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Geometric and asymptotic group theory

Gromov's polynomial growth theorem

Lecture by Goulnara Arzhantseva
Problem session by Damian Osajda
Dienstag, 10:00--12:00, Raum 2A310 UZA2

This course is aimed to present basic notions and techniques used within Geometric Group Theory. In particular we focus on the growth function. The ultimate goal is to demonstrate Kleiner's proof of Gromov's polynomial growth theorem.
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, Blatt 8, Blatt 9, Blatt 10

EXAM. February 7th, from 10h to 12h00, room 2A310. Note: 20 min preparation, 20 min oral presentation (time is strict !), one A4 format page of "reminder" is allowed.

References (advised but not obligatory!):
- Quasi-isometries:
Ch. 1.8. of the book by Bridson, Martin R., Haefliger, Andre, Metric spaces of non-positive curvature
- Free groups and group presentations:
Ch. 2 (pages 45 -69) of the book by Bogopolski, Oleg, Introduction to group theory
- Growth of groups:
Ch. 1, Ch. 3.1 and 3.2 of Nick, Scott, Growth of Finitely Generated Groups, available here
- Subgroups distortion (advanced reading):
Mitra, Mahan, Coarse extrinsic geometry: a survey, available here
Ch 3. of the book Gromov, Michael, Asymptotic invariants of infinite groups.