Calendar

Posted August 21, 2025
Last modified October 24, 2025

Applied Analysis Seminar Questions or comments?

Roy Goodman, New Jersey Institute of Technology
Leapfrogging and scattering of point vortices

The interaction among vortices is a key process in fluid motion. The n-vortex problem, which models the movement of a finite number of vortices in a two-dimensional inviscid fluid, has been studied since the late 1800s and remains relevant due to its strong link to quantum fluid dynamics. A foundational document in this area is Walter Gröbli's 1877 doctoral dissertation. We apply modern tools from dynamical systems and Hamiltonian mechanics to several problems arising from this work. First, we study the linear stability and nonlinear dynamics of the so-called leapfrogging orbit of four vortices, utilizing Hamiltonian reductions and a numerical visualization method known as Lagrangian descriptors. Second, we analyze the scattering of vortex dipoles using tools from geometric mechanics. While point vortices are typically modeled as massless particles, the final part of this talk will discuss the impact of endowing each particle with a small mass. Although some of the concepts are technical, the presentation will focus on a series of interesting and informative images and animations.

Event contact: Stephen Shipman

Posted November 4, 2025

Informal Analysis Seminar Questions or comments?

Phuc Nguyen, Department of Mathematics, Louisiana State University
Capacities, weighted norm inequalities, and nonlinear partial differential equations

I will present a survey of trace inequalities for fractional integrals, highlighting the role of capacities associated to Sobolev spaces and their connections to nonlinear potential theory and nonlinear partial differential equations

Event contact: Laura Kurtz

Posted November 6, 2025

Actuarial Student Association

ASA Meeting

We will be joined by Doug and Kaylee from Southern Farm Bureau Insurance. Pizza will be Served

Posted August 27, 2025
Last modified October 27, 2025

Informal Geometry and Topology Seminar Questions or comments?

Matthew Lemoine, Louisiana State University
Topological Data Analysis of Mortality Patterns During the COVID-19 Pandemic (joint work with Megan Fairchild)

This talk will be a brief overview of Topological Data Analysis and will go into some of the work that Megan and I have done. Topological Data Analysis is a relatively new field of study that uses topological invariants to study the shape of data. We analyze a dataset provided by the Centers for Disease Control and Prevention (CDC) using persistent homology and MAPPER. This dataset tracks mortality week-to-week from January 2020 to September 2023 in the United States during the COVID-19 pandemic. We examine the dataset as a whole and break the United States into geographic regions to analyze the overall shape of the data. Then, to explain this shape, we discuss events around the time of the pandemic and how they contribute to the observed patterns.

Posted September 1, 2025
Last modified November 10, 2025

Geometry and Topology Seminar Seminar website

Jayden Wang, University of Michigan
From Euclid’s first postulate to Lorentzian polynomials

Imagine a world where our basic intuition about points, lines, and planes no longer applies—a world where three points in a three-dimensional linear space need not lie in any plane. This is the tropical world. I will tell a story about tropical linear spaces, where many familiar incidence properties of classical linear geometry fail in surprising ways. I will also discuss how both the fulfillment and the violation of these properties resonate across other areas of mathematics, including algebraic curves, Lorentzian polynomials, and matroid combinatorics.

Posted August 1, 2025
Last modified November 3, 2025

Control and Optimization Seminar Questions or comments?

Thinh Doan, University of Texas at Austin AFOSR YIP and NSF CAREER Awardee
Multi-Time-Scale Stochastic Approximation as a Tool for Multi-Agent Learning and Distributed Optimization

