Calendar

1:00 pm – 4:00 pm Lockett 232

Qualifier Exam in Topology

Monday, August 18, 2025

Posted January 19, 2025

1:00 pm – 4:00 pm Lockett 232

Qualifier Exam in Analysis

Wednesday, August 20, 2025

Posted January 19, 2025

1:00 pm – 4:00 pm Lockett 232

Qualifier Exam in Algebra

Friday, August 22, 2025

Posted January 19, 2025

Algebra and Number Theory Seminar Questions or comments?

1:00 pm – 4:00 pm Lockett 232

Qualifier Exam in Applied Math

Tuesday, August 26, 2025

Posted August 2, 2025
Last modified August 20, 2025

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

Joseph DiCapua, Louisiana State University
Lubin–Tate Formal Group Laws

In this expository talk, we introduce Lubin–Tate formal group laws. The torsion points of a Lubin–Tate formal group law are defined, and we discuss the endomorphism ring of such a formal group law. Certain torsion points are used to define Coleman's trace operator, an important tool in Iwasawa theory. We briefly mention how Lubin–Tate formal group laws are used in one construction of the maximal abelian extension of a finite extension of the $p$-adics.

Posted August 18, 2025

Discussion and Training in Combinatorics

3:30 pm Lockett Hall 233

Gyaneshwar Agrahari, LSU
Emmanuel Astante, Louisiana State University
Organizational Meeting of DTC Seminar

The first meeting of the Discussion and Combinatorics Seminar will be held on this day and time. In this meeting, we will introduce everyone and give the details of how the seminar will be run.

Posted August 16, 2025
Last modified August 21, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 232

Moisés Gómez-Solís, Louisiana State University
Laura Kurtz, Louisiana State University
Organizational Meeting

Wednesday, August 27, 2025

Posted July 21, 2025
Last modified August 17, 2025

1:30 pm Lockett Hall 233

Krishnendu Kar, Louisiana State University
Matthew Lemoine, Louisiana State University
Organizational Meeting

Please join us for the Informal Geometry and Topology Seminar. This seminar is an opportunity for grad students to get experience talking in front of an audience and practicing giving talks. In this first meeting, we will decide which topic/book/paper that we will follow for our discussion during the Fall semester. We will also have opportunities for individual talks. For more information, feel free to contact Matthew Lemoine or Krishnendu Kar.

Friday, August 29, 2025

Posted August 23, 2025
Last modified August 26, 2025

Control and Optimization Seminar Questions or comments?

10:30 am – 11:20 am Zoom (click here to join)

Alex Olshevsky, Boston University AFOSR YIP and NSF CAREER Awardee
The Connection Between Reinforcement Learning and Gradient Descent

Temporal difference (TD) learning with linear function approximation is one of the earliest methods in reinforcement learning and the basis of many modern methods. We revisit the analysis of TD learning through a new lens and show that TD may be viewed as a modification of gradient descent. This leads not only to a better explanation of what TD does but also improved convergence times guarantees. We discuss applications of this result to more involved reinforcement learning methods, such as actor-critic and neural-network based methods.

Posted August 25, 2025

Algebra and Number Theory Seminar Questions or comments?

2:30 pm – 3:30 pm Lcokett 233 or click to to attend on Zoom

Yiwei Ge, Louisiana State University
Unavoidable cc-minors in large 2-connected graphs

A cycle-contraction minor (or cc-minor) of a graph is obtained by iteratively contracting cycles. These minors interact in interesting ways with other graph relations, such as induced subgraphs and minors. In this talk, we will introduce the notion of cc-minors and explain the motivation for studying them from both graphic and matroidal perspectives. A 2023 paper of Allred, Ding, and Oporowski identified a set of unavoidable induced subgraphs in sufficiently large 2-connected graphs. We present a dual version of this theorem by focusing on unavoidable cc-minors of large 2-connected graphs. This talk is based on joint work with James Oxley.

Tuesday, September 2, 2025

Posted August 2, 2025
Last modified August 20, 2025

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

Joseph DiCapua, Louisiana State University
Parametrization of Formal Norm Compatible Sequences

We give a classification of power series parametrizing Lubin–Tate trace compatible sequences. This proof answers a question posed in the literature by Berger and Fourquaux. Lubin–Tate trace compatible sequences are a generalization of norm compatible sequences, which arise in Iwasawa theory and local class field theory. The result we prove generalizes the interpolation theorem proved by Coleman in the classical norm compatible sequence case. We also, jointly with Victor Kolyvagin, give a method for finding such series explicitly in certain special cases.

Posted September 1, 2025

Discussion and Training in Combinatorics

3:30 pm Lockett Hall 233

Week 2: Review of Topology

This week, our speaker, Sayani Mukherjee, will kick off our discussion on the applications of the Borsuk-Ulam Theorem. Ms. Mukherjee is a second-year PhD student in our department. She will review the first two sections of the textbook: "Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry"

Posted August 30, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 232

Hari Narayanan, Louisiana State University
Introduction to Spectral Theory and Schrödinger Operators

This talk concentrates on the spectral theory of Schrödinger operators with a view toward modern research. The huge literature in this field was spawned by non-relativistic quan- tum mechanics and has led to rich advances in pure spectral theory and applications. After a brief review of finite dimensions, the talk first develops abstract spectral theory of self-adjoint operators in Hilbert space with some emphasis on classical ideas of harmonic analysis, namely spectral resolutions induced by symmetry groups. Then we introduce continuous and discrete Schrödinger operators with electric and magnetic potentials and some of the standard theorems. We treat periodic, quasi-periodic, and ergodic operators, in decreasing detail. The treatment of periodic operators will emphasize the connections to commutative algebra centering around the Fermi and Bloch algebraic or analytic varieties. This is followed by analysis in physical, momen- tum (dual), configuration, and reciprocal space; and a brief look at ergodic and quasi-periodic operators.

Wednesday, September 3, 2025

Posted August 27, 2025

1:30 pm Lockett Hall 233

Rachel Meyers, Louisiana State University
TBD

TBD

Posted August 28, 2025

Control and Optimization Seminar Questions or comments?

5:00 pm Kessler 3rd Floor Lounge (Lockett Hall)

ASA First Fall Meeting

Come meet other interested Actuaries as the Actuarial Student Association has it's first Fall semester meeting. Pizza will be served!

