Robert Müller: An Introduction to Amenable Groups Via Representation Theory and Group Theory

Abstract

The study of groups is arguably one of the most important in mathematics, involving many of the greatest mathematicians, like Hanna Neumann, Jacques Tits and (earlier) Alfred Tarksi. I will give a short introduction to representation theory in order to study groups and their amenability. We will study some basic examples of groups like the integers and the free group in two generators. In the end, we might dip into the so-called Property (T) and its connection with amenability.