that the case when $q=2$ is distinctive. Additionally, we show that the class of $GF(2)$-chordal matroids coincides with the class of binary matroids that have none of $M(K_4)$, $M^*(K_{3,3})$, or $M(C_n)$ for $n\geq 4$ as a flat. We also show that $GF(q)$-chordal matroids can be characterized by an analogous result to Rose's 1970 characterization of chordal graphs as those that have a perfect elimination ordering of vertices. We then describe the classes of binary matroids with pairs from the set $\{M(C_4),M(K_4\backslash e),M(K_4),F_7\}$ as excluded induced minors. Additionally, we prove structural lemmas toward characterizing the class of binary matroids that do not contain $M(K_4)$ as an induced minor.

Posted October 14, 2024
Last modified February 28, 2025

Mathematical Physics and Representation Theory Seminar

3:30 pm – 4:30 pm Thursday, March 6, 2025 Lockett 232

Alexandru Hening, Texas A&M University
Stochastic Population Dynamics in Discrete Time

I will present a general theory for coexistence and extinction of ecological communities that are influenced by stochastic temporal environmental fluctuations. The results apply to discrete time stochastic difference equations that can include population structure, eco-environmental feedback or other internal or external factors. Using the general theory, I will showcase some interesting examples. I will end my talk by explaining how the population size at equilibrium is influenced by environmental fluctuations.

Monday, March 10, 2025

Posted March 9, 2025

12:30 pm – 1:20 pm 233 Lockett Hall

David Boozer, Indiana University
Student Seminar on Instanton Homology and Foam Evaluations

This is to help prepare graduate students for David Boozer's talk at 2:30pm on the same day. He will discuss some of the basic definitions behind his 2:30pm talk and take questions from graduate students on the objects of study in his talk.

Posted February 10, 2025
Last modified February 24, 2025

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:20 pm 233 Lockett Hall

David Boozer, Indiana University
The combinatorial and gauge-theoretic foam evaluation functors are not the same

Kronheimer and Mrowka have outlined a new approach that could potentially lead to the first non-computer based proof of the four-color theorem. Their approach relies on a functor J-sharp, which they define using gauge theory, from a category of webs in R^3 to the category of finite-dimensional vector spaces over the field of two elements. They have also suggested a possible combinatorial replacement J-flat for J-sharp, which Khovanov and Robert proved is well-defined on a subcategory of planar webs. We exhibit a counterexample that shows the restriction of the functor J-sharp to the subcategory of planar webs is not the same as J-flat.

Wednesday, March 12, 2025

Posted February 3, 2025
Last modified March 10, 2025

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm

Emmanuel Astante, Louisiana State University
Rota's conjecture and Geometric Lattices

Rota defined homology groups for certain subsets, called cross-cuts, of a lattice. He showed that the value of the Euler characteristic associated with this homology theory depends only on the lattice, not on the choice of the cross-cut. It was conjectured that the homology groups themselves depend only on the lattice. First, we will prove Rota's conjecture. Using this result, we determine the structure of the homology groups of an important class of lattices called geometric lattices.

Posted February 10, 2025
Last modified March 9, 2025

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:20 pm Lockett 233

Maarten Mol, University of Toronto
Constructibility of momentum maps and variation of singular symplectic reduced spaces

Proper maps in various categories studied in singularity theory (for example, the real analytic category) are known to be constructible, in the sense that the image of the map can be stratified in such a way that the map is a topological fiber bundle over each stratum. Such stratifications provide insight into how the fibers of the map vary. In this talk we will discuss the existence of such a stratification for momentum maps of Hamiltonian Lie group actions (a natural class of maps studied in symplectic/Poisson geometry), which provides insight into how the so-called symplectic reduced spaces of the Hamiltonian action vary. Along the way we will also try to give an overview of some more classical results on the geometry of such maps.

Posted March 4, 2025
Last modified March 10, 2025

2:30 pm Lockett 233

Maarten Mol, University of Toronto
Constructibility of momentum maps and variation of singular symplectic reduced spaces (Joint with Mathematical Physics and Representation Theory Seminar)

Thursday, March 13, 2025

Posted February 19, 2025
Last modified March 10, 2025

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 232

Justin Holmer, Brown University
Dynamics of Solitary Waves

Solitary waves arise as exact coherent structures in a range of nonlinear wave equations, including the nonlinear Schrödinger, Korteweg–de Vries, and Benjamin–Ono equations. These equations have broad applications in areas such as water wave theory, plasma physics, and condensed matter physics. When certain types of perturbations are introduced, the solitary wave retains its overall form while its shape and position adjust to accommodate the new conditions. In this talk, I will present some theoretical results on the modulation of solitary wave profiles under such perturbations, supported by numerical simulations that illustrate and validate these findings.

