** "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.