Analysis Seminar: Choquet simplices of groups and C*-algebras (Itamar Vigdorovich, UCSD)
February 19 @ 4:15 pm - 5:15 pm
Abstract: Let C be a compact convex set (in a locally convex topological vector space). By Choquet’s theorem, every point in C is the barycenter of a probability measure supported on the extreme points. When this representing measure is unique, C is called a simplex.
Simplices arise naturally in various fields of mathematics: the space of invariant probability measures of a dynamical system is a simplex, and so is the space of tracial states on a C*-algebra. In the group case, the simplex of characters provides a framework for a non-commutative Fourier transform.
I will also discuss results and phenomena for traces of free products, fundamental groups of surfaces, Kazhdan groups, and related classes.