## EVENT DETAILS AND ABSTRACT

**Algebra Seminar**
**Title:** On simple amenable groups

**Speaker:** Kate Juschenko

**Speaker Info:** Vanderbilt University

**Brief Description:**

**Special Note**:

**Abstract:**

I will discuss amenability of the topological full group of
a minimal Cantor system. Together with the results of H. Matui this
provides examples of finitely generated simple amenable groups. For a
metric space (X,d) define a group W(X) as a group of all bijections g
of X such that sup{ d(g(x),x) : x in X } is finite. An important
ingredient of the proof of amenability of the full topological group
is a construction of an W(Z)-invariant mean on the set of finite
subsets of integers. In fact, one can show more for a general metric
spaces: if X satisfies Sobolev inequality then there is W(X)-invariant
mean on finite subsets of X.

**Date:** Wednesday, January 9, 2013

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Ezra Getzler

**Contact email:** getzler@northwestern.edu

**Contact Phone:**

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