Events for 09/24/2021 from all calendars

Seminar on Banach and Metric Space Geometry

Time: 09:00AM - 10:00AM

Location: BLOC 302

Speaker: Audrey Fovelle, Université Bourgogne Franche-Comté

Title: Hamming graphs and concentration properties in Banach spaces

Abstract: In 2008, Kalton and Randrianarivony introduced a concentration property for Lipschitz maps defined on Hamming graphs, that every reflexive asymptotically uniformly smooth Banach space $X$ satisfies. This property, that we will note HFC_p,d, provides an obstruction to the coarse Lipschitz embedding of certain spaces into X. Later, Lancien, Raja and Causey proved that this result could be extended to quasi-reflexive spaces, by using a weaker concentration property, that we will call HIC_p,d. The goal of this talk is to show that these two properties are stable under l_p sums of Banach spaces, in order to obtain a non quasi-reflexive space that satisfies property HIC_p,d.

Noncommutative Geometry Seminar

Time: 2:00PM - 3:00PM

Location: ZOOM

Speaker: Marc Rieffel , University of California at Berkeley

Title: Dirac Operators for Matrix Algebras Converging to Coadjoint Orbits

Abstract: In the high-energy physics literature one finds statements such as “matrix algebras converge to the sphere”. Earlier I provided a general precise setting for understanding such statements, in which the matrix algebras are viewed as C*-metric spaces, and convergence is with respect to a quantum Gromov-Hausdorff-type distance. But physicists want even more to treat structures on spheres (and other spaces like coadjoint orbits), such as vector bundles, Yang-Mills functionals, Dirac operators, etc., and they want to approximate these by corresponding structures on matrix algebras. I will sketch a somewhat unified construction of Dirac operators on coadjoint orbits and on the matrix algebras that converge to them. As Connes showed us, from Dirac operators we may obtain C*-metrics. Our unified construction enables us to prove our main theorem, whose content is that, for the C*-metric-space structures determined by the Dirac operators that we construct, the matrix algebras do indeed converge to the coadjoint orbits, for a quite strong version of quantum Gromov-Hausdorff distance. This is a long story, but I will sketch how it works.

Committee I&T Meeting

Time: 3:00PM - 4:00PM

Location: ZOOM

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Zhi Jiang, U. Michigan

Title: G-stable rank for tensors and its applications

Abstract: G-stable rank is a new notion of rank for tensors over perfect fields, it is closely related to the stability in geometric invariant theory. We will talk about the motivation of G-stable rank and some of it's properties. We will also discuss the connection to stability. Finally, as an example, we will look at the application of G-stable rank to Cap Set problem.