Groups and Dynamics Seminar

Date: September 13, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Robin Tucker-Drob, Texas A&M

Title: Invariant means and inner amenable groups

Abstract: An action of a group G on a set X is said to be amenable if X admits a G-invariant mean (i.e., finitely additive probability measure). The group G is said to be amenable if the left translation action of G on itself is an amenable action. While these notions were introduced in 1929 by von Neumann, a systematic study of amenable actions of nonamenable groups was not initiated until roughly 1990. I will discuss this setting, and how the tension which arises between the nonamenability of the group and the amenability of the action results in surprising structural consequences for the acting group. This tension becomes particularly pronounced in the case of an atomless mean for the conjugation action, i.e., when the group is inner amenable. I will highlight some recent results and applications of inner amenability, particularly to orbit equivalence and measured group theory.