Friday, March 14, 2025

Posted December 22, 2024
Last modified March 5, 2025

11:30 am – 12:20 pm Zoom (click here to join)

Serdar Yuksel, Queen’s University, Canada
Robustness to Approximations and Learning in Stochastic Control via a Framework of Kernel Topologies

Stochastic kernels represent system models, control policies, and measurement channels, and thus offer a general mathematical framework for learning, robustness, and approximation analysis. To this end, we will first present and study several kernel topologies. These include weak* (also called Borkar) topology, Young topology, kernel mean embedding topologies, and strong convergence topologies. Convergence, continuity, and robustness properties of optimal cost for models and policies (viewed as kernels) will be presented in both discrete-time and continuous-time stochastic control. For models viewed as kernels, we study robustness to model perturbations, including finite approximations for discrete-time models and robustness to more general modeling errors and study the mismatch loss of optimal control policies designed for incorrect models applied to a true system, as the incorrect model approaches the true model under a variety of kernel convergence criteria. In particular, we show that the expected induced cost is robust under continuous weak convergence of transition kernels. Under stronger Wasserstein or total variation regularity, a modulus of continuity is also applicable. As applications of robustness under continuous weak convergence via data-driven model learning, (i) robustness to empirical model learning for discounted and average cost criteria is obtained with sample complexity bounds, and (ii) convergence and near optimality of a quantized Q-learning algorithm for MDPs with standard Borel spaces, which we show to be converging to an optimal solution of an approximate model under both discounted and average cost criteria, is established. In the context of continuous-time models, we obtain counterparts where we show continuity of cost in policy under Young and Borkar topologies, and robustness of optimal cost in models including discrete-time approximations for finite horizon and infinite-horizon discounted/ergodic criteria. Discrete-time approximations under several criteria and information structures will then be obtained via a unified approach of policy and model convergence. This is joint work with Ali D. Kara, Somnath Pradhan, Naci Saldi, and Tamas Linder.

Posted March 12, 2025

11:30 am – 12:20 pm Zoom (See the Control Seminar Advertisement for the link.)

Serdar Yuksel, Queen’s University, Canada
Robustness to Approximations and Learning in Stochastic Control via a Framework of Kernel Topologies

Posted January 20, 2025

1:00 pm – 3:30 pm Saturday, March 15, 2025 Tulane University

Scientific Computing Around Louisiana (SCALA) 2025

http://www.math.tulane.edu/scala2025/index.html

Posted March 10, 2025

3:30 pm – 4:30 pm Lockett Hall 233 (Simulcast via Zoom)

Tan Nhat Tran, Binghamton University
Inductive and Divisional Posets: A Study of Poset Factorability

We introduce and study the notion of inductive posets and their superclass, divisionalposets, inspired by the concepts of inductive and divisional freeness for central hyperplane arrangements. A poset is called factorable if its characteristic polynomial has all positive integer roots. Motivated by this, we define inductive and divisional abelian (Lie group) arrangements, with their posets of layers serving as primary examples. Our first main result shows that every divisional poset is factorable. The second result establishes that the class of inductive posets includes strictly supersolvable posets, a class recently introduced by Bibby and Delucchi (2024), which extends the classical result by Jambu and Terao (1984) that every supersolvable hyperplane arrangement is inductively free. Finally, we present an application to toric arrangements, proving that the toric arrangement defined by any ideal of a root system of type A, B, or C, with respect to the root lattice, is inductive. This work is joint with R. Pagaria (Bologna), M. Pismataro (Bologna), and L. Vecchi (KTH).

Monday, March 17, 2025

Posted March 12, 2025

Mathematical Physics and Representation Theory Seminar

2:30 pm Lockett 232

Hye-Won Kang, University of Maryland, Baltimore County
Multiscale approximations in stochastic reaction networks

In this talk, I will discuss stochastic modeling and approximation techniques for chemical reaction networks. Stochastic effects can play a crucial role in biological and chemical processes, particularly when certain species exist in low copy numbers. A common stochastic model for such systems is the continuous-time Markov jump process. However, due to the large and nonlinear nature of chemical reaction networks, obtaining closed-form solutions for the desired statistical properties is often challenging. I will introduce multiscale approximation methods designed to reduce the complexity of these networks by considering various scales in species copy numbers and reaction rate constants. For each relevant time scale, we derive a simpler limiting model that approximates the behavior of the full model over specific time intervals. Additionally, I will explore the asymptotic behavior of the error between the full model and the limiting model. Throughout the talk, I will demonstrate the application of these multiscale approximation methods to several examples, highlighting their effectiveness in simplifying the analysis of complex systems.

Posted February 10, 2025
Last modified March 13, 2025

2:30 pm – 3:20 pm Monday, March 17, 0025 Lockett 233

Sam Gunningham, Montana State University
Geometric Satake Revisited

The geometric Satake equivalence is a fundamental result in the geometric Langlands program. It can be understood as a kind of Fourier transform, relating different flavors of sheaves on a dual pair of spaces. Just like the usual Fourier transform, the equivalence exchanges the structures of convolution and pointwise product on each side. In this talk, I will discuss a circle of ideas relating pointwise tensor product of sheaves on the affine Grassmannian, the Knop-Ngo action for the group scheme of regular centralizers, and Moore-Tachikawa varieties. This builds on past joint work with D. Ben-Zvi and some current work in progress with D. Ben-Zvi and S. Devalapurkar.

Tuesday, March 18, 2025

Posted January 28, 2025
Last modified March 12, 2025

Algebra and Number Theory Seminar Questions or comments?

2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom

Eun Hye Lee, Texas Christian University
Automorphic form twisted Shintani zeta functions over number fields

In this talk, we will be exploring the analytic properties of automorphic form twisted Shintani zeta functions over number fields. I will start by stating some basic facts from classical Shintani zeta functions, and then we will take a look at the adelic analogues of them. Joint with Ramin Takloo-Bighash.