Friday, September 5, 2025

Posted August 11, 2025
Last modified September 2, 2025

10:30 am – 11:20 am Zoom (click here to join)

Gabriela Gonzalez, Louisiana State University Member, US National Academy of Sciences
Feedback Loops in the LIGO Gravitational Wave Detectors

The Laser Interferometric Gravitational-wave Observatory (LIGO) operates two detectors in Livingston, LA and Hanford, WA to detect perturbations of space time produced by astrophysical events like the collision of black holes. The detectors have an amazing sensitivity, using laser beams traveling in vacuum detecting differences in two 4km long arms smaller than a thousandth of a proton diameter in a frequency band between 10 Hz and 5 kHz. To achieve this sensitivity, a large number of feedback control systems are used to damp suspended mirrors, to reduce the effect of ground motion, to keep optical cavities resonant, and much more. I will briefly describe these systems and the challenges for current and future detectors.

Posted September 3, 2025

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

Dylan King, California Institute of Technology
Lagrangians, Palettes, and Uniform Turan Densities

The Turan density of a forbidden hypergraph F is the largest edge density a large hypergraph H can have without containing any copy of F, and determining this number for various F is a notoriously difficult problem. One on-ramp to this question (from Erdos and Sos) is to furthermore require that the hyperedges of H are distributed nearly uniformly across the vertices, giving the uniform Turan density of F. All known examples of such uniformly dense H avoiding some F follow the so-called “palette” construction of Rodl. In this talk we will introduce each of these notions before discussing our main result, that any palette can be obtained as an extremal construction for some finite family of forbidden subgraph F, which will require the tools of hypergraph regularity and Lagrangians. Based on joint work with Simon Piga, Marcelo Sales, and Bjarne Schuelke.

Wednesday, September 10, 2025

Posted September 1, 2025
Last modified September 10, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 am Lockett 233

Kyle Binder, Louisiana State University
Cohomology of Toric Varieties Associated with Matroids

The Chow ring of a matroid is an important tool in studying the combinatorics of matroids through geometric techniques, and it played a central role in the Adiprasito, Huh, and Katz proof of the Rota—Heron—Welsh conjecture for matroids. This ring is defined to be the Chow ring of the smooth, quasi-projective toric variety associated with the Bergman fan of the matroid, and, remarkably, it enjoys many of the Hodge-theoretic properties of Chow rings of smooth, projective varieties. In this talk, we will extend the Chow ring of these toric varieties to the larger (singular) cohomology ring, compute the top-graded piece of cohomology in terms of the associated matroid, and describe how to compute all of the Betti numbers in the case of uniform matroids.

Posted August 27, 2025
Last modified September 10, 2025

1:30 pm Lockett Hall 233

Sayani Mukherjee, Louisiana State University
Khovanov Homology

Continuing our discussion of Khovanov Homology, follow Melissa Zhang's notes.

Friday, September 12, 2025

Posted September 8, 2025

Algebra and Number Theory Seminar Questions or comments?

8:30 am – 9:30 am Zoom (click here to join)

Tony Huynh, Institute for Basic Science (IBS)
Rainbow triangles and the Erdős-Hajnal problem in projective geometries

We formulate a geometric version of the Erdős-Hajnal conjecture that applies to finite projective geometries rather than graphs. In fact, we give a natural extension of the 'multicoloured' version of the Erdős-Hajnal conjecture. Roughly, our conjecture states that every colouring of the points of a finite projective geometry of dimension $n$ not containing a fixed colouring of a fixed projective geometry $H$ must contain a subspace of dimension polynomial in $n$ avoiding some colour. When $H$ is a 'triangle', there are three different colourings, all of which we resolve. We handle the case that $H$ is a 'rainbow' triangle by proving that rainbow-triangle-free colourings of projective geometries are exactly those that admit a certain decomposition into two-coloured pieces. This is closely analogous to a theorem of Gallai on rainbow-triangle-free coloured complete graphs. The two non-rainbow colourings of $H$ are handled via a recent breakthrough result in additive combinatorics due to Kelley and Meka. This is joint work with Carolyn Chun, James Dylan Douthitt, Wayne Ge, Matthew E. Kroeker, and Peter Nelson.

Tuesday, September 16, 2025

Posted August 2, 2025
Last modified September 10, 2025

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

Hang Xue, The University of Arizona
Fourier–Jacobi periods on unitary groups

We explain what Fourier–Jacobi periods on unitary groups are and prove the global Gan–Gross–Prasad conjecture about them. We also give an application to the Tate conjecture of product of unitary Shimura varieties.

Posted September 10, 2025

3:30 pm – 4:30 pm Lockett 136

Shalini Shalini, LSU
Gowri Priya Sunkara, LSU
The Elvis Problem with Convex Bifunctions/The Minimal Time Function Under More General Assumptions

The Elvis problem models a time optimal control problem across two regions having a common interface Sigma, each with a constant convex velocity set. We generalized this framework by introducing convex bifunctions of the form F_i(r, v) which are convex, lower semicontinuous, and proper. The minimization problem is min [ F_0(r_0, y - x_0) + F_1(r_1, x_1 - y) ], over r_0 > 0, r_1 > 0 and y in Sigma. The bifunctions F_i are jointly convex in (r, v) and convex analysis is used to derive optimality conditions. Under general assumptions on the target set S and the system dynamics, we show that the minimal time function is a proximal solution to a pair of Hamilton–Jacobi inequalities. Uniqueness is established via two distinct types of boundary conditions. We also introduce a new propagation result, which characterizes proximal sub gradients of the minimal time function in terms of normal cones and a boundary inequality condition. Furthermore, we provide necessary and sufficient conditions for the Lipschitz continuity of the minimal time function near S. In particular, a Petrov-type modulus condition is shown to guarantee such continuity. Our results extend earlier results to a broader class of time dynamics, even within non-Euclidean settings.

Posted September 15, 2025

5:30 pm Kessler Lounge (3rd Floord Lockett Hall)

ASA Meeting

Brief Presentation about the basics of becoming a credentialed actuary. Additional Tips about studying for exams/resumes Pizza will be served!

