Calendar

Informal Geometry and Topology Seminar Questions or comments?

12:30 pm – 1:30 pm Lockett 233

Han Nguyen, LSU
Introduction to Finite Element Methods

This talk serves as an exposition of ongoing work in Finite Element Methods.

Posted January 15, 2026

3:30 pm – 4:30 pm 233 Lockett Hall

To Be Filled In

Friday, January 30, 2026

Posted November 22, 2025
Last modified January 6, 2026

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

Henk van Waarde, University of Groningen IEEE L-CSS Outstanding Paper and SIAM SIAG/CST Prize Awardee
Data-Driven Stabilization using Prior Knowledge on Stabilizability and Controllability

Direct approaches to data-driven control design map raw data directly into control policies, thereby avoiding the intermediate step of system identification. Such direct methods are beneficial in situations where system modelling is computationally expensive or even impossible due to a lack of rich data. We begin the talk by reviewing existing methods for direct data-driven stabilization. Thereafter, we discuss the inclusion of prior knowledge that, in conjunction with the data, can be used to improve the sample efficiency of data-driven methods. In particular, we study prior knowledge of stabilizability and controllability of the underlying system. In the case of controllability, we prove that the conditions on the data required for stabilization are equivalent to those without the inclusion of prior knowledge. However, in the case of stabilizability as prior knowledge, we show that the conditions on the data are, in general, weaker. We close the talk by discussing experiment design methods. These methods construct suitable inputs for the unknown system, in such a way that the resulting data contain enough information for data-driven stabilization (taking into account the prior knowledge).

Posted January 26, 2026
Last modified January 27, 2026

Algebra and Number Theory Seminar Questions or comments?

2:30 pm – 3:30 pm Lockett 233 (Simulcast via Zoom)

Xiaonan Liu, Vanderbilt University
Counting $k$-cycles in $5$-connected planar triangulations

We show that every $n$-vertex $5$-connected planar triangulation has at most $9n-50$ many cycles of length $5$ for all $n\ge 20$ and this upper bound is tight. We also show that for every $k\geq 6$, there exists some constant $C(k)$ such that for sufficiently large $n$, every $n$-vertex $5$-connected planar graph has at most $C(k) \cdot n^{\lfloor k/3 \rfloor}$ many cycles of length $k$. This upper bound is asymptotically tight for all $k\geq 6$. This is joint work with Gyaneshwar Agrahari and Zhiyu Wang.

Tuesday, February 3, 2026

Posted January 16, 2026
Last modified February 2, 2026

2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom

Koustav Mondal, Louisiana State University
Theta series and their applications

Theta series play a central role in many areas of mathematics, especially number theory. In this talk, we begin with a brief overview of two applications of theta series: point counting for congruent quadratic forms, and the evaluation of special values of $L$-functions via Ramanujan's theory of elliptic functions to alternative bases for modular forms. Along the way, we state our main results in each setting. In the second part of the talk, we return to these applications to outline the key ideas and techniques involved in the proofs, as time permits.

Event contact: Gene Kopp

Wednesday, February 4, 2026

Posted January 22, 2026

12:30 pm – 1:30 pm Lockett 233

Hari Narayanan, Louisiana State University
Crash Course on Schrödinger Operators (Part 1)

An expository talk in spectral theory.

Posted January 28, 2026

Discussion and Training in Combinatorics

1:30 pm 233 Lockett Hall

Konrad Wrobel, University of Texas at Austin
Measure equivalence classification of Baumslag-Solitar groups

We complete the classification of Baumslag-Solitar groups up to measure equivalence by showing all Baumslag-Solitar groups with nonunimodular Bass-Serre tree are measure equivalent (i.e., BS(r,s) with r between 1 and s). The proof makes critical use of combinatorial descriptive set theory tools in the measure class preserving setting and passes through the world of measure equivalence of nonunimodular locally compact groups. In particular, as an intermediate step we obtain measure equivalence couplings between all groups of the form Aut(T_{r,s}) for r between 1 and s where T_{r,s} is the directed tree with r incoming edges and s outgoing edges at each vertex. This is joint work with Damien Gaboriau, Antoine Poulin, Anush Tserunyan, and Robin Tucker-Drob.

