Abstract: A trace on a group is a positive definite conjugation-invariant complex-valued function. These functions play an important role in harmonic analysis of discrete group, and their study found many exciting connections to rigidity, stability, and dynamics in the past couple of decades.
In this talk, I’d like to pay attention to the simplex of traces as a whole. For property (T) groups, this simplex is Bauer, i.e, the extreme points are closed. For the free group on the other hand, the simplex is Poulsen i.e, the extreme points are dense. I’ll discuss these results and other related topics such as character bounds, IRS, and more.
The talk is based on works with Levit, Orovitz and Slutsky
