** Geometric and asymptotic group theory II **

Baumslag-Solitar groups

Lecture by Goulnara Arzhantseva

and

Problem session by Damian Osajda

Dienstag, 10:00--12:00, Raum C2.07 UZA 4

This course is on the Baumslag-Solitar groups with applications. Since their introduction by Baumslag and Solitar in 1962, the family of Baumslag-Solitar groups has become a constant source of examples and counterexamples in the theory of infinite groups. The purpose of this course is to focus on the Baumslag-Solitar groups in order to introduce students to advanced topics of geometric group theory such as growth, curvature and limits of infinite groups. In particular, we will discuss the following fundamental concepts:

- (Non)-amenability (introduced by John von Neuman);

- Limits in the space of marked groups (used, for example, in the proof of the celebrated Gromov polynomial growth theorem);

- Bass-Serre theory (developed by Jean-Pierre Serre and Hyman Bass).

The lectures will be focused on concrete examples. The knowledge of Geometric and asymptotic group theory I (Winter semester course) is not required.

Course assessment: Presentation or test.

The first hour (10:00--10:45) is a lecture, and the second hour (11:00--11:45) is a problem session.

Lists of problems:
__Blatt 1__, __Blatt 2__,
__Blatt 3__, __Blatt 4__,
__Blatt 5__, __Blatt 6__

**References **(advised but not obligatory!):

- Basic group theory:

pages: 10-17, 20-26, 29-33, 35 of the book of Joseph J. Rotman, An introduction to the theory of groups