Multi-time-scale stochastic approximation (SA) is a powerful generalization of the classic SA method for finding roots (or fixed points) of coupled nonlinear operators. It has attracted considerable attention due to its broad applications in multi-agent learning, control, and optimization. In this framework, multiple iterates are updated simultaneously but with different step sizes, whose ratios loosely define their time-scale separation. Empirical studies and theoretical insights have shown that such heterogeneous step sizes can lead to improved performance compared to single-time-scale (or classical) SA schemes. However, despite these advantages, existing results indicate that multi-time-scale SA typically achieves only a suboptimal convergence rate, slower than the optimal rate attainable by its single-time-scale counterpart. In this talk, I will present our recent work on characterizing the convergence complexity of multi-time-scale SA. We develop a novel variant of this method and establish new finite-sample guarantees that achieves the optimal (O(1/k)) convergence rate. Building upon these results, I will also discuss how these advances enable the design of efficient algorithms for key problems in multi-agent learning and distributed optimization over networks.

Posted November 10, 2025

Probability Seminar Questions or comments?

Yangrui Xiang, LSU
Quantitative Hydrodynamics for a Generalized Contact Model

Abstract: We derive a quantitative version of the hydrodynamic limit for an interacting particle system inspired by integrate-and-fire neuron models. More precisely, we show that the L^2-speed of convergence of the empirical density of states in a generalized contact process defined over a d-dimensional torus of size n is of the optimal order O(n^{d/2}). In addition, we show that the typical fluctuations around the aforementioned hydrodynamic limit are Gaussian, and governed by a inhomogeneous stochastic linear equation. This is a joint work with Julian Amorim, Milton Jara.

Posted October 28, 2025
Last modified November 6, 2025

Student Colloquium

Jonathan Walters, Louisiana Tech University
Control Strategies for Flexible Wing Aircraft

Flexible wing aircraft are inspired by nature and are being studied and developed by many major aerospace companies.  In our work, we model small scale aircraft using partial differential equations and employ linear control strategies to shape the wings to a desired target state.  Our work has previously consisted of studying linear controllers such as LQR and LQG applied to our system and studying different damping mechanisms based on material composition. More recently, we've updated our model to incorporate piezo-ceramic patches as realistic controllers and sensors.  An overview of the project and current progress will be presented.

Posted October 30, 2025

Combinatorics Seminar Questions or comments?

Chris Wells, Auburn University
A discrete view of Gromov's filling area conjecture

In differential geometry, a metric surface $M$ is said to be an isometric filling of a metric curve $C$ if $\partial M=C$ and $d_M(x,y)=d_C(x,y)$ for all $x,y\in C$. Gromov's filling area conjecture from 1983 asserts that among all isometric fillings of the Riemannian circle, the one with the smallest surface area is the hemisphere. Gromov's conjecture has been verified if, say, $M$ is homeomorphic to the disk and in a few other cases, but it still open in general. Admittedly, I'm not a differential geometer in even the even the loosest of senses, so we consider instead a particular discrete version of Gromov's conjecture which is likely fairly natural to anyone who studies graph embeddings on arbitrary suraces. We obtain reasonable asymptotic bounds on this discrete variant by applying standard graph theoretic results, such as Menger's theorem. These bounds can then be translated to the continuous setting to show that any isometric filling of the Riemannian circle of length $2\pi$ has surface-area at least $1.36\pi$ (the hemisphere has area $2\pi$). This appears to be the first quantitative lower-bound on Gromov's conjecture that applies to an arbitrary isometric fillings. (Based on joint work with Joe Briggs)

Posted October 15, 2025
Last modified October 16, 2025

Mathematical Physics and Representation Theory Seminar

Paul Sobaje, Georgia Southern University
A Geometric Model For Steinberg Quotients

Let G be a reductive algebraic group over a field of characteristic p > 0. Over the last decade, the longstanding search for a character formula for simple G-modules has been replaced (subsumed even) by the same problem for characters of tilting G-modules. In recent years I began studying "Steinberg quotients" of certain tilting characters. These are formal characters with good combinatorial properties straightforwardly derived from the representation theory of G. In some ways they are also the best candidates to be described by a characteristic p version of Weyl's famous formula. In joint work with P. Achar, we prove that these formal characters are in fact actual characters of a natural class of objects coming from geometric representation theory.