Geometry and Analysis on Groups Research Seminar

"Geometry and Analysis on Groups" Research Seminar

Time: 2016.10.25, 15:00–17:00
Location: Seminarraum 9, Oskar-Morgenstern-Platz 1, 2.Stock
Title: "Subgroup dynamics, extreme boundaries, and \(C^*\)–simplicity."
Speaker: Nicolás Matte Bon (ETH Zürich)
Abstract: Let \(G\) be a countable group. The space of subgroups of \(G\), endowed with the Chabauty topology, is naturally a compact space on which \(G\) acts continuously by conjugation. The talk will focus on the study of the closed, minimal invariant subsets of this action, called uniformly recurrent subgroups (URS's). I will explain a general method to study URS's in a class of groups, that we call "infinitesimally supported groups of homeomorphisms". Examples of groups in this class are Thompson's groups, groups of piecewise projective homeomorphisms, branch groups, groups acting on trees with prescribed action almost everywhere, topological full groups. Applications will be given to \(C^*\)–simplicity criteria for groups in this class, and to some rigidity properties of their minimal actions on compact spaces. This is joint work with Adrien Le Boudec.