Calendar

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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

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Locket 233

Huong Vo, Louisiana State University
TBD

Wednesday, September 4, 2024

Posted August 27, 2024

Geometry and Topology Seminar Seminar website

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

Control and Optimization Seminar Questions or comments?

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.

Friday, September 6, 2024

Posted August 28, 2024

Combinatorics 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

Algebra and Number Theory Seminar Questions or comments?

Heidi Goodson, Brooklyn College, CUNY
TBA

Wednesday, September 11, 2024

Posted August 30, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Locket 233

Saumya Jain, Louisiana State University
TBD

Wednesday, September 11, 2024

Posted August 28, 2024

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233

Tristan Wells Filbert, Louisiana State University
TBD

Wednesday, September 11, 2024

Posted August 27, 2024

Harmonic Analysis Seminar

3:30 pm – 4:30 pm Lockett 232

Kabe Moen, University of Alabama
TBA

Wednesday, September 18, 2024

Posted August 30, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Locket 233

Rachel Meyers, Louisiana State University
TBD

Wednesday, September 25, 2024

Posted August 30, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Locket 233

Nilangshu Bhattacharyya, Louisiana State University
TBD

Friday, September 27, 2024

Posted August 27, 2024

Control and Optimization Seminar Questions or comments?

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.

Wednesday, October 2, 2024

Posted August 30, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Locket 233

Adithyan Pandikkadan, Louisiana State University
TBD

Friday, October 4, 2024

Posted August 11, 2024

Control and Optimization Seminar Questions or comments?

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

Panagiotis Tsiotras, Georgia Institute of Technology AIAA and IEEE Fellow
TBA

Friday, October 4, 2024

Posted August 28, 2024

Combinatorics Seminar Questions or comments?

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.

Tuesday, October 8, 2024

Posted August 21, 2024
Last modified August 29, 2024

Algebra and Number Theory Seminar Questions or comments?

2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom

Wanlin Li, Washington University in St. Louis
TBA

Wednesday, October 9, 2024

Posted August 30, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Locket 233

Krishnendu Kar, Louisiana State University
TBD

Thursday, October 10, 2024

Posted July 13, 2024