Wednesday, September 17, 2025

Posted September 1, 2025
Last modified September 15, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 am Lockett 233

Kevin Schreve, Louisiana State University
L^2-homology of right-angled Coxeter groups

A flag triangulation of an (n-1)-dimensional sphere determines a right-angled Coxeter group and a closed n-manifold which is a K(G,1) for the commutator subgroup. The Singer Conjecture predicts that the L^2-homology of the universal cover is only nonzero in dimension n/2. We will show the Singer conjecture holds if 1) L is the barycentric subdivision of the boundary of a simplex, 2) L is the barycentric subdivision of a triangulation of an odd-dimensional sphere Based on joint work with Grigori Avramidi and Boris Okun.

Posted August 27, 2025
Last modified September 14, 2025

1:30 pm Lockett Hall 233

Anurakti Gupta, Louisiana State University
Continuing our Discussion of Khovanov Homology

We are continuing our discussion of Khovanov Homology following Melissa Zhang's notes. (https://arxiv.org/abs/2501.03115)

Friday, September 19, 2025

Posted September 15, 2025

Algebra and Number Theory Seminar Questions or comments?

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

Rose McCarty, Georgia Institute of Technology
Neighborhood complexity and matroids

Abstract: We will discuss neighborhood complexity in graphs and some of its many applications. We will touch on applications to graph coloring, discrete geometry, and first-order logic. However, our main focus will be using neighborhood complexity to find the "unavoidable" GF(q)-representable cosimple matroids of large girth. This talk is based on joint work with James Davies, Meike Hatzel, Kolja Knauer, and Torsten Ueckerdt.

Tuesday, September 23, 2025

Posted August 2, 2025
Last modified September 10, 2025

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

Andreas Mono, Vanderbilt University
A modular framework for generalized Hurwitz class numbers

We discover a neat linear relation between the mock modular generating functions of the level $1$ and level $N$ Hurwitz class numbers. This relation gives rise to a holomorphic modular form of weight $\frac{3}{2}$ and level $4N$ for $N > 1$ odd and square-free. This follows from a more general inspection of the weight $\frac{1}{2}$ Maass–Eisenstein series of level $4N$v at its spectral point $s = \frac{3}{4}$. This idea goes back to Duke, Imamoğlu and Tóth in level $4$ and relies on the theory of so-called sesquiharmonic Maass forms. Furthermore, we connect the aforementioned results to a regularized Siegel theta lift as well as a regularized Kudla–Millson theta lift for odd prime levels, which builds on earlier work by Bruinier, Funke and Imamoğlu. This is joint work with Olivia Beckwith. We conclude by presenting the situation in higher weights as well, which is sole work.

Posted September 18, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 136

Matthew McCoy, Louisiana State University
Introduction to Ergodic Theory, Chebyshev Polynomial Expansions, and Schur Complements

This talk will serve as an introductory talk to Ken Beard's talk on 9/30: Momentum Space Algorithm for Electronic Structure of Double-Incommensurate Trilayer Graphene. We will introduce relevant concepts in spectral theory.

Event contact: Laura Kurtz

Wednesday, September 24, 2025

Posted August 27, 2025
Last modified September 21, 2025

1:30 pm Lockett Hall 233

Gargi Patil, Louisiana State University
Continuing our discussion of Khovanov Homology

We are continuing our discussion of Khovanov Homology following Melissa Zhang's notes. (https://arxiv.org/pdf/2501.03115)

Posted September 1, 2025
Last modified September 23, 2025

3:30 pm Lockett 233

Robin Koytcheff, University of Louisiana, Lafayette
Milnor invariants and thickness of spherical links

Various authors have studied the question of how long a rope of a given thickness is needed to tie a given isotopy class of knot or link. In joint work with Rafal Komendarczyk and Fedya Manin, we generalize this work to spherical links in arbitrary dimensions. In more detail, we study their Milnor invariants in terms of Massey products and prove asymptotically optimal upper bounds on Milnor invariants in terms of embedding thickness. Interestingly, there is a dichotomy between polynomial and exponential bounds, depending on the dimensions of the spheres. We apply our results to answer a question of Freedman and Krushkal about exponentially thin 2-complexes in 4-space.

Friday, September 26, 2025

Posted September 24, 2025

Algebra and Number Theory Seminar Questions or comments?

2:30 pm – 3:30 pm Lockett Hall 233 click here to attend on Zoom

Caleb McFarland, Georgia Institute of Technology
Coloring Graphs With No Totally Odd Clique Immersion

We prove that graphs that do not contain a totally odd immersion of $K_t$ are $\mathcal{O}(t)$-colorable. In particular, we show that any graph with no totally odd immersion of $K_t$ is the union of a bipartite graph and a graph which forbids an immersion of $K_{\mathcal{O}(t)}$. Our results are algorithmic, and we give a fixed-parameter tractable algorithm (in $t$) to find such a decomposition.

Tuesday, September 30, 2025

Posted September 23, 2025

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

Liang Chang, Nankai University
Modular data of non-semisimple modular categories

Modular tensor categories are semisimple tensor categories with nondegenerated braiding, which have many applications in low dimensional topology and topological physics. Recently, the notion of modularity is extended to non-semisimple tensor category. In this talk, we will talk about the work to extend the well-understood theory of semisimple modular categories, such as the SL(2, Z)-representation and rank finiteness, to the non-semisimple case by using representations of factorizable ribbon Hopf algebras.

Posted September 18, 2025

3:30 pm – 4:30 pm Lockett 136

Ken Beard, LSU
Momentum Space Algorithm for Electronic Structure of Double-Incommensurate Trilayer Graphene

Although recent experimental results seem to indicate the existence of flat bands for twisted trilayer graphene (TTG), at present there is no convergent algorithm for approximating the density of states (or other desirable observables). We attempt to address this by using kernel polynomial approximation with an ab initio momentum-space tight-binding model. The unique challenge in the case of TTG is the lack of a periodic moir\'{e} supercell. This is addressed by modifying the truncation to account for more complex Umklapp scattering.

Event contact: Laura Kurtz

Posted September 26, 2025

Informal Geometry and Topology Seminar Questions or comments?

5:30 pm Kessler Lounge (3rd Floor Lockett Hall)

ASA Meeting

Ryan Witko of Caresource joins us for a presentation. Pizza will be served.