Wednesday, March 19, 2025

Posted February 3, 2025
Last modified March 17, 2025

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm

Saumya Jain, Louisiana State University
Handle Trading

Equipped with the tools developed in the previous talks, we will begin by outlining the idea of the proof of the h-cobordism theorem. We will see that if the algebraic "d-pairing" can be realized geometrically, then the proof follows. To this end, we will explore a way to handle low and high handles, introducing handle-trading.

Posted February 12, 2025
Last modified March 6, 2025

3:30 pm Lockett 241

Hye-Won Kang, University of Maryland, Baltimore County
Deterministic and Stochastic Modeling of Chemical Reactions in Biology

In this talk, I will introduce how mathematical models are used to describe chemical reactions. Reaction networks play a key role in various fields, including systems biology, population dynamics, epidemiology, and molecular and cellular biology. We will start by exploring models based on the law of mass action, where chemical species interact in a well-mixed environment, and their concentrations change over time according to differential equations. However, when certain species exist in low quantities, random fluctuations can significantly impact the system's behavior. In such cases, a stochastic model--using a continuous-time Markov jump process--better captures the discrete and probabilistic nature of reaction events. To illustrate the differences between deterministic and stochastic approaches, I will present simple examples, including enzyme kinetics, and compare their dynamic behaviors. For systems that are spatially distributed, we can describe the movement and interaction of chemical species using reaction-diffusion partial differential equations. When some species have low molecular counts, we can extend stochastic models by dividing the spatial domain into smaller regions, assuming each region is well-mixed. I will also introduce several examples of spatially-distributed systems, including applications in developmental biology.

Posted March 10, 2025

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Scott Baldridge, Louisiana State University
A new way to prove the four color theorem using gauge theory

In this talk, I show how ideas coming out of gauge theory can be used to prove that certain configurations in the list of "633 unavoidable's" are reducible. In particular, I show how to prove the most important initial example, the Birkhoff diamond (four “adjacent" pentagons), is reducible using our filtered $3$- and $4$-color homology. In this context reducible means that the Birkhoff diamond cannot show up as a “tangle" in a minimal counterexample to the 4CT. This is a new proof of a 111-year-old result that is a direct consequence of a special (2+1)-dimensional TQFT. I will then indicate how the ideas used in the proof might be used to reduce the unavoidable set of 633 configurations to a much smaller set. This is joint work with Ben McCarty.

Friday, March 21, 2025

Posted December 9, 2024
Last modified March 14, 2025

11:30 am – 12:20 pm Zoom (click here to join)

Serkan Gugercin, Virginia Tech
What to Interpolate for L2 Optimal Approximation: Reflections on the Past, Present, and Future

In this talk, we revisit the L2 optimal approximation problem through various formulations and applications, exploring its rich mathematical structure and diverse implications. We begin with the classical case where the optimal approximant is a rational function, highlighting how Hermite interpolation at specific reflected points emerges as the necessary condition for optimality. Building on this foundation, we consider extensions that introduce additional structure to rational approximations and relax certain restrictions, revealing new dimensions of the problem. Throughout, we demonstrate how Hermite interpolation at reflected points serves as a unifying theme across different domains and applications.

Posted March 17, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)

Zach Walsh, Auburn University
Delta-Wye exchange for matroids over pastures

Delta-Wye exchange is a fundamental graph operation that preserves many natural embeddability properties of graphs. This operation generalizes to matroids, and preserves many natural representability properties of matroids. We will present a result showing that Delta-Wye exchange preserves matroid representability over any pasture, which is an algebraic object that generalizes partial fields and hyperfields. This is joint work with Matt Baker, Oliver Lorscheid, and Tianyi Zhang.

Wednesday, March 26, 2025

Posted February 3, 2025
Last modified March 24, 2025

1:30 pm

Peter Ramsey, Louisiana State University
The Orlik-Solomon Algebra and the Cohomology Ring of Hyperplane Arrangements

A hyperplane is a subspace of codimension one in a given vector space. A finite collection of hyperplanes is called a hyperplane arrangement. The compliment of such an arrangement in complex space defines a connected manifold whose topology can be studied via its cohomology ring. A fundamental result by Brieskorn, Orlik, and Solomon shows that this cohomology ring can be computed in a purely combinatorial way using the Orlik-Solomon Algebra. In this talk, we will explore this construction and, if time permits, discuss its implications for the Poincaré polynomial.

Posted March 26, 2025

2:30 pm – 3:30 pm Lockett 233

Scott Baldridge, Louisiana State University
A new way to prove the four color theorem using gauge theory, Part 2

This is a continuation of last week’s talk in which we explain the definition of the homology theory used to prove that Birkhoff’s diamond is reducible. I will quickly summarize last week's discussion before heading into new material, so people can attend this week even if they couldn’t attend last week. This is joint work with Ben McCarty at University of Memphis.

