Colloquium Abstracts Spring 2026

Abstracts will be posted here for the colloquium talks when they are available.

Linus Setiabrata

Massachusetts Institute of Technology
January 29, 2026

Newton Polytopes and Schubert Calculus

Schubert calculus studies the cohomology ring of the variety of complete flags. Many problems in Schubert calculus have meaningful implications in geometry and representation theory yet are amenable to combinatorial techniques. I will discuss striking classical applications of combinatorics to Schubert calculus, as well as some of my recent work on Newton polytopes of Schubert and Grothendieck polynomials. Joint work with Jack Chou.

Geng Chen

University of Kansas
March 12, 2026

The Stability of Shock Waves and the Physical Inviscid Limit

The solutions of compressible Euler equations often form shock waves, in finite time, notably observed behind supersonic planes. A very natural way to justify these singularities involves studying solutions from inviscid limits of Navier-Stokes solutions. The mathematical study of this problem is however very difficult because of the destabilization effect of the viscosities. Bianchini and Bressan proved the inviscid limit to small BV solutions in one space dimension using the so-called artificial viscosities in 2004. However, until recently, achieving this limit with physical viscosities remained an open question. In this presentation, the recent advances on the L2 theory of compressible fluid mechanics will be introduced. This method is employed to describe the physical inviscid limit in the context of the barotropic Euler equations, and to solve the Bianchini and Bressan's conjecture. This is a joint work with Kang and Vasseur. This result is based on our earlier uniqueness and stability theory of shock waves for Euler equations (join with Krupa, Faile and Vasseur). We will then introduce the very recent progress on another long-standing problem: the L2 contraction and stability of dispersive shock with infinite oscillations for the KdV-Burgers equation. The zero dissipation and dispersion limit of KdV-Burgers equation will also be introduced. This is a joint work with Eun, Kang and Shen.

Ravindra Girivaru

University of Missouri, St. Louis
March 26, 2026

Matrix Factoriazation of Polynomials and Lefschetz Theorems

A matrix factorization of a polynomial F is a pair of  square matrices (A, B) such that their product is F times the identity matrix. After spending some time on preliminaries, I will explain the main questions, what is known and their relevance to the geometry of the set of zeroes of the polynomial F.  I will also talk about its connection to the problem of determining the minimum number of polynomials required to define curves in  three dimensional space and analogous questions.

Hung Vinh Tran

University of Wisconsin
April 2, 2026

Homogenization of First-order Hamilton-Jacobi Equations: Recent Progress

I will discuss recent progress on the quantitative homogenization of first-order Hamilton–Jacobi equations. In the periodic setting, I will present optimal convergence rates and sketch the main ideas of the proofs. I will then turn to the random setting, where I will describe new results motivated by a frictionless (inviscid) KPZ equation, including quantitative large-time behavior and related open problems.

Sunder Sethuraman

University of Arizona
May 7, 2026

On the Derivation of Mean-curvature Flow and its Fluctuations from Microscopic Interactions

The emergence of mean-curvature flow of an interface between different phases or populations is a phenomenon of long-standing interest in statistical physics.   In this talk, we review recent progress with respect to a class of reaction-diffusion stochastic particle systems on an n-dimensional lattice. In such a process, particles can move across sites as well as be created/annihilated according to diffusion and reaction rates.

These rates will be chosen so that there are two preferred particle mass density levels a_1, a_2 in 'balance'.  One may understand, when the diffusion and reaction schemes are appropriately scaled, that a rough interface forms between the regions where the mass density is close to a_1 or a_2.  Via notions in the theory of hydrodynamic limits, we discuss that the scaled limit of the particle mass density field in n>2 is a sharp interface flow by mean-curvature. We also discuss the fluctuation field limit of the mass near the forming interface, informing on the approach to the continuum view in a certain stationary regime in n=1,2.