Wednesday, October 1, 2025

Posted August 27, 2025
Last modified September 29, 2025

1:30 pm Lockett Hall 233

Saumya Jain, Louisiana State University
Manifold models for hyperbolic graph braid groups

Given a finite graph X, the associated graph braid group B_n(X) is the fundamental group of the unordered n-point configuration space of X. For the 3-point case, Genevois classified which graph braid groups are Gromov hyperbolic and asked the question: When do these groups arise as 3-manifold groups? In this talk, we give a partial answer for B_3(X) when X is a generalized Theta graph.

Posted September 29, 2025

Informal Geometry and Topology Seminar Questions or comments?

1:55 pm Lockett Hall 233

Yongho Lee, Louisiana State University
A representation of the holonomy Lie algebra of a matroid

Let $\mathcal{M}$ be a simple matroid for which the cardinality of each rank-two flat is at most 3. For any such matroid $\mathcal{M}$, we produce a representation of the holonomy Lie algebra of $\mathcal{M}$ using the combinatorial Laplacian.

Posted September 29, 2025

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 233

Scott Baldridge, Louisiana State University
What does the Four Color Theorem have to do with the sound a drum makes?

Mark Kac famously asked in 1966, “Can one hear the shape of a drum?” While the answer to this question is now known to not be true in general, it popularized an investigation into eigenvalues of Laplacians that continues to this day. One formulation of it is as follows: two closed Riemannian manifolds are said to {\em isospectral} if the eigenvalues of their Laplace-Beltrami operator, counted with multiplicities, coincide. Modern questions ask to what extent having the same eigenvalues determine the geometry of the two manifolds. In this talk, we introduce a Laplace-de Rham operator on a cochain complex derived from a cellularly embedded graph into a surface. (When the surface is a $2$-sphere, this is simply a plane graph.) In degree zero, the dimension of the subspace of the harmonic solutions to this operator counts the number of $4$-face colorings of the graph. Therefore, there are zero eigenvalue solutions for a plane graph if and only if the graph does not have a bridge (the Four Color Theorem). The nonzero eigenvalues of this operator are also quite interesting, which leads us to pose the following isospectral conjecture by the end of the talk, "Can one hear the shape of the CW structure of a surface?”

Friday, October 3, 2025

Posted August 14, 2025
Last modified September 26, 2025

10:30 am – 11:20 am Zoom (click here to join)

Xin Zhang, New York University
Exciting Games and Monge-Ampère Equations

We consider a competition between d+1 players, and aim to identify the “most exciting game” of this kind. This is translated, mathematically, into a stochastic optimization problem over martingales that live on the d-dimensional sub-probability simplex and terminate on the vertices of the simplex, with a cost function related to a scaling limit of Shannon entropies. We uncover a surprising connection between this problem and the seemingly unrelated field of Monge-Ampère equations, and identify the optimal martingale via a detailed analysis of boundary asymptotics of a Monge-Ampère equation.

Posted September 19, 2025
Last modified September 25, 2025

1:30 pm Coates Hall 168

Jason Cantarella, University of Georgia
How and why to teach a computer to untangle knots

Unknot recognition is a classical 'hard problem' in computational topology. At the moment, the leading candidate for a full solution is Lackenby's quasi-polynomial algorithm which has theoretical complexity 2^(O(log n)^3). So far, this hasn't led to a really efficient practical method for knot identification. A different idea for knot simplification (knot energies) goes back to Freedman (and before). In this method, we try to put some energy function on a test curve such as a repulsive charge and then follow the evolution of the curve, hoping that it will lead to a recognizable configuration. This has proved to be computationally intractable for numerical reasons. In this talk, we describe a hybrid approach which alternates between using powerful diagrammatic simplifications and a new semigeometric energy defined on diagrams. We'll give results on benchmark sets of hard unknots and then discuss how this method allowed us to give strong new evidence supporting the 'knot entropy conjecture' for random knots in self-avoiding walks. This has consequences for knots in polymer chemistry and (perhaps) for knots in DNA and other biopolymers. The talk will include various animations and demonstrations, a couple of puzzles, and some open questions. It should be fairly accessible to undergraduates.

Posted September 30, 2025

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

Joseph Bonin, George Washington University
Characterizations of certain matroids by maximizing valuative invariants

Luis Ferroni and Alex Fink recently introduced a polytope of all unlabeled matroids of rank r on n elements, and they showed that the vertices of this polytope come from matroids that can be characterized by maximizing a sequence of valuative invariants. In this talk, we will first sketch the background that is needed to understand their polytope and valuative invariants. We will then provide the needed characterizations of many of the matroids that Ferroni and Fink conjectured to yield vertices, we will give additional examples of such matroids, and we will mention some open problems.

Posted March 28, 2025
Last modified October 1, 2025

3:30 pm Lockett 232

Wenxiong Chen , Yeshiva University
Qualitative properties of solutions to fractional elliptic and parabolic equations

In this talk, I will introduce the fractional Laplacian and other nonlocal elliptic and parabolic operators and list some recent developments in the study of qualitative properties including symmetry, asymptotic symmetry, and monotonicity of solutions for nonlinear fractional elliptic and parabolic equations such as $$ (-\triangle)^s u=f(x,u(x))$$ and $$ \frac{\partial u}{\partial t}+( -\triangle)^s u=f(x,u(x, t)) $$ I will also introduce other typical fractional parabolic operators, such as the dual fractional heat operator with Marchaud time derivative $∂^\alpha t+(-\triangle)^s$ and the master operator $(\partial_t-\triangle)^s$. The extent of their non-locality will be illustrated by simple examples with pictures. I will also mention some of our recent results on interior regularity estimates for nonnegative solutions to fractional Laplace equations and fully fractional parabolic equations.