Posted March 21, 2025

3:30 pm – 4:30 pm Lockett 237

Barbara Rüdiger, Bergische Universität Wuppertal, Germany
Identification and existence of Boltzmann processes

A stochastic differential equation of the McKean-Vlasov type is identified such that its Fokker-Planck equation coincides with the Boltzmann equation. Its solutions are called Boltzmann processes. They describe the dynamics (in position and velocity) of particles expanding in vacuum in accordance with the Boltzmann equation. Given a good solution of the Boltzmann equation, the existence of solutions to the McKean-Vlasov SDE is established for the hard sphere case. This is a joint work with P. Sundar.

Thursday, March 27, 2025

Posted March 25, 2025

Control and Optimization Seminar Questions or comments?

3:00 pm – 4:50 pm Lockett 243

Beamer Presentation

Join us for a Beamer Presentation where we'll explore how to style and organize Beamer slides, share tips to enhance your presentations, and introduce helpful drawing tools.

Friday, March 28, 2025

Posted March 21, 2025
Last modified March 25, 2025

9:30 am – 10:20 am Note the Special Earlier Seminar Time For Only This Week. This is a Zoom Seminar. Zoom (click here to join)

Denis Dochain, Université Catholique de Louvain IEEE Fellow, IFAC Fellow
Automatic Control and Biological Systems

This talk aims to give an overview of more than 40 years of research activities in the field of modelling and control of biological systems. It will cover different aspects of modelling, analysis, monitoring and control of bio-systems, and will be illustrated by a large variety of biological systems, from environmental systems to biomedical applications via food processes or plant growth.

Posted March 21, 2025

11:30 am – 12:30 pm Zoom Link

Jorn van der Pol, University of Twente
Turán densities for matroid basis hypergraph

What is the maximum number of bases of an n-element, rank-r matroid without a given uniform matroid U as a minor? This question arises in the problem of determining the Turán density of daisy-hypergraphs. Ellis, Ivan, and Leader recently showed that this density is positive, thus disproving a conjecture by Bollobás, Leader, and Malvenuto. Their construction is a matroid basis hypergraph, and we show that their construction is best-possible within the class of matroid basis hypergraphs. This is joint work with Zach Walsh and Michael C. Wigal.

Saturday, March 29, 2025

Posted March 28, 2025

Mathematical Physics and Representation Theory Seminar

until Sunday, March 30, 2025

Southern Regional Number Theory Conference

The conference will take place from Saturday, March 29th to Sunday, March 30th at Coates Hall, LSU, and also streamed over Zoom. The talk information and zoom links are at our website: https://www.math.lsu.edu/~srntc/nt2025/schedule.html

Monday, April 7, 2025

Posted March 16, 2025
Last modified April 2, 2025

2:30 pm – 3:20 pm Lockett 233

Justin Lanier, University of Sydney
Twisting cubic rabbits

A polynomial can be viewed as a branched cover of the sphere over itself that is compatible with a complex structure. If handed a topological branched cover of the sphere, we can ask whether it can arise from a polynomial, and if so, which one? In 2006, Bartholdi and Nekrashevych used group theoretic methods to explicitly solve this problem in certain special cases, including Hubbard’s twisted rabbit problem. Using a combinatorial topology approach that draws from the theory of mapping class groups, we solve an infinite family of twisted polynomial problems that are cubic generalizations of Hubbard’s twisted rabbit problem. This is joint work with Becca Winarski.

Tuesday, April 8, 2025

Posted March 31, 2025

Algebra and Number Theory Seminar Questions or comments?

2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom

Be'eri Greenfeld , University of Washington
Complexity and Growth of Infinite Words and Algebraic Structures

Given an infinite word (for example, 01101001$\ldots$), its complexity function counts, for each n, the number of distinct subwords of length n. A longstanding open problem is the "inverse problem": Which functions $f:\mathbb N\to \mathbb N$ arise as complexity functions of infinite words? We resolve this problem asymptotically, showing that, apart from submultiplicativity and a classical obstruction found by Morse and Hedlund in 1938, there are essentially no further restrictions. We then explore parallels and contrasts with the theory of growth of algebras, drawing on noncommutative constructions associated with symbolic dynamical systems.

Wednesday, April 9, 2025

Posted February 3, 2025
Last modified April 7, 2025

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm

Adithyan Pandikkadan, Louisiana State University
Whitney Trick

In the previous talk, we outlined the proof of the h-cobordism theorem. The key step is realizing the algebraic intersection number +1 between the attaching sphere of the k-handle and the belt sphere of the (k+1)-handle as an actual geometric intersection. Achieving this requires eliminating pairs of intersection points with opposite signs by the "Whitney Trick". In this talk, we will focus on understanding the "Whitney Trick" in detail and how it enables these critical geometric manipulations.

Posted March 8, 2025
Last modified March 9, 2025

3:30 pm – 4:30 pm Lockett 232

Tomoyuki Kakehi, University of Tsukuba
Snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation

In this talk, we deal with snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation. For simplicity, let us consider the wave equation $\partial_t^2 u - \Delta u =0$ on $\mathbb{R}^n$ with the condition $u|_{t=t_1} =f_1, \cdots, u|_{t=t_m} =f_m$. It is natural to ask when the above equation has a unique solution. We call the above problem the snapshot problem for the wave equation, and call the set of $m$ functions $\{ f_1, \cdots, f_m \}$ the snapshot data. Roughly speaking, one of our main results is as follows. {\bf Theorem.} We assume that $m=3$ and $(t_3-t_1)/(t_2 -t_1)$ is irrational and not a Liouville number. In addition, we assume a certain compatibility condition on the snapshot data $\{ f_1, f_2, f_3 \}$. Then the snapshot problem for the wave equation has a unique solution. We also consider a similar snapshot problem for the Euler-Poisson-Darboux equation. This is a joint work with Jens Christensen, Fulton Gonzalez, and Jue Wang.

