** Geometric and asymptotic group theory II **

Analytic properties of infinite groups

Lecture by Goulnara Arzhantseva

and

Problem session by Damian Osajda

Dienstag, 10:00--12:00, Raum D1.07 UZA 4

The theory of infinite discrete groups was revolutionized by an infusion of ideas from geometry, topology, and analysis. We will give an introduction to the subject. We will start with the fundamental group-theoretical constructions such as free and amalgamated products of groups, HNN-extensions. Then we will discuss analytic properties of infinite groups such as Kazhdan's property T, amenability, and their modern generalizations. The course 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__,
__Blatt 7__

**2nd EXAM.** September 22, from 17:00h. Note: 20 min preparation, 20 min oral presentation (time is strict !), one A4 format page of "reminder" is allowed.

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

- Fundamental group:

Ch. 1.1 and 1.2 of the book
by Allen Hatcher, __Algebraic topology__

- Free groups, group presentations, free and amalgamated products, HNN extensions:

Ch. 2 (pages 52-56, 58-60, 71-74, 81-84) of the book
by Oleg Bogopolski, Introduction to group theory

- The group SL(2,Z):

the article by Agnes F. Beaudry,
__Generators of SL(2, Z)__, The Delta Epsilon, Issue 1