Calendar
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
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.
Posted March 9, 2025
Last modified April 9, 2025
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.
Posted November 7, 2024
Last modified March 13, 2025
Control and Optimization Seminar Questions or comments?
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
Faculty Meeting Questions or comments?
12:30 pm – 1:20 pm ZoomMeeting of the Tenured Faculty
Posted January 21, 2025
Combinatorics Seminar Questions or comments?
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.
Posted April 12, 2025
12:00 pm – 1:30 pm Keisler Lounge, Lockett Hall 3rd FloorLife 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
Applied Analysis 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)
Posted January 26, 2025
Last modified April 14, 2025
Algebra and Number Theory Seminar Questions or comments?
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.
Posted April 12, 2025
LSU AWM Student Chapter LSU AWM Student Chapter Website
12:30 pm – 1:30 pm Keisler Lounge, Lockett 3rd FloorAutomation 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.
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
Applied Analysis 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).
Posted April 14, 2025
Algebra and Number Theory Seminar Questions or comments?
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.
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 April 21, 2025
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.
Posted January 10, 2025
Last modified March 26, 2025
Control and Optimization Seminar Questions or comments?
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
Combinatorics Seminar Questions or comments?
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.
Posted December 10, 2024
Last modified April 27, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 232
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.
Posted April 16, 2025
Algebra and Number Theory Seminar Questions or comments?
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.
Posted January 12, 2025
Last modified April 29, 2025
Zi Li Lim, UCLA
Rational function progressions
Szemeredi proved that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions. Subsequently, Szemeredi's theorem was generalized to the polynomial and multidimensional settings. We will discuss finding the progressions involving rational functions via Fourier analysis and algebraic geometry.
Posted January 23, 2025
Last modified April 29, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Annette Karrer, The Ohio State University
Connected Components in Morse boundaries of right-angled Coxeter groups
Every finitely generated group G has an associated topological space, called a Morse boundary, that captures the hyperbolic-like behavior of G at infinity. It was introduced by Cordes generalizing the contracting boundary invented by Charney--Sultan. In this talk, we study subgroups arising from connected components in Morse boundaries of right-angled Coxeter groups and of such that are quasi-isom
Posted April 7, 2025
Last modified April 21, 2025
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.
Posted January 16, 2025
Last modified April 5, 2025
Control and Optimization Seminar Questions or comments?
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
Combinatorics 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.
Posted February 19, 2025
Last modified April 24, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Nina Amini, Laboratory of Signals and Systems, CentraleSupélec
Feedback Control of Open Quantum Systems
First, we provide an overview of control strategies for open quantum systems, that is, quantum systems interacting with an environment. This interaction leads to a loss of information to the environment, a phenomenon commonly referred to as decoherence. One of the principal challenges in controlling open quantum systems is compensating for decoherence. To address robustness issues, feedback control methods are considered. Secondly, we consider the feedback stabilization of open quantum systems under repeated indirect measurements, where the evolution is described by quantum trajectories. I will present our recent results concerning the asymptotic behavior, convergence speed, and stabilization of these trajectories.