Posted February 3, 2026

2:30 pm Lockett 233

Joy Harris
Ramsey Number of Daisies

Given the set of vertices $[n]=\{1,\ldots,n\}$, an \emph{$r$-daisy}, given by disjoint sets $K,M \subset [n]$, is the $(r+|K|)$-uniform hypergraph defined as \[ \{K \cup P : P \subset M \text{ and } |P|=r\}. \] In this talk, we will discuss the \emph{Ramsey number of daisies}. This is the minimum number of vertices $n$ such that no coloring of the subsets of $[n]$ by $\ell$ colors yields a monochromatic daisy. We will give a probabilistic proof showing a lower bound for this number.

Event contact: Gyaneshwar Agrahari and Emmanuel Asante

Posted January 15, 2026
Last modified February 4, 2026

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett Hall 233

Matthew Lemoine, Louisiana State University
Sliding Window Embedding

When we are looking at a dataset that has a time-dependency and is periodic (or quasi-periodic), we are interested in noticing differences in the period. Using sliding window embeddings (also known as time-delay reconstructions), we can look at the periods of a given dataset and analyze the persistent homology to detect changes in our periods. In this talk, we will be discussing the foundational paper in this area of Topological Data Analysis by Jose Perea and John Harer (arxiv:1307.6188).

Friday, February 6, 2026

Posted February 1, 2026
Last modified February 2, 2026

Control and Optimization Seminar Questions or comments?

9:30 am – 10:30 am Lockett 233 or Zoom (click here to join)

R. Tyrrell Rockafellar, University of Washington
Variational Analysis and Convexity in Optimal Control

Optimal control theory was considered by its originators to be a new subject which superseded much of the classical calculus of variations as a special case. In reality, it was more a reformulation of existing theory with different goals and perspectives. Now both can be united in a broader setting of variational analysis in which Lagrangian and Hamiltonian functions need not be differentiable or even continuous, but extended-real-valued, and convexity has a central role. The Control and Optimization Seminar for this talk will be held in person, with a Zoom option available for remote attendees.

Event contact: Gowri Priya Sunkara

Posted January 30, 2026

Colloquium Questions or comments?

2:30 pm – 3:30 pm Lockett 233 (Simulcast via Zoom)

Tung Nguyen, University of Oxford, UK
Polynomial $\chi$-boundedness for excluding $P_5$

We discuss some ideas behind the recent resolution of a 1985 open problem of Gyárfás, that there is a positive integer k for which every graph with no induced five-vertex path has chromatic number at most the kth power of their clique number.

Posted December 29, 2025
Last modified February 3, 2026

3:30 pm Lockett 232 or click here to attend on Zoom

R. Tyrrell Rockafellar, University of Washington
Dual Problems of Optimization

A surprising discovery in the early days of optimization theory was the prevalence of a new kind of duality. Typical problems then of interest, in which a linear function was to be minimized subject to constraints consisting of equations or inequalities imposed on other linear functions, couldn't be solved without simultaneously solving a partnered problem of maximization in the same category. The solutions to the two problems could be viewed moreover as the best strategies for two opponents is a sort of zero-sum game. This theme is now understood much more broadly as a feature of optimization theory that has been important not only in the design of solution algorithms, but also in extending mathematical analysis beyond the traditions of calculus.

Monday, February 9, 2026

Posted December 17, 2025
Last modified February 8, 2026

Applied Analysis Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 232

Tuoc Phan, University of Tennessee–Knoxville
On Lin type Hessian estimates for solutions to a class of singular-degenerate parabolic equations

We disscuss a class of parabolic equations in non-divergence form with measurable coefficients that exhibit singular and/or degenerate behavior governed by weights in a Muckenhoupt class. We present new results on weighted F.-H. Lin type estimates of the Hessian matrices of solutions. As examples, we demonstrate that the results are applicable to equations whose leading coefficients are of logistic-type singularities, as well as those are of polynomial blow-up or vanishing with sufficiently small exponents. A central component of the approach is the development of local quantitative lower estimates for solutions, which are interpreted as the mean sojourn time of sample paths, a stochastic-geometric perspective that generalizes the seminal work of L. C. Evans. By utilizing intrinsic weighted cylinders and perturbation arguments alongside with parabolic ABP estimates, we effectively manage the operator's degeneracies and singularities. We also briefly address regularization and truncation strategies that ensure our estimates are robust. We conclude with a discussion of future applications and related developments in the field.

