Calendar
Posted October 6, 2025
Last modified October 15, 2025
Mathematical Physics and Representation Theory Seminar
1:30 pm – 2:20 pm Lockett 233
John O'Brien, Louisiana State University
The Splitting-Rank Derived Satake Equivalence
This talk is based on joint work with Tsao-Hsien Chen, Mark Macerato, and David Nadler. We discuss a generalization of Bezrukavnikov-Finkelberg's Derived Satake Equivalence from complex reductive groups to certain real reductive groups--or equivalently, from compact Lie groups to the corresponding symmetric spaces. We use Nadler's Real Geometric Satake to compute the equivariant cohomology of the based loop space of a splitting-rank symmetric space, then use Achar's parity-vanishing machinery to establish the equivalence of derived categories.
Posted August 27, 2025
Last modified October 15, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett Hall 233
Xuenan Li, Columbia University
Soft modes in mechanism-based mechanical metamaterials: modeling, analysis, and applications
Mechanism-based mechanical metamaterials are synthetic materials that exhibit unusual microscale buckling in response to mechanical deformations. These artificial materials are like elastic composites but sometimes more degenerate since they can deform with zero elastic energy. We call such zero energy deformations mechanisms. Origami and Kirigami are typical examples of these mechanism-based mechanical metamaterials. Other than mechanisms, these metamaterials also have "soft modes" -- macroscopic deformations with very little elastic energy, some but not all of which resemble modulated mechanisms. A key question is to identity all the soft modes for a given mechanism-based metamaterial. In this talk, I will address the two-fold challenge in identifying the soft modes and our treatments: first, we establish the existence of an effective energy for a broad class of lattice metamaterials; and second, we identify soft modes as macroscopic deformations where this energy vanishes, including a complete characterization of the zero sets of the effective energy in some conformal metamaterials. Together, these results provide a rigorous link between mechanisms and soft modes, laying a mathematical foundation for future analysis and design of mechanical metamaterials. This is joint work with Robert V. Kohn.
Event contact: Stephen Shipman
Posted September 2, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm Lockett 233 or click here to attend on Zoom
Guanyu Li, Cornell University
Derived Commuting Schemes, Representation Homology, and Cohomology of Lie Algebras
The commuting schemes of an algebraic group or a Lie algebra play important roles in many areas of mathematics. They can be viewed as special cases of representation schemes, which are often highly singular. Derived algebraic geometry provides tools to remedy the deficiency. In particular, the derived representation scheme, together with its associated algebraic invariant known as representation homology, offers deeper insights into the structure of representation schemes. While the representation homology of reductive groups and reductive Lie algebras has been studied in the literature, it is natural to ask about the behavior of these objects and their relationships in the non-reductive setting. In this talk, I will discuss the derived commuting scheme of a maximal unipotent subgroup of a semisimple group scheme, as well as the derived commuting scheme of its Lie algebra. First, the higher structure of the derived commuting scheme detects whether the underlying commuting scheme is a complete intersection. Unlike the reductive case, the derived commuting scheme of a unipotent subgroup is equivalent to that of its Lie algebra. Using an analogue of the trace map, most of the homology classes can be explained in terms of the classical cohomology of a maximal nilpotent Lie algebra, described via the root system of the semisimple Lie algebra. This could be interpreted that the singularities of the commuting scheme of a maximal nilpotent subalgebra are largely determined by root system data. If time permits, I will also discuss a possible nilpotent analogue of the Macdonald identity, together with an interpretation in terms of representation homology.
Posted October 19, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 136
Laura Kurtz, Louisiana State University
Stochastic Homogenization
In this talk, we develop tools of stochastic homogenization of elliptic operators. We focus mainly on the periodic case and discuss the implications of the stochastic case.
Event contact: Moises Gomez-Solis
Posted October 6, 2025
Last modified October 8, 2025
Paul Kirk, Indiana University
The SU(2) character variety "Functor" from the bordism category of 2+1 manifolds to the Weinstein symplectic "category"
Around 1990, Atiyah-Floer made a "conjecture" advocating for the study of 3-manifolds by using the symplectic properties of the SU(2) character varieties of 2 and 3-manifolds. This conjecture and surrounding philosophy has had a profound influence on the development of low dimensional topology ever since (with its most powerful consequences the construction of Heegard-Floer theory and the growth of symplectic topology). I'll explain what all these words mean in down to earth terms, and why there are "scare quotes" everywhere, and discuss history and related areas of mathematics. Tip: To help you get something out of the talk, spend a few minutes looking at: (a) the definition of the fundamental group of a space, and the Seifert-Van Kampen theorem, (b) the definition of the quaternions, and in particular the unit quaternions=SU(2), and (c) the definition of a symplectic manifold and a Lagrangian submanifold.