Event contact: Jiuyi Zhu

Monday, October 6, 2025

Posted March 16, 2025
Last modified October 5, 2025

2:30 pm Lockett 233

Nicola Garofalo, Arizona State University Charles Wexler Professor in Mathematics,
Strichartz estimates for degenerate dispersive equations

I will discuss some new Ginibre-Velo estimates for a class of Schrodinger equations with a possibly strongly degenerate Hamiltonian. The talk will have a self-contained character and I will focus on some interesting examples

Event contact: Phuc/Zhu

Posted August 3, 2025
Last modified October 5, 2025

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett 233

Donatella Danielli, Arizona State University School Director and Foundation Professor
Obstacle Problems for Fractional Powers of the Laplacian

In this talk we will discuss a two-penalty boundary obstacle problem for a singular and degenerate elliptic operator naturally arising in the extension procedure for the fractional Laplacian $(-\Delta)^s$ when s between 1 and 2. Our goals are to establish regularity properties of the solution and the structure of the free boundary. To this end, we combine classical techniques from PDEs and the calculus of variations with more modern methods, such as the localization of the operator and monotonicity formulas. In particular, we will emphasize the striking differences with the cases s between 0 and 1 and s=$3/2$. This is joint work with A. Haj Ali (University of Michigan) and G. Gravina (Loyola University-Chicago).

Event contact: Phuc/Zhu

Posted October 3, 2025

LSU SIAM Student Chapter

5:00 pm – 6:00 pm Keisler Lounge, Lockett Hall

Grad School Panel Night

LSU SIAM Student Chapter and the Math Club will be hosting a joint meeting for a Grad School Panel Night. The goal of the event is to inform undergraduate students about the graduate school application process, focusing on topics such as application materials, deadlines, CVs, selecting a suitable graduate school, and transitioning to grad life. If you are a graduate student or a faculty member and would like to share your experience with the undergraduates, feel free to swing by. Food will be provided for in-person attendees.

Event contact: Segolene Ntipouna and Maganizo Kapita

Tuesday, October 7, 2025

Posted September 30, 2025

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

Jianqi Liu, University of Pennsylvania
Modular invariance of intertwining operators from the factorization theorem of conformal blocks

The notion of conformal blocks on stable curves defined by modules over a vertex operator algebra (VOA) generalizes the WZNW-conformal blocks defined by modules over affine Lie algebras. Recent advances in the theory of VOA-conformal blocks have shed new light on the representation theory of VOAs. In particular, the factorization theorem and the vector bundle property of the sheaves of VOA-conformal blocks lead to the modular invariance of intertwining operators for strongly rational VOAs. In this talk, I will explain the proof of this theorem and present a short proof of the associativity of fusion rings for VOAs. This talk is based on joint work with Xu Gao.

Posted October 7, 2025

Faculty Meeting Questions or comments?

3:00 pm Zoom

Meeting of the Tenured Faculty

Posted October 5, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 136

Bart Rozenweig, Ohio State University
Borel Summability in Quantum Theory

Borel summation is a canonical summation technique which associates to a divergent power series an analytic function, for which the power series is its asymptotic expansion. This talk gives an overview of asymptotic expansions and the fundamental results on Borel summability, before surveying two major applications of the theory: first, in building actual solutions out of divergent formal power series solutions of ODEs and PDEs; and second, in making sense of divergent Rayleigh-Schrödinger perturbation expansions in quantum mechanics. Along the way, we will touch upon some key aspects of “resurgence theory”, a paradigm for the application of Borel summation ideas in quantum field theory.

Wednesday, October 8, 2025

Posted August 27, 2025
Last modified October 4, 2025

1:30 pm Lockett Hall 233

Krishnendu Kar, Louisiana State University
Khovanov Homology

Continuing our discussion of Khovanov Homology following Melissa Zhang's notes.

Posted October 7, 2025

Faculty Meeting Questions or comments?

1:30 pm Zoom

Meeting of the Tenured Faculty

Posted October 6, 2025

3:30 pm Lockett 233

Scott Baldridge, Louisiana State University
How to Build a Toy 2+1 ``Theory of Everything’’ model of the universe in 137 Easy Steps

Can a simple 2D combinatorial model already show us how to fuse matter and geometry into one quantum framework? String Theory (with its background-choice and vacuum-multiplicity issues) and Loop Quantum Gravity (with its dynamical ambiguities) both leave gaps. To keep the talk simple, I stay on a closed 2D surface and use metric triangulations to build a refinement-invariant Penrose polynomial (invariant under 1-3 Pachner refinements) that, under resampling, converges to a smooth metric. This polynomial is then an invariant of the triangulation-refinement class of a Riemannian manifold. I next tie the Penrose polynomial to the Regge action to produce a quantum gravity action whose equations of motion match the Einstein equations of general relativity (in 2D), and I use 2-2 Pachner flips as a ``discrete time step’’ in the toy model to illustrate dynamics. The talk focuses on explicit, easy-to-follow graph constructions and computations suitable for graduate students (and advanced undergraduates). If time, I conclude by outlining how the same blueprint extends to 3D, actual spacetime, where the model becomes genuinely dynamical. Note: The 137 steps is obviously a joke! It’s more like 35 steps, but I’ll only show you a few of them to give you the idea of how it works. Also: This talk is NOT a continuation of last week’s talk. However, the full theory does use aspects of it for those who attended.

Thursday, October 9, 2025

Posted October 2, 2025

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 232

Wilhelm Schlag, Yale University
On uniqueness of excited states and related questions

This talk will present the long-standing problem of excited states uniqueness for the nonlinear Schroedinger equation. We will describe the history of the problem, it's relevance to long-term dynamics of nonlinear wave equations, related spectral problems, and progress on the uniqueness question via rigorous numerics. The recent breakthrough by Moxun Tang, who found an analytical proof, will be discussed.

Friday, October 10, 2025

Posted August 1, 2025
Last modified October 3, 2025

10:30 am – 11:20 am Zoom (click here to join)

Felix Schwenninger, University of Twente, The Netherlands
Infinite-Dimensional Input-to-State Stability (ISS) -- Peculiarities of Sup-Norms

E. Sontag’s input-to-state stability (ISS), dating back to the late 80ies, is a cornerstone of modern mathematical control theory. While originally studied for finite-dimensional systems, the theory about infinite-dimensional systems, and in particular models involving partial differential equations, has been developed in the past 15 years. Somewhat surprisingly, the linear case, which is trivial in finite-dimensions, even offered challenges with respect to the mutual relations of several variants of ISS. In this talk we will focus in particular on “integral ISS” for linear and bilinear systems and discuss established results as well as more recent findings. The underlying reason for these subtleties is primarily due to the nontrivial interplay of supremum-norms, which naturally arise in ISS), and the (Banach space) geometry of the state spaces.