Tuesday, February 10, 2026

Posted January 15, 2026
Last modified February 3, 2026

Student Colloquium

3:30 pm – 4:30 pm Wednesday, February 11, 2026 Lockett Hall 232

Joshua Sabloff, Haverford College
Informal Discussion with Joshua Sabloff

Join us for an informal discussion with Joshua Sabloff. We will be discussion what it is like working in a primarily undergraduate institution.

Wednesday, February 11, 2026

Posted February 3, 2026
Last modified February 4, 2026

Student Colloquium

10:30 am Lockett Hall 233

Joshua Sabloff, Haverford College
How to Tie Your Unicycle in Knots: An Introduction to Legendrian Knot Theory

You can describe the configuration of a unicycle on a sidewalk using three coordinates: two position coordinates x and y for where the wheel comes into contact with the ground and one angle coordinate t that describes the angle that the direction the wheel makes with the x axis. How are the instantaneous motions of the unicycle constrained (hint: do you want your tire to scrape sideways)? How can we describe that constraint using generalizations of tools from vector calculus? The system of constraints at every point in (x,y,t)-space is an example of a "contact structure," and a path that obeys the constraints is a "Legendrian curve." If the curve returns to its starting point, then it is called a "Legendrian knot." A central question in the theory of Legendrian knots is: how can you tell two Legendrian knots apart? How many are there? In other words, how many ways are there to parallel park your unicycle? There will NOT be a practical demonstration.

Posted January 22, 2026

12:30 pm – 1:30 pm Lockett 233

Matthew McCoy, Louisiana State University
Crash Course on Schrödinger Operators (Part 2)

An expository talk in spectral theory.

Posted January 28, 2026
Last modified February 3, 2026

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm 233 Lockett Hall

Joshua Sabloff, Haverford College
On the Non-Orientable Genera of a Knot: Connections and Comparisons

We define a new quantity, the Euler-normalized non-orientable genus, to connect a variety of ideas in the theory of non-orientable surfaces bounded by knots. We use this quantity to explore the geography of non-orientable surfaces bounded by a fixed knot in 3 and 4 dimensions. In particular, we will use the Euler-normalized non-orientable genus to reframe non-orientable slice-torus bounds on the (ordinary) non-orientable 4-genus and to bound below the Turaev genus as a measure of distance to an alternating knot. This is joint work with Julia Knihs, Jeanette Patel, and Thea Rugg.

Posted February 4, 2026
Last modified February 5, 2026

3:30 pm Lockett Hall 233

Justin Lanier, Louisiana State University
Every Surface is a Leaf

We'll start by discussing the fact that every closed 3-manifold admits foliations, where the leaves are surfaces. This fact raises the question: for a given closed 3-manifold, which surfaces can appear as leaves of some foliation of that 3-manifold? Kerékjártó and Richards gave a classification up to homeomorphism of noncompact surfaces, which includes surfaces with infinite genus or infinitely many punctures. In their 1985 paper "Every surface is a leaf", Cantwell–Conlon prove a universality theorem: for every closed 3-manifold M and every orientable noncompact surface L, M has a foliation where L appears as a leaf. We will discuss their paper and the surrounding context.

Posted February 6, 2026

Actuarial Student Association

5:30 pm Lockett Hall

ASA x Cabe C.

We will be joined by the President of Lewis and Ellis (LSU Alumni!!!) Pizza Will be served

Friday, February 13, 2026

Posted November 26, 2025
Last modified January 29, 2026

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

Anthony Bloch, University of Michigan AMS, IEEE, and SIAM Fellow
Control, Stability and Learning on Dynamic Networks

In this talk we consider various aspects of dynamics, control and learning on graphs. We discuss diffusively coupled network dynamical systems and the role of coupling in stabilizing and destabilizing such systems. We also discuss dynamic networks of this type and in particular Lyapunov-based methods for analyzing the stability of networks undergoing switching. In addition we analyze the problem of learning the dynamics of switched systems from data, including linear and polynomial systems and systems on graphs. In addition we consider the control and dynamics of systems on hypergraphs which have applications to biological networks.