Posted August 27, 2025
Last modified October 22, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Remi Mandal, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology following Melissa Zhang's notes.
Posted September 1, 2025
Last modified October 9, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Matthew Haulmark, UT Rio Grande Valley
Cubes from Divisions
Actions on CAT(0) cube complexes have played an important role in advances in low-dimensional topology. Most notably, they are central to Wise's Quasiconvex Hierarchy Theorem and Agol's proof of the Virtual Haken Conjecture. In group theory, one way of obtaining an action on a cube complex is via the Sageev construction. Given a group G and a collection of codimension-1 subgroups of G, Sageev's construction gives an isometric action on a CAT(0) cube complex. In recent work with Jason Manning, we give an alternate route to the Sageev construction, which is potentially applicable to new situations. Much of this talk will be spent on background. We will introduce the notion of a wall space, as well as the cube complex dual to a wallspace. We will then construct an action on a CAT(0) cube complex given a group action on a sufficiently nice topological space and a system of divisions of that space.
Posted October 6, 2025
Last modified October 13, 2025
Colloquium Questions or comments?
3:30 pm Lockett 232
Paul Kirk, Indiana University
On the SU(2) character variety of a closed oriented genus 2 surface
A celebrated theorem of Narasimhan-Ramanan asserts that the singular variety $X(F_2)=Hom(\pi_1(F_2),SU(2))/Conjugation$ is homeomorphic to $CP^3$. The proof passes through the (mysterious) Narasimhan-Seshadri correspondence. I'll outline an elementary differential topology proof that $X(F_2)$ is a manifold, homeomorphic to CP^3, and discuss how 3-manifolds with genus 2 boundary determine embedded lagrangians in $X(F_2)$. If time permits, I'll end the talk with a discussion of context, particularly with a program known as the Atiyah-Floer conjecture.
Posted September 5, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Naira Hovakimyan, University of Illinois Urbana-Champaign
Fellow of AIAA, ASME, IEEE, and IFAC
Safe Learning in Autonomous Systems
Learning-based control paradigms have seen many success stories with autonomous systems and robots in recent years. However, as these robots prepare to enter the real world, operating safely in the presence of imperfect model knowledge and external disturbances is going to be vital to ensure mission success. We introduce a class of distributionally robust adaptive control architectures that ensure robustness to distribution shifts and enable the development of certificates for validation and verification of learning-enabled systems. An overview of different projects at our lab that build upon this framework will be demonstrated to show different applications.
Posted October 22, 2025
LSU AWM Student Chapter LSU AWM Student Chapter Website
11:30 am – 12:20 pm https://lsu.zoom.us/j/7469727061?pwd=Q1E1b0lUL1Z3WnJxY1lTNVRtVVNmUT09
Naira Hovakimyan, University of Illinois Urbana-Champaign
Fellow of AIAA, ASME, IEEE, and IFAC
Q&A session with Dr. Naira Hovakimyan
This is an online event (over Zoom) following her talk on Safe Learning in Autonomous Systems at the Control and Optimization seminar. This is an opportunity to engage with Professor Naira Hovakimyan in an informal setting and ask questions about her research, career path, and experiences in Mathematics and Engineering.
Event contact: jgarc86@lsu.edu
Posted October 17, 2025
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 click here to attend on Zoom
Christine Cho, Louisiana State University
The symmetric strong circuit elimination property
A set $\mathcal{C}$ of incomparable non-empty subsets of a finite set $E$ is the set of circuits of a matroid on $E$ when $\mathcal{C}$ satisfies either the weak circuit elimination axiom or the strong circuit elimination axiom. The strong circuit elimination axiom is inherently asymmetric. In this talk, we will present the symmetric strong circuit elimination property (SSCE) and characterize the class of connected matroids that possess this property. We will also explore the notion of skew circuits in a matroid, both in relation to the class of matroids satisfying SSCE and beyond. This talk is based on joint work with James Oxley and Suijie Wang.
Posted September 9, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Kalani Thalagoda, Tulane University
A summation formula for Hurwitz class numbers
The Hurwitz class numbers, $H(n)$, count ${\rm SL}(2,\mathbb{Z})$-classes of binary quadratic forms inversely weighted by stabilizer size. They are famously connected to the sum of three squares problem and to class numbers of imaginary quadratic fields. The work of Zagier in 1975 showed that their generating functions are related to a weight $3/2$ Harmonic Maass form. In this talk, I will discuss a summation formula for mock modular forms of moderate growth, with an emphasis on its application to Hurwitz class numbers. This is joint work with Olivia Beckwith, Nicholas Diamantis, Rajat Gupta, and Larry Rolen.