Posted October 6, 2025

Algebra and Number Theory Seminar Questions or comments?

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

Lina Li, University of Mississippi
Lipschitz functions on weak expanders

Given a connected finite graph $G$, an integer-valued function $f$ on $V(G)$ is called $M$-Lipschitz if the value of $f$ changes by at most $M$ along the edges of $G$. In 2013, Peled, Samotij, and Yehudayoff showed that random $M$-Lipschitz functions on graphs with sufficiently good expansion typically exhibit small fluctuations, giving sharp bounds on the typical range of such functions, assuming $M$ is not too large. We prove that the same conclusion holds under a relaxed expansion condition and for larger $M$, (partially) answering questions of Peled et al. Our approach combines Sapozhenko’s graph container method with entropy techniques from information theory. This is joint work with Krueger and Park.

Tuesday, October 14, 2025

Posted October 3, 2025
Last modified October 8, 2025

LSU SIAM Student Chapter

12:00 pm – 1:30 pm Keisler Lounge, Lockett Hall

A Conversation with SIAM President

The SIAM Student Chapter and AWM Student Chapter are excited to host a Special Q and A session with the President of SIAM. This event provides students with an opportunity to directly engage with the President, ask questions, and gain insights into the world of Applied Mathematics and Computational Science. Refreshments will be provided.

Event contact: Gowri Priya Sunkara and Laura Kurtz

Posted August 2, 2025
Last modified October 8, 2025

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

Kenz Kallal, Princeton University
Algebraic theory of indefinite theta functions

Jacobi's theta function $\Theta(q) := 1 + 2q + 2q^4 + 2q^9 + \cdots $, and more generally the theta functions associated to positive-definite quadratic forms, have the property that they are modular forms of half-integral weight. The usual proof of this fact is completely analytic in nature, using the Poisson summation formula. However, $\Theta$ was originally invented by Fourier (Théorie analytique de la chaleur, 1822) for the purpose of studying the diffusion of heat on a uniform circle-shaped material: it is the fundamental solution to the heat equation on a circle. By algebraically characterizing the heat equation as a specific flat connection on a certain bundle on a modular curve, we produce a completely algebraic technique for proving modularity of theta functions. More specifically, we produce a refinement of the algebraic theory of theta functions due to Moret-Bailly, Faltings–Chai, and Candelori. As a consequence of the algebraic nature of our theory and the fact that it applies to indefinite quadratic forms / non-ample line bundles (which the prior algebraic theory does not), we also generalize the Kudla–Millson analytic theory of theta functions for indefinite quadratic forms to the case of torsion coefficients. This is joint work in progress with Akshay Venkatesh.

Posted October 10, 2025

3:30 pm – 4:30 pm Lockett 136

Long Teng, LSU
Nodal Sets of Harmonic Functions

In this talk, we study the size of nodal sets of harmonic functions. We introduce the frequency function N(r), which quantifies the growth rate of a harmonic function and plays a crucial role in understanding its zero set. I will first define this frequency function and show its monotonicity property. Then, using this tool, we establish that the (n−1)-dimensional Hausdorff measure of the nodal set is bounded above by C(n)N, where C(n) depends only on the dimension. This result highlights how quantitative unique continuation connects analytic growth properties of harmonic functions to the geometric complexity of their nodal sets.

Event contact: Laura Kurtz

Wednesday, October 15, 2025

Posted September 26, 2025
Last modified October 13, 2025

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Virtual

Naageswaran Manikandan, Max Planck Institute
Obstructions to positivity notions using Khovanov-type theories.

In this talk, we discuss how Khovanov homology theories can be employed to construct obstructions to various notions of positivity in knot theory. We begin by discussing a result showing that, for a positive link, the first Khovanov homology is supported in a single quantum grading, is free abelian, and its rank reflects whether the link is fibered. We extend these results to (p,q)-cables of positive knots whenever $q \geq p$. We then turn to ongoing work investigating how odd-Khovanov homology and Khovanov-Rozansky homology can be used to construct obstructions to these positivity notions.

Posted August 27, 2025
Last modified October 15, 2025

3:30 pm Lockett Hall 233

Adithyan Pandikkadan, Louisiana State University
Khovanov Homology

Continuing our discussion of Khovanov Homology, follow Melissa Zhang's notes.

Posted September 10, 2025
Last modified October 14, 2025

Harmonic Analysis Seminar

3:30 pm – 4:30 pm Lockett 138

Bruno Poggi, University of Pittsburgh
The Dirichlet problem as the boundary of the Poisson problem

We review certain classical quantitative estimates (known as non-tangential maximal function estimates) for the solutions to the Dirichlet boundary value problem for the Laplace equation in a smooth domain in Euclidean space, when the boundary data lies in an $L^p$ space, $p>1$. A natural question that arises is: what might an analogous estimate for the inhomogeneous Poisson problem look like? We will answer this question precisely, and in so doing, we will unravel deep and new connections between the solvability of the (homogeneous) Dirichlet problem for the Laplace equation with data in $L^p$ and the solvability of the (inhomogeneous) Poisson problem for the Laplace equation with data in certain Carleson spaces. We employ this theory to solve a 20-year-old problem in the area, to give new characterizations and a new local T1-type theorem for the solvability of the Dirichlet problem under consideration. Some of the new results are the product of joint works with Mihalis Mourgoglou and Xavier Tolsa.

Event contact: Phuc C. Nguyen

Monday, October 20, 2025

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

Algebra and Number Theory 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

Tuesday, October 21, 2025

Posted September 2, 2025

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

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

Wednesday, October 22, 2025

Posted October 6, 2025
Last modified October 8, 2025

Informal Geometry and Topology Seminar Questions or comments?

11:30 am Lockett 241

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

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

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.

Thursday, October 23, 2025

Posted October 6, 2025
Last modified October 13, 2025

Control and Optimization Seminar 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.

Friday, October 24, 2025

Posted September 5, 2025

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

Algebra and Number Theory 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.

Tuesday, October 28, 2025

Posted September 9, 2025

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 Geometry and Topology 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.

Wednesday, October 29, 2025

Posted August 27, 2025
Last modified October 27, 2025

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

Control and Optimization Seminar Questions or comments?

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.