Posted February 8, 2026

2:30 pm – 3:30 pm Lockett 233 (Simulcast via Zoom)

Yiwei Ge, Louisiana State University
Extremal connectivity in graphs

A $k$-connected graph is minimally (respectively, critically) $k$-connected if the deletion of any edge (respectively, vertex) results in a graph that is not $k$-connected. A graph is uniformly $k$-connected if there are exactly $k$ internally disjoint paths between every pair of vertices. These classes have played a prominent role in graph connectivity theory. We introduce super-minimally $k$-connected graphs, defined as $k$-connected graphs with no proper $k$-connected subgraph. In this talk, we will give a brief introduction to these connectivity classes, with particular emphasis on extremal problems for $3$-connected graphs.

Wednesday, February 18, 2026

Posted January 28, 2026
Last modified February 17, 2026

Discussion and Training in Combinatorics

1:30 pm 233 Lockett Hall

Nilangshu Bhattacharyya, Louisiana State University
Steenrod Square on Khovanov Homology

Khovanov homology assigns a knot or a link to a bigraded homology theory that categorifies the Jones polynomial. It has concrete applications, for instance Rasmussen’s $s$-invariant, extracted from Lee’s deformation, which gives a lower bound on the smooth slice genus. At the same time, while the theory is very combinatorial and closely tied to the representation theory of $U_q(\mathfrak{sl}_2)$, it can be hard to see the underlying geometric picture directly from the homology groups. The stable homotopy refinement, introduced by Lipshitz and Sarkar, upgrades Khovanov homology to a space-level invariant: a spectrum whose cohomology recovers Khovanov homology while supporting additional structure that is invisible at the level of homology. This refinement induces stable cohomology operations, such as Steenrod squares, on Khovanov homology. In this talk, I will explain how to compute $Sq^1$ and $Sq^2$ on Khovanov homology.

Posted February 17, 2026

2:30 pm 112

Gyaneshwar Agrahari, LSU
An Introduction to the Crapo Beta Invariant in Matroid Theory

We will define the Crapo beta invariant of a matroid and prove a few of its fundamental properties, including how it behaves under standard matroid operations. We will also investigate the connection of certain matroid properties like connectivity with the invariant.

Event contact: Gyaneshwar Agrahari and Emmanuel Asante

Friday, February 20, 2026

Posted December 7, 2025
Last modified December 28, 2025

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

Richard Vinter, Imperial College London IEEE Fellow
Control of Lumped-Distributed Control Systems

Lumped-distributed control systems are collections of interacting sub-systems, some of which have finite dimensional vector state spaces (comprising ‘lumped’ components) and some of which have infinite dimensional vector state spaces (comprising ‘distributed’ components). Lumped-distributed control systems are encountered, for example, in models of thermal or distributed mechanical devices under boundary control, when we take the control actuator dynamics or certain kinds of dynamic loading effects into account. This talk will focus on an important class of (possibly non-linear) lumped-distributed control systems, in which the control action directly affects only the lumped subsystems and the output is a function of the lumped state variables alone. We will give examples of such systems, including a temperature-controlled test bed for measuring semiconductor material properties under changing temperature conditions and robot arms with flexible links. A key observation is an exact representation of the mapping from control inputs to outputs, in terms of a finite dimensional control system with memory. (We call it the reduced system representation.) The reduced system representation can be seen as a time-domain analogue of frequency response descriptions involving the transfer function from input to output. In contrast to frequency response descriptions, the reduced system representation allows non-linear dynamics, hard constraints on controls and outputs, and non-zero initial data. We report recent case studies illustrating the computational advantages of the reduced system representation. We show that, for related output tracking problems, computation methods based on the new representation offer significantly improved tracking and reduction in computation time, as compared with traditional methods, based on the approximation of infinite dimensional state spaces by high dimensional linear subspaces.

