Calendar

Posted November 15, 2025
Last modified January 21, 2026

Algebra and Number Theory Seminar Questions or comments?

Kiran Kedlaya, University of California San Diego
TBA

Event contact: Gene Kopp

Posted March 17, 2026

Geometry and Topology Seminar Seminar website

Jonathan Fruchter, University of Bonn
Virtual homological torsion in low dimensions

A long-standing conjecture of Bergeron and Venkatesh predicts that in closed hyperbolic 3-manifolds, the amount of torsion in the first homology of finite-sheeted normal covers should grow exponentially with the degree of the cover as the covers become larger, at a rate reflecting the volume of the manifold. Yet no finitely presented residually finite group is known to exhibit such behaviour, and meaningful lower bounds on torsion growth are rare. In this talk I will explain how a particular two-dimensional lens offers a clearer view of some of the underlying mechanisms that create homological torsion in finite covers, and how they might relate to its growth. If time allows, I will also discuss how these ideas connect to the question of profinite rigidity: how much information about a group is encoded in its finite quotients.

Posted March 5, 2026
Last modified March 9, 2026

Informal Analysis Seminar Questions or comments?

Long Teng, LSU
Doubling Inequalities for Schrodinger operators with power growth potentials

TBD

Posted January 15, 2026

Informal Geometry and Topology Seminar Questions or comments?

Sayani Mukherjee, Louisiana State University
TBD

TBD

Posted December 1, 2025
Last modified March 5, 2026

Control and Optimization Seminar Questions or comments?

Khai Nguyen, North Carolina State University
On the Structure of Viscosity Solutions to Hamilton–Jacobi Equations

This talk presents regularity results for viscosity solutions to a class of Hamilton-Jacobi equations arising from optimal exit-time problems in nonlinear control systems under a weak controllability condition. A representation formula for proximal supergradients, based on transported normals, is derived, with applications to optimality conditions, the propagation of singularities, and the Hausdorff measure of the singular set.

Posted March 16, 2026

Combinatorics Seminar Questions or comments?

Weihao Xia, Louisiana State University
An improved $\chi$-binding function for chair-free graphs

We show that if a graph \(G\) does not contain the chair (the graph obtained from \(K_{1,3}\) by subdividing an edge once) as an induced subgraph, then its chromatic number satisfies \(\chi(G) \leq \omega(G)^2\), where \(\chi(G)\) and \(\omega(G)\) denote the chromatic number and clique number of \(G\), respectively. This result improves the recent upper bound of $7\omega(G)^2$ proved by Liu, Schroeder, Wang, and Yu [J. Combin. Theory Ser. B 162 (2021) 118--133].

Posted January 11, 2026
Last modified March 6, 2026

Applied Analysis Seminar Questions or comments?

Zhiyuan Geng, Purdue University
Asymptotics for 2D vector-valued Allen-Cahn minimizers

For the scalar two-phase (elliptic) Allen–Cahn equation, there is a rich literature on the celebrated De Giorgi conjecture, which reveals deep connections between diffuse interfaces and minimal surfaces. On the other hand, for three or more equally preferred phases, a vector-valued order parameter is required, and the resulting diffuse interfaces are expected to resemble weighted minimal partitions. In this talk, I will present recent results on minimizers of a two-dimensional Allen–Cahn system with a multi-well potential. We describe the asymptotic behavior near the junction of three phases by analyzing the blow-up limit, which is a global minimizing solution converging at infinity to a Y-shaped minimal cone. A key ingredient in our approach is the derivation of sharp upper and lower energy bounds via a slicing argument, which allows us to localize the diffuse interface within a small neighborhood of the sharp interface. As a consequence, we obtain a complete classification of global two-dimensional minimizers in terms of their blow-down limits at infinity. This is joint work with Nicholas Alikakos.

Posted March 14, 2026

Student Colloquium

Aditya Guntuboyina, University of California, Berkeley
Totally Concave Regression

We provide a general overview of regression under concavity shape constraints. In the multivariate setting, several notions of concavity exist, each with substantially different properties. We review these variants and highlight their key differences. Our main focus is on an approach based on total concavity, originally studied by T. Popoviciu, which avoids the usual curse of dimensionality and can be effective in practical applications.

Posted March 11, 2026

Computational Mathematics Seminar

Yanzhao Cao, Auburn University
A training-free diffusion model for generative learning

Abstract: In this talk, I will first present a framework for training generative models for density estimation using stochastic differential equations (SDEs). Unlike conventional diffusion models that train neural networks to learn the score function, we introduce a score-estimation method that is training-free. This approach uses mini-batch-based Monte Carlo estimators to directly approximate the score function at any spatiotemporal location while solving the ordinary differential equation (ODE) corresponding to the reverse-time SDE. Our method provides high accuracy and significant reductions in neural network training time. Algorithm development and convergence analysis will be discussed. At the end, I will present an application of the diffusion model to fusion plasma.