Friday, October 31, 2025

Posted October 7, 2025
Last modified October 9, 2025

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

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

Algebra and Number Theory Seminar 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.

Saturday, November 1, 2025

Posted October 22, 2025
Last modified October 23, 2025

Conference

until Sunday, November 2, 2025 Lockett Hall 232

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

Tuesday, November 4, 2025

Posted October 26, 2025
Last modified November 1, 2025

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 Geometry and Topology 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

Wednesday, November 5, 2025

Posted August 27, 2025
Last modified October 27, 2025

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

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.

Thursday, November 6, 2025

Posted August 19, 2025
Last modified November 2, 2025

Control and Optimization Seminar 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.

Friday, November 7, 2025

Posted July 26, 2025

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 November 4, 2025

Conference

10:30 am – 5:00 pm Lockett 233 and Zoom

Bayou Arithmetic Research Day (BARD 6)

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

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

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.

Monday, November 10, 2025

Posted August 21, 2025
Last modified October 24, 2025

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

Tuesday, November 11, 2025

Posted November 4, 2025

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

Informal Geometry and Topology Seminar Questions or comments?

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

Wednesday, November 12, 2025

Posted August 27, 2025
Last modified October 27, 2025

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

Control and Optimization Seminar Questions or comments?

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.

Friday, November 14, 2025

Posted August 1, 2025
Last modified November 3, 2025

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

12:30 pm Lockett 138

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

Mathematical Physics and Representation Theory Seminar

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)

Monday, November 17, 2025

Posted October 15, 2025
Last modified October 16, 2025

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 14, 2025

Computational Mathematics Seminar

4:00 pm

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.

Tuesday, November 18, 2025

Posted November 3, 2025
Last modified November 10, 2025

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.

Posted November 13, 2025

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.

Wednesday, November 19, 2025

Posted November 5, 2025

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Online

Advika Rajapakse, UCLA
TBA

Posted August 27, 2025
Last modified October 27, 2025

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 November 14, 2025

3:30 pm

Aaron Calderon, University of Chicago
Pants decompositions and dynamics on moduli spaces

Every closed hyperbolic surface X (or Riemann surface or smooth algebraic curve over C) can be described by gluing together pairs of pants (three-holed spheres). Each X can be glued out of pants in many different ways, and Mirzakhani showed that the count of these decompositions is closely related to a certain Hamiltonian flow on the moduli space of hyperbolic surfaces. In the field of Teichmüller dynamics, counting problems on flat surfaces can be related to a different dynamical system on a different moduli space, which, by work of Eskin--Mirzakhani--Mohammadi and Filip, is in turn controlled by special algebraic subvarieties. In this talk, I will survey some of these results and describe a bridge between the two worlds that can be used to transfer theorems between flat and hyperbolic geometry.

Thursday, November 20, 2025

Posted November 12, 2025
Last modified November 13, 2025

Control and Optimization Seminar Questions or comments?

3:30 pm

Benjamin Zhang, University of North Carolina at Chapel Hill
A mean-field games laboratory for generative artificial intelligence: from foundations to applications in scientific computing

We demonstrate the versatility of mean-field games (MFGs) as a mathematical framework for explaining, enhancing, and designing generative models. We establish connections between MFGs and major classes of flow- and diffusion-based generative models by deriving continuous-time normalizing flows and score-based models through different choices of particle dynamics and cost functions. We study the mathematical structure and properties of each generative model by examining their associated MFG optimality conditions, which consist of coupled forward-backward nonlinear partial differential equations (PDEs). We present this framework as an MFG laboratory, a platform for experimentation, invention, and analysis of generative models. Through this laboratory, we show how MFG structure informs new normalizing flows that robustly learn data distributions supported on low-dimensional manifolds. In particular, we show that Wasserstein proximal regularizations inform the well-posedness and robustness of generative flows for singular measures, enabling stable training with less data and without specialized architectures. We then apply these principled generative models to operator learning, where the goal is to learn solution operators of differential equations. We present a probabilistic framework that reveals certain classes of operator learning approaches, such as in-context operator networks (ICON), as implicitly performing Bayesian inference. ICON computes the mean of the posterior predictive distribution of solution operators conditioned on example condition-solution pairs. By extending ICON to a generative setting, we enable sampling from the posterior predictive distribution. This provides principled uncertainty quantification for predicted solutions, demonstrating how mathematical foundations translate to trustworthy applications in scientific computing.

Friday, November 21, 2025

Posted July 13, 2025
Last modified November 4, 2025

10:30 am – 11:20 am Zoom (click here to join)

Dimitra Panagou, University of Michigan AFOSR YIP, NASA Early Career Faculty, and NSF CAREER Awardee
Safety-Critical Control via Control Barrier Functions: Theory and Applications

This seminar will focus on control barrier functions, as a tool for encoding and enforcing safety specifications, as well as their recent extensions (e.g., robust, adaptive, and predictive) to handle additive perturbations, parametric uncertainty and dynamic environments, with applications to (multi)-robot/vehicle motion planning and coordination. Time permitting, we will also cover how time constraints can be encoded as fixed-time control Lyapunov functions, and the trade-offs between safety and timed convergence.

Posted November 12, 2025

3:30 pm

Colleen Robichaux, University of California, Los Angeles
Deciding Schubert positivity

We survey the study of structure constants in Schubert calculus and its connection to combinatorics and computational complexity.

Monday, November 24, 2025

Posted November 12, 2025
Last modified November 14, 2025

Computational Mathematics Seminar

4:00 pm

Keegan Kirk, George Mason University
Nonsmooth Variational Problems, Optimal Insulation, and Digital Twins

How should a fixed amount of insulating material be placed on a heat-conducting body to maximize thermal performance? A thin-shell model of the insulating layer yields, through rigorous asymptotic analysis, a convex but nonsmooth, nonlocal variational problem. To handle the resulting nonsmooth terms, we develop an equivalent Fenchel-dual formulation together with a semi-smooth Newton method built on the discrete duality inherited by Raviart–Thomas and Crouzeix–Raviart elements. We establish a priori and a posteriori error estimates and validate the theory through numerical experiments, including optimal home insulation and spacecraft heat shielding. Beyond its intrinsic mathematical interest, this problem serves as a building block for digital twins, virtual replicas of physical systems that incorporate sensor data and quantify uncertainty to inform decisions about their physical counterparts. One concrete example arises in the refurbishment of a spacecraft’s heat shield after atmospheric re-entry, where available data can be used to infer how much insulation remains on the surface. The model could then optimize where and how much new material to add, under uncertainty about the residual thickness and anticipated thermal loads. The outcome is a high-dimensional, nonsmooth variational problem representative of the optimal control tasks encountered in digital twin settings. The efficient numerical solution of these high-dimensional optimal control problems remains a formidable challenge for the widespread deployment of digital twins. We therefore highlight two complementary research directions aimed at reducing the computational burden: (i) structure aware preconditioning strategies for nonsmooth optimal control problems, including applications to neural network training, and (ii) adaptive tensor-decomposition techniques that enable efficient approximation of high-dimensional stochastic variational problems.

