Department Mathematik



                                  Student Seminar
                    Randomness and geometry of groups

                                   Winter semester 2019/2020

In the first part, we study the geometry of a “random group”, in particular we study Gromov’s density model and aim to understand why a certain class of random groups is typically hyperbolic. 
In the second part, we investigate random processes on groups, in particular the connection between behaviour of the process and the geometry of the group.

The topic is at the intersection of group theory, geometry, probability theory, combinatorics, and cryptography.

Target group: Master students in Mathematics. Bachelor students with strong background in geometric group theory or discrete probability theory and keen interest in the topic may apply for admission.

Literature (preliminary):

Time:  Fridays, 8:30 - 10:00 in room B251; dates as listed below.
Followed by breakfast in a nearby café (optional).

Lecturers: Prof. Dr. Sebastian Hensel and Prof. Dr. Markus Heydenreich

Topic Topic
15 Nov
Random groups are hyperbolic I
22 Nov
Random groups are hyperbolic II
29 Nov
Random groups are hyperbolic III
06 Dec

13 Dec
Random walk on generating sets
20 Dec

10 Jan
Stratified random walk on the n-cube
17 Jan
D.G. Percolation on Fuchsian groups
24 Jan

31 Jan
Percolation thresholds under covering maps
07 Feb
Random matrices and random permutations