Posted February 16, 2026

Mathematical Physics and Representation Theory Seminar

2:30 pm – 3:30 pm Zoom (click here to join)

William Linz, University of South Carolina
On the maximum second eigenvalue of outerplanar graphs

A typical spectral Turan problem is to determine the maximum spectral radius of a graph in some given family of graphs on a fixed number of vertices. Spectral Turan problems have been well-studied in part because they are variations on classical Turan problems from extremal graph theory. Nikiforov proposed the much more general question of determining which graphs maximize a fixed linear combination of eigenvalues of a graph among a given family of graphs. In this talk, I will survey some of the results that are known about these problems. The main highlight of the talk will be a recent result on the maximum second eigenvalue of an outerplanar graph on a fixed number of vertices, a result which is joint work with George Brooks, Maggie Gu, Jack Hyatt and Linyuan Lu.

Monday, February 23, 2026

Posted February 17, 2026

LSU SIAM Student Chapter

12:30 pm – 1:30 pm Keisler Lounge

Laura Kurtz, Louisiana State University
Rerun: Accesibility in LaTeX Workshop

Learn how to make your LaTeX documents readable by screen readers.

Posted February 3, 2026

1:30 pm – 2:20 pm Lockett 233

Karl-Hermann Neeb, Universität Erlangen-Nürnberg
Coadjoint orbits carrying Gibbs ensembles

Coadjoint orbits are orbits for the action of a Lie group on the dual of its Lie algebra. They carry a natural symplectic structure and are models for homogeneous systems in classical mechanics. Gibbs measures on these orbits provide a natural setting for models of thermodynamic systems. We say that a coadjoint orbit carries a Gibbs ensemble if the set of all $x$, for which the function $\alpha \mapsto e^{-\alpha(x)}$ on the orbit is integrable with respect to the Liouville measure, has non-empty interior $\Omega_\lambda$. We describe a classification of all coadjoint orbits with this property. In the context of Souriau's Lie group thermodynamics, the subset $\Omega_\lambda$ is the geometric temperature, a parameter space for a family of Gibbs measures on the coadjoint orbit. The corresponding Fenchel--Legendre transform maps $\Omega_\lambda$ (modulo central shifts) diffeomorphically onto the interior of the convex hull of the coadjoint orbit $\cO_\lambda$. This provides an interesting perspective on the underlying information geometry.

Tuesday, February 24, 2026

Posted November 15, 2025
Last modified January 21, 2026

Algebra and Number Theory Seminar Questions or comments?

2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom

Marco Sangiovanni Vincentelli, Columbia University
An Euler system for the adjoint of a modular form

Euler systems have proven to be versatile tools for understanding Selmer groups and their connections to special values of $L$-functions. However, despite the key role they have played in making progress toward foundational conjectures in number theory, such as the Birch and Swinnerton-Dyer and Bloch–Kato Conjectures, only a handful of provably non-trivial Euler systems have been constructed to date. A significant obstacle to constructing Euler Systems lies in producing candidate Galois cohomology classes. This lecture series presents joint work with Chris Skinner that develops a method to overcome this obstacle. Using this method, we construct an Euler system for the adjoint of a modular form.

Event contact: Gene Kopp

Posted February 6, 2026

Actuarial Student Association

5:30 pm Lockett Hall

ASA Excel Workshop

We will be joined by our SOA Liason Matthew who will continue his Excel Workshop from last year! Pizza Will be Served

Today, Wednesday, February 25, 2026

Posted February 9, 2026
Last modified February 23, 2026

12:30 pm – 1:30 pm Lockett 233

Gustavs Tobiss, Louisiana State University
Bloch's Theorem, Wannierization, and Tight-binding

This talk presents the mathematical framework and numerical methods behind tight-binding models for electrons in a one-dimensional periodic potential, focusing on the transition from Bloch states to Wannier functions. We start by revisiting Bloch’s theorem, which leads to a decomposition into independent Hamiltonians for each wavevector in the Brillouin zone. This immediately allows us to describe the system in terms of its band structure. We then introduce Wannier functions, localized eigenstates derived from band eigenfunctions. The Wannier functions possess many nice qualities, such as being exponentially localized and orthonormal, with the decay tied to the analyticity of the band structure. Next, we derive the tight-binding Hamiltonian by projecting onto a single band subspace. This Hamiltonian is expressed as a sum of hopping terms, with hopping amplitudes related to the band structure, providing a link to the system's dispersion relation and physical properties. Finally, we discuss how this simple model will be used to analyze more complicated structures.

Posted January 28, 2026
Last modified February 17, 2026