Thursday, April 10, 2025

Posted March 9, 2025
Last modified April 9, 2025

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 385

Tomoyuki Kakehi, University of Tsukuba
Inversion formulas for Radon transforms and mean value operators on the sphere

This talk consists of two parts. In the first part, we explain the Radon transfrom associated with a double fibration briefly and then we introduce several inversion formulas. In the second part, we deal with the mean value operator $M^r$ on the sphere. Here we define $M^r: C^{\infty} (\mathbb{S}^n) \to C^{\infty} (\mathbb{S}^n)$ by $$ M^r f (x) = \frac{1}{\mathrm{Vol} (S_r (x))} \int_{y \in S_r (x)} f(y) d\mu(y), \qquad f \in C^{\infty} (\mathbb{S}^n), $$ where $S_r (x)$ is the geodesic sphere with radius $r$ and center $x$ and $d\mu$ is the measure on $S_r (x)$ induced from the canonical measure on $\mathbb{S}^n$. We will give conditions on $r$ for $M^r$ being injective or surjective. For example, in the case $n=3$, $M^r$ is injective but not surjective if and only if $r/\pi$ is a Liouville number. We will also give some related results on Gegenbauer polynomials. This is a joint work with J. Christensen, F. Gonzalez, and J. Wang.

Friday, April 11, 2025

Posted November 7, 2024
Last modified March 13, 2025

11:30 am – 12:20 pm Zoom (click here to join)

Irena Lasiecka, University of Memphis AACC Bellman Control Heritage Awardee, AMS Fellow, SIAM Fellow, and SIAM Reid Prize Awardee
Mathematical Theory of Flow-Structure Interactions

Flow-structure interactions are ubiquitous in nature and in everyday life. Flow or fluid interacting with structural elements can lead to oscillations, hence impacting stability or even safety. Thus problems such as attenuation of turbulence or flutter in an oscillating structure (e.g., the Tacoma bridge), flutter in tall buildings, fluid flows in flexible pipes, nuclear engineering flows about fuel elements, and heat exchanger vanes are just a few prime examples of relevant applications which place themselves at the frontier of interests in applied mathematics. In this lecture, we shall describe mathematical models describing the phenomena. They are based on a 3D linearized Euler equation around unstable equilibria coupled to a nonlinear dynamic elasticity on a 2D manifold. Strong interface coupling between the two media is at the center of the analysis. This provides for a rich mathematical structure, opening the door to several unresolved problems in the area of nonlinear PDEs, dynamical systems, related harmonic analysis, and differential geometry. This talk provides a brief overview of recent developments in the area, with a presentation of some new methodology addressing the issues of control and stability of such structures. Part of this talk is based on recent work with D. Bonheur, F. Gazzola and J. Webster (in Annales de L’Institute Henri Poincare Analyse from 2022), work with A. Balakrishna and J. Webster (in M3AS in 2024), and also work completed while the author was a member of the MSRI program "Mathematical problem in fluid dynamics" at the University of California Berkeley (sponsored by NSF DMS -1928930).

Posted April 9, 2025

12:30 pm – 1:20 pm Zoom

Meeting of the Tenured Faculty

Posted January 21, 2025

3:30 pm – 4:30 pm Zoom Link

Joseph Bonin, George Washington University
Results on positroids from the perspective of structural matroid theory

A matroid of rank $r$ on $n$ elements is a positroid if it has a representation by an $r$ by $n$ matrix over $\mathbb{R}$ with the property that the determinant of each $r$ by $r$ submatrix is nonnegative. Positroids are commonly studied through the lens of algebraic combinatorics, where a fixed linear order on the ground set is regarded as part of the positroid. We focus on the matroid structure per se, without a priori fixing a linear order on the ground set. A number of earlier characterizations of positroids involve connected flats and non-crossing partitions; we provide a new characterization of a similar flavor and discuss some of its applications. One application is finding conditions under which two positroids can be glued together along a common restriction, in the freest way possible, to yield another positroid: for instance, if $M$ and $N$ are positroids and the intersection of their ground sets is an independent set and a set of clones in both $M$ and $N$, then the free amalgam of $M$ and $N$ is a positroid (that encompasses parallel connections and much more). Also, the class of positroids is minor-closed, and we identify many multi-parameter infinite families of excluded minors for this class, while more excluded minors remain to be discovered.

Monday, April 14, 2025

Posted April 12, 2025

12:00 pm – 1:30 pm Keisler Lounge, Lockett Hall 3rd Floor

Life after a Ph.D!

What’s harder than finishing a Ph.D.? Probably finding a job you truly enjoy and that pays well. If you’re wondering what comes after grad school, join the LSU SIAM Chapter for a Job Panel on Monday, April 14, from 12:00–1:30 PM in Keisler Lounge. Our panel — including Prof. Shipman, Dr. Nadejda Drenska, Casey Cavanaugh, and graduate students Jeremy Shanan, Dylan Douthitt, and Christian Ennis — will share insights on the job search process, from applications and interviews to networking and career paths in academia and industry.

