11:30
Application of Uniform Recurrent Subgroups to Operator Algebras
Abstract
In 2014, Glasner and Weiss introduced the theory of uniformly recurrent subgroups (URSs) as a topological analogue of the theory of invariant random subgroups. Later, Matte Bon and Todor showed that every URS arises from a minimal topological action of the group on a compact space. Subsequently, in 2020, Kennedy established a complete characterization of C ∗ -simplicity in terms of URSs, proving that a group is C ∗ -simple if and only if it admits no amenable URS.
More recently, Bray and Kennedy proved that the reduced crossed product associated with a minimal action X is simple if and only if the set of points in X whose stabilizers are C ∗ -simple is comeager in X. Their proof relies on the theory of URSs, the existence of a minimal amenable URS, established by Le Boudec and Matte Bon, and a finiteness condition related to C ∗ -simplicity.
In this talk, I will introduce the theory of uniformly recurrent subgroups and present a proof of the aforementioned result of Bray and Kennedy.