Posted February 3, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Huong Vo, Louisiana State University
TBD
Posted November 21, 2024
Last modified March 5, 2025
Applied Analysis Seminar Questions or comments?
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.
Posted February 24, 2025
Combinatorics Seminar Questions or comments?
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
Applied Analysis Seminar Questions or comments?
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.
Posted March 9, 2025
Mathematical Physics and Representation Theory Seminar
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.
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 March 4, 2025
Last modified March 10, 2025
Geometry and Topology Seminar Seminar website
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)
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 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 February 19, 2025
Last modified March 10, 2025
Colloquium 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.
Posted March 12, 2025
Probability Seminar Questions or comments?
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
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 December 22, 2024
Last modified March 5, 2025
Control and Optimization Seminar Questions or comments?
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 January 20, 2025
1:00 pm – 3:30 pm Saturday, March 15, 2025 Tulane UniversityScientific Computing Around Louisiana (SCALA) 2025
http://www.math.tulane.edu/scala2025/index.html
Posted March 10, 2025
Combinatorics Seminar Questions or comments?
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).
Posted February 10, 2025
Last modified March 13, 2025
Mathematical Physics and Representation Theory Seminar
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.
Posted March 12, 2025
Probability Seminar Questions or comments?
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 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.
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 March 10, 2025
Geometry and Topology Seminar Seminar website
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.
Posted February 12, 2025
Last modified March 6, 2025
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 December 9, 2024
Last modified March 14, 2025
Control and Optimization Seminar Questions or comments?
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
Combinatorics 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.
Posted February 3, 2025
Last modified March 24, 2025
Informal Geometry and Topology Seminar Questions or comments?
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
Geometry and Topology Seminar Seminar website
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
Probability Seminar Questions or comments?
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.
Posted March 25, 2025
3:00 pm – 4:50 pm Lockett 243Beamer 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.
Posted March 21, 2025
Last modified March 25, 2025
Control and Optimization Seminar Questions or comments?
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
Combinatorics Seminar Questions or comments?
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.
Posted March 28, 2025
until Sunday, March 30, 2025Southern 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