Posted October 27, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Monday, October 27, 2025 Lockett 136
Sanjeet Sahoo, LSU
Introduction to Invariant Measures and Ergodicity for Markov Processes
In this talk, we will introduce the concept of transition probability measures and establish criteria for the existence and uniqueness of invariant measures.
Posted August 27, 2025
Last modified October 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Nilangshu Bhattacharyya, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology following Melissa Zhang's notes.
Posted September 1, 2025
Last modified October 29, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Chen Zhang, Simons Center for Geometry and Physics
Plane Floer homology and the odd Khovanov homology of 2-knots
In this talk, I will discuss joint work with Spyropoulous and Vidyarthi in which we prove a conjecture of Migdail and Wehrli regarding the maps which odd Khovanov homology associates to knotted spheres. Our main tool is the spectral sequence from reduced OKH to Plane Floer homology.
Posted October 7, 2025
Last modified October 9, 2025
Control and Optimization Seminar Questions or comments?
9:30 am – 10:20 am Note: First of 2 Seminars for 10/31. Zoom (click here to join)
Alexandre Mauroy, Université de Namur
Dual Koopman Operator Formulation in Reproducing Kernel Hilbert Spaces for State Estimation
The Koopman operator acts on observable functions defined over the state space of a dynamical system, thereby providing a linear global description of the system dynamics. A pointwise description of the system is recovered through a weak formulation, i.e. via the pointwise evaluation of observables at specific states. In this context, the use of reproducing kernel Hilbert spaces (RKHS) is of interest since the above evaluation can be represented as the duality pairing between the observables and bounded evaluation functionals. This representation emphasizes the relevance of a dual formulation for the Koopman operator, where a dual Koopman system governs the evolution of linear evaluation functionals. In this talk, we will leverage the dual formulation to build a Luenberger observer that estimates the (infinite-dimensional) state of the Koopman dual system, and equivalently the (finite-dimensional) state of the nonlinear dynamics. The method will be complemented with theoretical convergence results that support numerical Koopman operator-based estimation techniques known from the literature. Finally, we will extend the framework to a probabilistic approach by solving the problem of moments in the RKHS setting.
Posted October 8, 2025
Last modified October 28, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Note: Second of 2 Seminars for 10/31. Zoom (click here to join)
Umesh Vaidya, Clemson University
Koopman Meets Hamilton and Jacobi: Data-Driven Control Beyond Linearity
In this talk, we present recent advances in operator-theoretic methods for controlling nonlinear dynamical systems. We begin by establishing a novel connection between the spectral properties of the Koopman operator and solutions of the Hamilton–Jacobi (HJ) equation. Since the HJ equation lies at the core of optimal control, robust control, dissipativity theory, input–output analysis, and reachability, this connection provides a new pathway for leveraging Koopman spectral representations to address control problems in a data-driven setting. In particular, we show how Koopman coordinates can shift the classical curse of dimensionality associated with solving the HJ equation into a curse of complexity that is more manageable through modern computational tools. In the second part of the talk, we discuss safe control synthesis using the Perron–Frobenius operator. A key contribution is the analytical construction of a navigation density function that enables safe motion planning in both static and dynamic environments. We further present a convex optimization formulation of safety-constrained optimal control in the dual (density) space, allowing safety constraints to be incorporated systematically. Finally, we demonstrate the application of this unified operator-theoretic framework to the control of autonomous ground vehicles operating in off-road environments.
Posted October 27, 2025
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Matthew Mizell, LSU
Unavoidable minors of matroids with minimum cocircuit size four
When a graph $G$ is a 2-connected and loopless, the set of edges that meet a fixed vertex of $G$ is a bond of $G$ and a cocircuit of its cycle matroid $M(G)$. Because of this, it is common in matroid theory to take minimum cocircuit size as a matroid analog of minimum vertex degree in a graph. Halin and Jung proved in 1963 that every simple graph with minimum degree at least four has $K_5$ or $K_{2,2,2}$ as a minor. In this talk, we will provide a characterization of matroids with minimum cocircuit size four in terms of their unavoidable minors. This talk is based on joint work with James Oxley.
Posted October 21, 2025
Colloquium Questions or comments?
