Events for 03/19/2025 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

Time: 2:00PM - 2:50PM

Location: BLOC 302

Speaker: Matt Powell, Georgia Institute of Technology

Title: A coupled 3d Kac evolution and its approach to equilibrium

Abstract: In 1956 Mark Kac introduced a simple model for the evolution of a gas of hard spheres undergoing elastic collisions. The Kac master equation, due to its simplicity, occupies a special place among the models describing a gas of interacting particles. Its many uses includes providing a reasonably satisfactory derivation of the spatially homogeneous Boltzmann equation and giving a mathematical framework for investigating the approach to equilibrium. These issues were, in fact, the motivation for Kac’s original work. The classical Kac master equation is a 1D model based on simple probabilistic principles and yields a linear evolution equation for the velocity distribution for N 1-dimensional particles undergoing collisions. In this talk, we will discuss new and ongoing work studying properties of a 3-dimensional Kac evolution, the analysis of which differs from that of the original 1-dimensional model due to additional conservation laws. These results are all joint with F. Bonetto and M. Loss.

Seminar in Random Tensors

Time: 3:00PM - 4:00PM

Location: BLOC 306

Speaker: B. McKenna, Georgia Tech

Title: Injective norm of real and complex random tensors

Abstract: The injective norm is a natural generalization to tensors of the operator norm of a matrix. In quantum information, the injective norm is one important measure of genuine multipartite entanglement of quantum states, where it is known as the geometric entanglement. We give a high-probability upper bound on the injective norm of real and complex Gaussian random tensors, corresponding to a lower bound on the geometric entanglement of random quantum states. The proof is based on spin-glass methods, the Kac—Rice formula, and recent progress coming from random matrices. Joint work with Stéphane Dartois. ​

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Santiago Radi Severo, Texas A&M University

Title: On finite generation, the congruence subgroup property and just-infiniteness in groups of finite type

Abstract: Groups of finite type (also known as finitely constrained groups) are closed subgroups of Aut(T), the automorphism group of a regular rooted tree T, whose action locally around every vertex is determined by a finite group of allowed actions. They were introduced in 2005 by Grigorchuk, who proved that the closure of regular branch groups belongs to this class. In 2006, Sunic proved the converse. In the study of groups acting on rooted trees, three important notions play a significant role: the congruence subgroup property (CSP), just-infiniteness (j-oo) and topologically finitely generation (tfg). For instance, if CSP holds, then the group is isomorphic to its profinite completion.
In my talk, I will prove that these three notions are equivalent for groups of finite type that satisfy the so-called Property (E), a property that will be developed in the talk and seems to be true for any group of finite type. As a consequence of this result, it will be shown that the Hanoi tower group in 3 pegs, a group introduced in 2006 by Grigorchuk and Sunic, and known not to be just-infinite, unexpectedly has a just-infinite closure.