Posted February 21, 2025
Last modified April 8, 2025

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett 232

John Jairo Lopez, Tulane University
Riemann-Hilbert Approach to the Asymptotic Distribution of Zeros of Orthogonal Polynomials

Orthogonal polynomials possess a variety of properties and characterizations. For instance, it is well known that the zeros of a family of orthogonal polynomials with respect to a weight function $ w(x) $ supported on an interval $ (a,b) $ are all distinct and lie within the interval. This talk will introduce the Riemann-Hilbert problem characterization of orthogonal polynomials, which will then be used to obtain asymptotic information about the polynomials and their zeros. In particular, we will consider Jacobi polynomials $ p_n(x) = p_n^{(\alpha_n,\beta_n)}(x) $, with varying parameters $ \alpha_n $ and $ \beta_n $ in the weight function \[ w(x;\alpha,\beta) = (1-x)^\alpha(1+x)^\beta. \] In the classical case the parameters satisfy $ \alpha, \beta > -1 $. By analytic continuation in the parameters $ \alpha $ and $ \beta $, these polynomials can be studied for more general values. However, when $ \alpha \le -1 $ or $ \beta \le -1 $, the classical orthogonality property on $[-1,1]$ does not hold, and consequently, the zeros may no longer be real or simple. We will see how the Riemann-Hilbert formulation can be extended beyond the classical case to study the asymptotics and zeros of these polynomials. This talk is based on joint work with Victor Moll and Kenneth McLaughlin. (Host: Stephen Shipman)

Tuesday, April 15, 2025

Posted January 26, 2025
Last modified April 14, 2025

2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom

Kairi Black, Duke University
How might we generalize the Kronecker-Weber Theorem?

Hilbert's Twelfth Problem asks for a generalization of the Kronecker-Weber Theorem: cyclotomic units generate the abelian extensions of $\mathbb{Q}$, but what about for other ground fields? We consider a number field $K$ with exactly one complex embedding. In the 1970s, Stark conjectured formulas for (the absolute values of) units inside abelian extensions of $K$. We refine Stark's conjectures with a proposed formula for the units themselves, not just their absolute values.

Wednesday, April 16, 2025

Posted April 12, 2025

LSU AWM Student Chapter LSU AWM Student Chapter Website

12:30 pm – 1:30 pm Keisler Lounge, Lockett 3rd Floor

Automation Workshop: Streamline Your TA Duties with Python and Excel!

Join the LSU AWM Student Chapter for a hands-on workshop designed to help Math 1021 instructors and graduate TAs save time and stay organized. Whether you're looking to automate end-of-semester reports or integrate Excel and Python into your teaching workflow. This session, led by AWM officer Christian Ennis, will walk you through two practical Python tools: one for generating end-of-semester data sheets and another for classifying lab participation grades based on passing thresholds. We'll also discuss ideas for streamlining other Math 1021 tasks and explore ways to optimize workflows in courses you teach as a TA.

Posted February 3, 2025
Last modified April 22, 2025

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm

Matthew Lemoine, Louisiana State University
Topological Data Analysis and The Persistent Laplacian

In this talk, we will go through some basic information about Topological Data Analysis (TDA) such as Persistent Homology with the goal of getting to the Persistent Laplacian and how these tools are used to analyze data.

Monday, April 21, 2025

Posted February 10, 2025
Last modified April 14, 2025

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:20 pm Lockett 233

Joshua Mundinger, University of Wisconsin
Hochschild homology of algebraic varieties in characteristic p

Hochschild homology is an invariant of noncommutative rings. When applied to a commutative ring, the Hochschild-Kostant-Rosenberg theorem gives a formula for Hochschild homology in terms of differential forms. This formula extends to the Hochschild-Kostant-Rosenberg decomposition for complex algebraic varieties. In this talk, we quantitatively explain the failure of this decomposition in positive characteristic.

Posted March 25, 2025
Last modified April 20, 2025

Algebra and Number Theory Seminar Questions or comments?

3:30 pm – 4:20 pm Lockett 232

Robert Lipton, Mathematics Department, LSU
Dynamic Fast Crack Growth

Nonlocal modeleling for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. The material displacement field is uniquely determined by the initial boundary value problem. The theory naturally satisfies energy balance, with positive energy dissipation rate in accord with the Clausius-Duhem inequality. Notably, these properties are not imposed but follow directly from the constitutive law and evolution equation. The limit of vanishing non-locality is analyzed using simple arguments from geometric measure theory to identify the limit damage energy and weak convergence methods of pde to identify the limit solution. The limiting energy is the Griffith fracture energy. The limit evolution is seen to be a weak solution for the wave equation on a time dependent domain. The existence theory for such solutions was recently developed in Dal Maso and Toader, J. Differ. Equ. 266, 3209–3246 (2019).