3:30 pm Lockett 232
Michael Lacey, Georgia Institute of Technology
Prime Wiener Wintner Theorem
The classical Wiener Wintner Theorem has an extension to prime averages. Namely, for all measure preserving system $(X,m,T)$, and bounded function $f$ on $X$, there is a set of full measure $X_f\subset X$ so that for all $x\in X_f$, the averages below $$ \frac 1N \sum_{n=1}^N \phi(n) \Lambda (n) f(T^n x ) $$ converge for all continuous $2\pi$ periodic $\phi $. Above, $\Lambda$ is the von Mangoldt function. The proof uses the structure theory of measure preserving systems, the Prime Ergodic Theorem, and higher order Fourier properties of the Heath-Brown approximate to the von Mangoldt function. Joint work with J. Fordal, A. Fragkos, Ben Krause, Hamed Mousavi, and Yuchen Sun.
Posted October 22, 2025
Last modified October 23, 2025
Southern Regional Harmonic Analysis Conference
The Southern Regional Harmonic Analysis Conference will focus on current research in harmonic analysis and its applications, featuring plenary talks by Michael Lacey and Irina Holmes. For more details, please refer to conference webpage: https://www.math.lsu.edu/~ha2025/
Event contact: Rui Han, Gestur Olafsson, Naga Manasa Vempati, Fan Yang
Posted October 26, 2025
Last modified November 1, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Che-Wei Hsu, National Taiwan University
Hypergeometric Evaluations of L-values and Harmonic Maass Forms
In their earlier work, Bruinier, Ono, and Rhoades asked for an explicit construction of good harmonic Maass forms associated with CM newforms. Building on Ramanujan's theories of elliptic functions to alternative bases, we express $L$-values of certain weakly holomorphic cusp forms in terms of hypergeometric functions. As an application, we construct harmonic Maass forms with explicitly computable Fourier coefficients that are good for specific Hecke eigenforms including certain CM cusp forms.
In this talk, I will briefly review the basic notions of harmonic Maass forms and then present the ongoing joint work with Jia-Wei Guo, Fang-Ting Tu, and Yifan Yang.
Posted October 29, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm Lockett 136
Christopher Bunting, LSU
Ergodicity of solutions to the stochastic Navier-Stokes equations
The stochastic Navier-Stokes equations has been extensively studied over the past few decades. In this talk, we consider the 2D stochastic Navier-Stokes equations perturbed by an additive noise. We begin by establishing results regarding solutions and provide essential estimates. Using these results, we prove the existence and uniqueness of invariant measure for the solutions of the equations.
Event contact: Laura Kurtz
Posted August 27, 2025
Last modified October 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Evan Short, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology following Melissa Zhang's notes.
Posted August 21, 2025
Last modified October 9, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Matthew Zaremsky, University at Albany (SUNY)
On the Sigma-invariants of pure symmetric automorphism groups
An automorphism of the free group F_n is "pure symmetric" if it sends each generator to a conjugate of itself. The group of all pure symmetric automorphisms of F_n, sometimes called the "McCool group" of F_n, is an interesting and important group with connections to braid groups, motion planning, and mathematical physics. The "Sigma-invariants" of a group are a family of geometric invariants due to Bieri, Neumann, Strebel, and Renz, which are notoriously difficult to compute in general, but reveal a wealth of information about the group and its fibering properties. In recent joint work with Mikhail Ershov, we compute large parts of the Sigma-invariants of the McCool groups, and in particular prove that they are always either empty or dense in the relevant character sphere. One key tool to highlight is an underutilized criterion due to Meinert, which seems likely to have additional future applications.
Posted August 19, 2025
Last modified November 2, 2025
Colloquium Questions or comments?
3:30 pm Lockett 232
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
10:30 am – 5:00 pm Lockett 233 and ZoomBayou 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?
10:30 am – 11:20 am Zoom (click here to join)
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
12:30 pm – 1:30 pm Keiser Lounge
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?
2:30 pm – 3:30 pm Lockett 138 or click here to attend on Zoom
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?
3:30 pm Lockett Hall 233
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?
3:30 pm – 4:30 pm Lockett 136
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
5:30 pm Kessler Lounge (3rd Floor Lockett Hall)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?
1:30 pm Lockett Hall 233
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
3:30 pm Locket 233
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?
10:30 am – 11:20 am Zoom (click here to join)
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?
11:00 am – 12:00 pm Lockett 233
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
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?
2:30 pm – 3:30 pm Zoom
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
1:30 pm – 2:20 pm Lockett 233
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.
