Random Groups

 

Organizers: Talia Shlomovich & Rafaela Ioannou
 

Description: If you are interested in infinite group theory, probabilistic methods or random walks, join us for our reading group on random groups!

The topic of random groups is motivated by a fundamental question: what are the properties of a ‘typical’ group? We’ll use probability distributions to build these typical groups and explore how this relates to their characteristics.

Schedule: Thursdays 15:00 – 17:00, CMT.01 (Heriot-Watt) & Online

22/01: Introductory session

29/01: Rafaela Ioannou: Motivations and Gromov’s Density Model   

Notes: Random Groups Talk 1

05/02: Critical Densities for Various Properties   

12/02: Few Relators Model and 1-Relator Groups   

19/02: Typical Elements in a Group   

26/02: Stalling’s Graphs and Random Subgroups I   

05/03: Stalling’s Graphs and Random Subgroups II   

12/03: Non-Uniform Distributions    

19/03: Open Problems and Perspectives     

26/03: Possible Bonus Lecture – Proof of Density ½ Theorem    

 

Resources:

[1] Bassino et. al, Random Presentations and Random Subgroups: A Survey (2020)

[2] Ollivier, An Invitation to Random Groups (2005)