Tuesday, April 22, 2025

Posted April 14, 2025

2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom

Qing Zhang, University of California Santa Barbara
Realizing Modular Data from Centers of Near-Group Categories

In this talk, I will discuss modular data arising from the Drinfeld centers of near-group categories. The existence of near-group categories of type $G+n$ can be established by solving a set of polynomial equations introduced by Izumi; a different set of equations, also due to Izumi, can then be used to compute the modular data of their Drinfeld centers. Smaller-rank modular categories can often be obtained from these centers via factorization and condensation. After introducing the background of this framework, I will show the existence of a near-group category of type $\mathbb{Z}/4\mathbb{Z} \times \mathbb{Z}/4\mathbb{Z} + 16$ and explain how the modular data of its Drinfeld center can be computed. I will then show that modular data of rank 10 can be obtained via condensation of its Drinfeld center and present an alternative realization of this data through the Drinfeld center of a fusion category of rank 4. Finally, I will discuss the modular data of the Drinfeld center of a near-group category of type $\mathbb{Z}/8\mathbb{Z} + 8$ and demonstrate that the non-pointed factor of its condensation coincides with the modular data of the quantum group category $C(g_2, 4)$. This talk is based on joint work with Zhiqiang Yu.

Today, Wednesday, April 23, 2025

Posted February 3, 2025
Last modified April 22, 2025

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm

Nilangshu Bhattacharyya, Louisiana State University
Proof of h-cobordism, Whitney trick and issues in the 4 dimension.

In this presentation, I will begin by recapping the complete proof of the h-cobordism theorem, which states that in dimensions greater than four, a homotopically trivial, simply connected cobordism between two simply connected compact manifolds is smoothly trivial. As a corollary, this implies the higher-dimensional Poincaré conjecture. A central tool in the proof is the Whitney trick, which is effective in higher dimensions. However, in dimension four, a framing obstruction naturally arises, presenting significant challenges. In the latter part of the presentation, I will discuss some of the technical aspects and difficulties associated with applying the Whitney trick.

Posted January 27, 2025
Last modified April 14, 2025

3:30 pm Lockett 233

Cancelled

Galen Dorpalen-Barry, Texas A&M
TBA

Posted April 21, 2025

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 138

Christopher Kees, Louisiana State University
Application of CutFEM to the modeling of coastal processes through vegetation

Understanding the effects of sea level rise on coastal ecosystems involves complex solid materials, such as mixed sediments and vegetation. Physical flume and basin studies have long been used in coastal engineering to understand wave and current dynamics around such structures. Numerical flumes based on computational fluid dynamics and fluid-structure interaction have recently begun to augment physical models for design studies, particularly for engineered structures where established Arbitrary Lagrangian-Eulerian (ALE) methods based on boundary-conforming meshes and isoparametric or isogeoemtric finite element methods are effective. The rapid growth of lidar and photogrammetry techniques at large scales and computed tomography at small scales has introduced the possibility of constructing numerical experiments for the complex natural materials in coastal ecosystems. These methods tend to produce low-order geometric representations with uneven resolution, which are typically not appropriate for conforming mesh generation. To address this challenge, recent work [1] extended an existing ALE method to include embedded solid dynamics using a piecewise linear CutFEM approach [2]. The implementation is based on equivalent polynomials [3]. The approach retains the convergence properties of the CutFEM method while having a simple implementation within the existing twophase RANS model, which has been used frequently for numerical flume studies. This presentation will consider application and performance of the method for two critical coastal processes: wave interaction with vegetation and sediment dynamics.

Friday, April 25, 2025

Posted January 10, 2025
Last modified March 26, 2025

11:30 am – 12:20 pm Zoom (click here to join)

Carolyn Beck, University of Illinois Urbana-Champaign IEEE Fellow
Discrete State System Identification: An Overview and Error Bounds

Classic system identification methods focus on identifying continuous-valued dynamical systems from input-output data, where the main analysis of such approaches largely focuses on asymptotic convergence of the estimated models to the true models, i.e., consistency properties. More recent identification approaches have focused on sample complexity properties, i.e., how much data is needed to achieve an acceptable model approximation. In this talk I will give a brief overview of classical methods and then discuss more recent data-driven methods for modeling continuous-valued linear systems and discrete-valued dynamical systems evolving over networks. Examples of the latter systems include the spread of viruses and diseases over human contact networks, the propagation of ideas and misinformation over social networks, and the spread of financial default risk between banking and economic institutions. In many of these systems, data may be widely available, but approaches to identify relevant mathematical models, including underlying network topologies, are not widely established or agreed upon. We will discuss the problem of modeling discrete-valued, discrete-time dynamical systems evolving over networks, and outline analysis results under maximum likelihood identification approaches that guarantee consistency conditions and sample complexity bounds. Applications to the aforementioned examples will be further discussed as time allows.

Posted April 21, 2025

3:30 pm – 4:30 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)

Songling Shan, Auburn University
Linear arboricity of graphs with large minimum degree

In 1980, Akiyama, Exoo, and Harary conjectured that any graph $G$ can be decomposed into at most $\lceil(\Delta(G)+1)/2\rceil$ linear forests. We confirm the conjecture for sufficiently large graphs with large minimum degree. Precisely, we show that for any given $0<\varepsilon<1$, there exists $n_0 \in \mathbb{N}$ for which the following statement holds: If $G$ is a graph on $n\ge n_0$ vertices of minimum degree at least $(1+\varepsilon)n/2$, then $G$ can be decomposed into at most $\lceil(\Delta(G)+1)/2\rceil$ linear forests. This is joint work with Yuping Gao.