Tuesday, November 25, 2025

Posted November 3, 2025
Last modified November 9, 2025

3:30 pm – 4:30 pm Digital Media Center 1034

Monika Pandey, Louisiana State University
Adaptive proximal Barzilai–Borwein method for nonlinear optimization

In this presentation, I will discuss adaptive proximal algorithms that builds on the Barzilai–Borwein (BB) stepsize strategy to accelerate gradient-based methods for solving nonlinear composite optimization. For convex problems, we design adaptive rules that automatically adjust the stepsizes using local curvature information, removing the need for traditional line searches, and enhancing both robustness and computational efficiency. These ideas are further extended to nonconvex problems by developing a new nonmonotone line search strategy that preserves global convergence. I will present theoretical guarantees and numerical experiments showing that the proposed Adaptive Proximal Barzilai–Borwein (AdProxBB) method achieves faster convergence and stronger performance than existing proximal gradient algorithms.

Wednesday, November 26, 2025

Posted August 27, 2025
Last modified October 27, 2025

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett Hall 233

Huong Vo, Louisiana State University
TBD (Independent Talk)

TBD (Independent Talk)

Monday, December 1, 2025

Posted November 12, 2025

Mathematical Physics and Representation Theory Seminar

1:30 pm – 2:20 pm Lockett 233

Iain Moffatt, Royal Holloway, University of London
Hypermap minors

As mathematicians we conventionally model networks as graphs. In a graph, each edge has exactly two ends, each lying on a vertex. Hypergraphs generalise graphs by allowing an edge to have any number of ends. As the edges of a hypergraph can connect any number of vertices, not just two, they offer a way to model higher-order interactions in networks. Graphs often arise in applications with the additional structure of an embedding in a surface. This is also happens for hypergraphs: a hypermap is a hypergraph embedded in a closed surface. This talk is about hypermaps. I'll begin by reviewing the basics of hypermaps, including various ways to describe them. I'll go on to present a theory of hypermap minors based upon a smoothing operation in cubic graphs. I'll discuss various aspect of this theory such as commutativity, duality and Tutte's triality, polynomials, and relations with Farr's theory of alternating dimaps. This is joint work with Jo Ellis-Monaghan and Steven D. Noble.

Posted November 13, 2025
Last modified November 14, 2025

3:30 pm

Sky Cao, Massachusetts Institute of Technology
Yang-Mills, probability, and stochastic PDE

Originating in physics, Yang-Mills theory has shaped many areas of modern mathematics. In my talk, I will present Yang-Mills theory in the context of probability, highlighting central questions and recent advances. In particular, I will discuss the role of stochastic partial differential equations (SPDEs) in these developments and survey some of the recent progress in this field.

Tuesday, December 2, 2025

Posted November 13, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm

Mengxuan Yang, Princeton University
To be announced

Wednesday, December 3, 2025

Posted August 27, 2025
Last modified October 27, 2025

1:30 pm Lockett Hall 233

Krishnendu Kar, Louisiana State University
Khovanov Homology

Wrapping up our discussion on Khovanov Homology from this semester.

Posted September 10, 2025
Last modified September 23, 2025

3:30 pm Lockett 233

Corey Bregman, Tufts University
TBA

TBA

Posted November 13, 2025

3:30 pm

Peter Bradshaw, University of Illinois Urbana-Champaign
To be announced

Thursday, December 4, 2025

Posted November 12, 2025

Control and Optimization Seminar Questions or comments?

3:30 pm Lockett 232

Iain Moffatt, Royal Holloway, University of London
Graphs in surfaces, their one-face subgraphs, and the critical group

Critical groups are groups associated with graphs. They are well-established in combinatorics; closely related to the graph Laplacian and arising in several contexts such as chip firing and parking functions. The critical group of a graph is finite and Abelian, and its order is the number of spanning trees in the graph, a fact equivalent to Kirchhoff’s Matrix--Tree Theorem.

What happens if we want to define critical groups for graphs embedded in surfaces, rather than for graphs in the abstract?

In this talk I'll offer an answer to this question. I'll describe an analogue of the critical group for an embedded graph. We'll see how it relates to the classical critical groups, as well as to Chumtov's partial-duals, Bouchet's delta-matroids, and a Matrix--quasi-Tree Theorem of Macris and Pule, and describe how it arises through a chip-firing process on graphs in surfaces.

This is joint work with Criel Merino and Steven D. Noble.

Friday, December 5, 2025

Posted July 22, 2025
Last modified November 13, 2025

10:30 am – 11:20 am Zoom (click here to join)

Javad Velni, Clemson University
Optimal Supplemental Lighting in Controlled Environment Agriculture: Data-driven and Model-based Perspectives

This seminar presents one aspect of my lab’s research focused on developing optimal supplemental lighting control strategies using LED lamps in controlled environment agriculture. The work aims to minimize electricity costs associated with supplemental lighting by integrating model-based optimization techniques with advanced machine learning methods, such as deep neural networks and Markov chains, used to predict uncertain environmental variables. Several scenarios are explored, ranging from a baseline optimal lighting approach for a single crop to more complex settings involving large-scale greenhouses with multiple crops and spatial light distribution considerations. Experimental results from a research greenhouse, where an Internet of Agricultural Things (IoAT) system was developed to grow lettuce, are presented and discussed. The seminar concludes with a roadmap highlighting several emerging research directions inspired by these findings.

Posted November 13, 2025
Last modified November 14, 2025