A Survey of Geometric Group Theory Spring 2020

Matthew Cordes
Xenia Flamm

The seminar takes place on Thursdays from 15h to 17h at HG E 33.5 home .


In this class we will cover some of the tools, techniques, and groups central to the study of geometric group theory. After introducing the basic concepts (groups and metric spaces), we will branch out and sample different topics in geometric group theory based on the interest of the participants. Possible topics include: properties of free groups and groups acting on trees, large scale geometric invariants (Dehn functions, hyperbolicity, ends of groups, asymptotic dimension, growth of groups), and examples of notable and interesting groups (Coxeter groups, right-angled Artin groups, lamplighter groups, Thompson's group, mapping class groups, and braid groups).

This seminar will have 24 participants and 13 class periods. In the first week, Matthew Cordes will give an introductory overview of some of the basic tools/ideas of geometric group theory. That means that there are 12 weeks left and 12 other topics which will each be covered by a pair of students in the form of two 45 minute talks.

Please also consult the details in the course catalog.

Coronavirus Precautions

To allow a smooth continuation of the seminar we will hold the seminar talks online via Zoom. An invitation will be sent out in time. There is a screen share feature on Zoom, so every student will prepare notes that they can share and explain to the class. One can also connect the tablet and write as one talks.

In order to make things a bit simpler and give enough time to prepare, there will be no seminar on Thursday, 19th of March. The updated time table can be found below. In the final week of the semester, we will have three seminar talks.

It is expected that all participants in the seminar will join the Zoom.


One should be familiar with the basics of groups, metric spaces, and topology (should be familiar with the fundamental group). Note that the seminar is open to Bachelor and Master students, so the participants should choose their topic according to their current level. A detailed list of prerequisites for each talk can be found here.

One requirement for this class is that the speakers meet with either one of the organisers at least one week before their presentation. They must present a written outline of their talk.

List of Talks

Once the speakers for the talks have been fixed they will be posted below.

Feel free to contact the organizers if you want to give a talk.

Title Date Speaker(s)
Groups and Spaces February 20 Cordes
Quasi-Isometries February 27 Bramato, Reinhard
Groups Acting on Trees, Free Groups and Folding March 5 Bosshard, Wiedmer
The Ping-Pong Lemma and Automorphisms of Free Groups March 12 Schlagenhauf, Zbinden
Dehn Functions March 19 March 26 Chopard, Paunovic
Hyperbolic Groups March 26 April 2 Invernizzi, Jaeck
Ends of Groups (and Braid Groups) April 2 April 9 Lambert, Ostini
Growth of Groups April 9 April 23 Apolloni, Fratini
Coxeter Groups April 23 April 30 Cao, Mukherjee
Right-Angled Artin Groups April 30 May 7 Maunoir, Python
Lamplighter Groups May 7 May 14 Deligios, Morrone
Mapping Class Groups May 14 May 28 Amrhein, Hiltbrunner
Braids and Configuration Spaces May 28 Schmitz