Monday, April 28, 2025

Posted December 10, 2024
Last modified January 5, 2025

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett

Yuanzhen Shao, University of Alabama
Some recent developments in the study of magnetoviscoelastic fluids

In this talk, we consider the motion of a magnetoviscoelastic fluid in a nonisothermal environment. When the deformation tensor field is governed by a regularized transport equation, the motion of the fluid can be described by a quasilinear parabolic system. We will establish the local existence and uniqueness of a strong solution. Then it will be shown that a solution initially close to a constant equilibrium exists globally and converges to a (possibly different) constant equilibrium. Further, we will show that that every solution that is eventually bounded in the topology of the natural state space exists globally and converges to the set of equilibria. If time permits, we will discuss some recent advancements regarding the scenario where the deformation tensor is modeled by a transport equation. In particular, we will discuss the local existence and uniqueness of a strong solution as well as global existence for small initial data.

Tuesday, April 29, 2025

Posted April 16, 2025

2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom

Andrew Riesen, MIT
Orbifolds of Pointed Vertex Algebras

We will discuss the interplay of tensor categories $C$ with some group action $G$ and orbifolds $V^G$ of vertex operator algebras (VOAs for short). More specifically, we will show how the categorical structure of $\mathrm{TwMod}_G V$ allows one to not only simplify previous results done purely through VOA techniques but vastly extend them. One such example is the Dijkgraaf-Witten conjecture, now a theorem, which describes how the category of modules of a holomorphic orbifold should look like. Additionally, our techniques also allow us to expand the modular fusion categories known to arise from VOAs, we show that every group-theoretical fusion category comes from a VOA orbifold. This talk is based on joint work with Terry Gannon.

Wednesday, April 30, 2025

Posted January 23, 2025
Last modified January 27, 2025

3:30 pm Lockett 233

Annette Karrer, The Ohio State University
TBA

Posted January 12, 2025
Last modified January 16, 2025

3:30 pm Lockett 232

Zi Li Lim, UCLA
TBA

Thursday, May 1, 2025

Posted April 7, 2025
Last modified April 21, 2025

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 241

Mark Ellingham, Vanderbilt University
Twisted duality for graph embeddings and conditions for orientability and bipartiteness

*Twisted duals* of embeddings of graphs in surfaces were introduced by Ellis-Monaghan and Moffatt in 2012. They generalize edge twists, well known since the representation of embeddings using rotation schemes and edge signatures was introduced in the 1970s, and partial duals, defined by Chmutov in 2009. I will explain how twisted duals can be found using combinatorial representations of an embedding known as the *gem* (graph-encoded map) and *jewel*. Several important properties of embedded graphs are linked to parity conditions for closed walks in the gem or jewel, and to orientations of the half-edges of the medial graph of the embedding. Using these conditions, I will discuss how we can characterize which twisted duals are orientable or bipartite. This is joint work with Blake Dunshee.

Friday, May 2, 2025

Posted January 16, 2025
Last modified April 5, 2025

11:30 am – 12:20 pm Zoom (click here to join)

Bahman Gharesifard, Queen's University
Structural Average Controllability of Ensembles

In ensemble control, the goal is to steer a parametrized collection of independent systems using a single control input. A key technical challenge arises from the fact that this control input must be designed without relying on the specific parameters of the individual systems. Broadly speaking, as the space of possible system parameters grows, so does the size and diversity of the ensemble — making it increasingly difficult to control all members simultaneously. In fact, an important result among the recent advances on this topic states that when the underlying parameterization spaces are multidimensional, real-analytic linear ensemble systems are not L^p-controllable for p>=2. Therefore, one has to relax the notion of controllability and seek more flexible controllability characteristics. In this talk, I consider continuum ensembles of linear time-invariant control systems with single inputs, featuring a sparsity pattern, and study structural average controllability as a relaxation of structural ensemble controllability. I then provide a necessary and sufficient condition for a sparsity pattern to be structurally average controllable.

Posted April 18, 2025

Control and Optimization Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 233 (Simulcast via Zoom)

Mark Ellingham, Vanderbilt University
Maximum genus directed embeddings of digraphs

In topological graph theory we often want to find embeddings of a given connected graph with minimum genus, so that the underlying compact surface of the embedding is as simple as possible. If we restrict ourselves to cellular embeddings, where all faces are homeomorphic to disks, then it is also of interest to find embeddings with maximum genus. For undirected graphs this is a very well-solved problem. For digraphs we can consider directed embeddings, where each face is bounded by a directed walk in the digraph. The maximum genus problem for digraphs is related to self-assembly problems for models of graphs built from DNA or polypeptides. Previous work by other people determined the maximum genus for the very special case of regular tournaments, and in some cases of directed 4-regular graphs the maximum genus can be found using an algorithm for the representable delta-matroid parity problem. We describe some recent work, joint with Joanna Ellis-Monaghan of the University of Amsterdam, where we have solved the maximum directed genus problem in some reasonably general situations.

Friday, May 9, 2025

Posted February 19, 2025

11:30 am – 12:20 pm Zoom (click here to join)

Nina Amini, Laboratory of Signals and Systems, CentraleSupélec
TBA

Friday, August 15, 2025

Posted January 19, 2025