Department of Mathematics

Historically, the first examples of simple groups (found by Galois) were alternating groups. We will discuss their infinite generalizations associated with discrete dynamical systems on Cantor sets. Properties of these groups are intimately related to classical properties of dynamical systems. Such conditions as simplicity and finite generation of the groups are equivalent to standard conditions for dynamical systems: minimality and expansivity. This class of groups is also a source of examples of simple groups with prescribed properties: amenability, torsion, intermediate growth, and others, all of which are proved by analyzing the underlying dynamical system. 

Host: Alexander Olshanskiy