Events for 09/15/2023 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Emmanuel Trelat, Sorbonne University

Title: From microscopic to macroscopic scale equations: mean field, hydrodynamic and graph limits

Abstract: Considering finite particle systems, we elaborate on various ways to pass to the limit as the number of agents tends to infinity, either by mean field limit, deriving the Vlasov equation, or by hydrodynamic or graph limit, obtaining the Euler equation. We provide convergence estimates. We also show how to pass from Liouville to Vlasov or to Euler by taking adequate moments. Our results encompass and generalize a number of known results of the literature.

As a surprising consequence of our analysis, we show that sufficiently regular solutions of any quasilinear PDE can be approximated by solutions of systems of N particles, to within 1/log(log(N)).

This is a work with Thierry Paul.

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Laura Matusevich, TAMU

Title: Combinatorics of Gorenstein affine semigroup rings

Abstract: Affine semigroup rings are algebras that are generated by finitely many monomials. They are very suitable for combinatorial treatment, so people in commutative algebra like to translate algebraic properties into combinatorial terms (and vice versa) if possible. In this talk, I will describe the combinatorial mechanics of the Gorenstein property for affine semigroup rings. I will give a definition of "Gorenstein" in the talk that is useful for computations, but is a bit technical. As for an intuitive definition, let me just say that assuming your ring is Gorenstein has a habit of making theorems work... This is joint work with Byeongsu Yu.

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Chong-Kyu Han, Seoul National University

Title: First integrals, stability of dynamics, and affine control with prescribed invariant subsets

Abstract: Starting with the classical theory of first integrals I will talk about the notion of weak first integral and how to find implicit solutions of quasi-linear systems of first order PDEs. In determined cases this method has applications to determining the stability and affine control of the population dynamics of Volterra-Kolmogorov type.