Posted November 12, 2025
Last modified November 16, 2025
Colloquium Questions or comments?
4:00 pm 232 Lockett Hall
Quanjun Lang, Duke University
Low-Rank Methods for Multitype Interacting Particle Systems and Quantum Superoperator Learning
We introduce a multi-type interacting particle system on graphs to model heterogeneous agent-based dynamics. Within this framework, we develop algorithms that jointly learn the interaction kernels, the latent type assignments, and the underlying graph structure. The approach has two stages: (i) a low-rank matrix sensing step that recovers a shared interaction embedding, and (ii) a clustering step that identifies the discrete types. Under the assumption of the restricted isometry property (RIP), we obtain theoretical guarantees on sample complexity and convergence for a wide range of model parameters. Building on the same low-rank matrix sensing framework, I will then discuss quantum superoperator learning, encompassing both quantum channels and Lindbladian generators. We propose an efficient randomized measurement design and use accelerated alternating least squares to estimate the low-rank superoperator. The resulting performance guarantees follow from RIP conditions, which are known to hold for Pauli measurement ensembles.
Posted November 15, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Jiaqi Hou, Louisiana State University
Restriction bounds for Maass forms
I will talk about the analytic problem of bounding Hecke–Maass forms. From the general theory of bounding Laplace eigenfunctions on Riemannian manifolds, one obtains local bounds for many different kinds of norms, and these bounds are believed to be far from optimal if the manifold is negatively curved. I will discuss how Hecke–Maass forms on arithmetic hyperbolic 3-folds behave along totally geodesic surfaces and present an improved L^2 bound by the method of arithmetic amplification.
Posted November 13, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Room 136
Anan Saha, LSU
Learning of Stochastic Differential Equations with integral-drift
Stochastic differential equations (SDEs) with integral drift arise naturally in multiscale systems and in applications where effective dynamics are obtained by averaging over latent or unobserved processes. In such settings, the drift takes the form b̅(x) = ∫ b(x, y) π(dy), with π an unknown probability measure. Our primary goal is the nonparametric estimation of the averaged drift b̅ directly from observable data on X, thereby bypassing the need to recover the unidentifiable measure π, which is of secondary importance for understanding the dynamics of these types of SDE models. In this paper, we develop a nonparametric Bayesian framework for estimating b̅ based on L´evy process priors, which represent π via random discrete supports and weights. This induces a flexible prior on the drift function while preserving its structural relationship to b(x, y). Posterior inference is carried out using a reversible-jump Hamiltonian Monte Carlo (RJHMC) algorithm, which combines the efficiency of Hamiltonian dynamics with transdimensional moves needed to explore random support sizes. We evaluate the methodology on multiple SDE models, demonstrating accurate drift recovery, consistency with stationary distributions, and robustness under different data-generating mechanisms. The framework provides a principled and computationally feasible approach for estimating averaged dynamics in SDEs with integral drift.
Event contact: Laura Kurtz
Posted November 5, 2025
3:30 pm Lockett 276
Paul Sobaje, Georgia Southern University
Affine Group Schemes and Frobenius Kernels
We will give an introduction to affine group schemes over a field k from the viewpoint of k-group functors. These objects generalize the notion of an affine algebraic group over k. One of the most important examples of affine group schemes that are not algebraic groups come from the Frobenius kernels of algebraic groups in characteristic p > 0. We will discuss these objects and, time permitting, their representation theory.
Posted November 3, 2025
Last modified November 10, 2025
Computational Mathematics Seminar
3:30 pm – 4:30 pm Digital Media Center 1034
Jai Tushar, Louisiana State University
Recent Advances in Polytopal Finite Element Methods with Application to Domain Decomposition Methods
Polytopal finite element methods (FEMs) have gained popularity in recent years due to their ability to relax conformity constraints on meshes. This flexibility makes them well-suited for handling complex geometries, adaptive mesh refinement, and coarsening. The design of efficient, robust, scalable solvers for linear systems arising from these kinds of discretizations is important to make them competitive with traditional methods. Non-overlapping domain decomposition methods (DDMs) provide one such family of pre-conditioners. In this talk we first give a heuristic answer to “Why polytopal FEMs?” We then outline several routes from traditional conforming FEMs to polytopal formulations. Next, we present recent tools—rooted in discrete functional analysis and mimicing the continuous setting—that yield condition-number estimates for non-overlapping DDM pre-conditioners arising from these discretizations. Finally, we show robustness and scalability of our pre-conditioner for up to several hundreds of processors performed using the open-source finite element library Gridap.jl.