250100 VO Geometric and asymptotic group theory 2 (2013S)

The course is on Geometry and Analysis of free groups. Free groups are universal objects in the theory of infinite groups. Since their appearance at the end of 19th century they are a constant source of examples and counterexamples.

The purpose of this course is to focus on free groups, their subgroups, and automorphisms in order to introduce students to advanced topics of geometric and analytic group theory such as curvature, randomness, and group C*-algebras. In particular, we will discuss the following fundamental concepts:

Random subgroups and the technique of Stallings foldings;
C*-exactness and C*-simplicity / (non)-amenability (introduced by John von Neumann);
Growth and random walks.

The knowledge of Geometric and asymptotic group theory I (Winter semester course) is not required.