Calendar

Posted August 19, 2025
Last modified November 2, 2025

Colloquium Questions or comments?

David Roberts, University of Minnesota, Morris
From fewnomials to hypergeometric motives

Understanding the solutions to a given polynomial equation is a central theme in mathematics. In algebraic geometry, one most commonly is focused on solutions in the complex number field $\mathbb{C}$. In number theory, solutions in finite fields $\mathbb{F}_p$ also play an important role.

In this colloquium, I will discuss the case where the given equation has $d+3$ monomials in $d+1$ variables, this being the first generically-behaving case. I will explain how many standard questions about the solutions to these equations in $\mathbb{C}$ and $\mathbb{F}_p$ are concisely and uniformly answered via the theory of hypergeometric motives.

Posted November 4, 2025

Conference

Bayou Arithmetic Research Day (BARD 6)

See the event schedule and speakers here: https://bardsmath.com/bard6-schedule/

Posted July 26, 2025

Control and Optimization Seminar Questions or comments?

Rami Katz, Università degli Studi di Trento, Italy
Oscillations in Strongly 2-Cooperative Systems and their Applications in Systems Biology

The emergence of sustained oscillations (via convergence to periodic orbits) in high-dimensional nonlinear dynamical systems is a non-trivial question with important applications in control of biological systems, including the design of synthetic bio-molecular oscillators and the understanding of circadian rhythms governing hormone secretion, body temperature and metabolic functions. In systems biology, the mechanism underlying such widespread oscillatory biological motifs is still not fully understood. From a mathematical perspective, the study of sustained oscillations is comprised of two parts: (i) showing that at least one periodic orbit exists and (ii) studying the stability of periodic orbits and/or characterizing the initial conditions which yield solutions that converge to periodic trajectories. In this talk, we focus on a specific class of nonlinear dynamical systems that are strongly 2-cooperative. Using the theory of cones of rank k, the spectral theory of totally positive matrices and Perron-Frobenius theory, we will show that strongly 2-cooperative systems admit an explicit set of initial conditions of positive measure, such that every solution emanating from this set converges to a periodic orbit. We further demonstrate our results using the n-dimensional Goodwin oscillator and a 4-dimensional biological oscillator based on RNA–mediated regulation.

Posted October 28, 2025
Last modified November 3, 2025

LSU AWM Student Chapter LSU AWM Student Chapter Website

Galen Dorpalen-Barry, Texas A&M
Discussion Session with Dr. Galen Dorpalen-Barry

This is a special AWM-presented discussion session with Dr. Galen Dorpalen-Barry (Texas AM University). It will occur before her talk in the Combinatorics seminar.

Event contact: jgarc86@lsu.edu

Posted October 30, 2025

Combinatorics Seminar Questions or comments?

Galen Dorpalen-Barry, Texas A&M
Combinatorics and Topology of Conditional Oriented Matroids

Oriented matroids are combinatorial objects that capture much of the topology of (central) real arrangements. A well-know theorem of Salvetti, for example, describes the homotopy type of the complexitied complement of a real arrangement using only the data of its oriented matroid. A conditional oriented matroid plays the role of an oriented matroid when one has a convex body cut by hyperplanes in a real vector space. These arise, for example, in the study of Coxeter arrangements, convex polytopes, and affine arrangements. In this talk, we will give an overview of what’s known about conditional oriented matroids and share new results about their combinatorics and topology. This is a combination of several joint works with various authors including Nick Proudfoot, Jayden Wang, and Dan Dugger.

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 4, 2025

Applied Analysis Seminar Questions or comments?

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: Stephen Shipman, Laura Kurtz

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 September 23, 2025

Geometry and Topology Seminar Seminar website

Jayden Wang, University of Michigan
TBA

TBA