Date:	Tue, June 23, 2015
Time:	14:15
Place:	Research I Seminar Room

Abstract: Self-similar groups (groups generated by automata) appeared in early eighties as interesting examples. It was discovered that very simple automata generate groups with complicated structure and exotic properties (such as intermediate growth) which are hard to find among groups defined by more "classical" methods.

The main activity in the area is concentrated in deep understanding of these nice example with a goal to unify them in a general theory. It happens that the study of branching properties of the group is very important for this matter.

In the talk I will first quickly introduce the relevant notions and overview the current status of studies of algebraic properties of IMGs. In the remaining part of the talk I will present my recent progress in this area. Namely, I will look into a specific example of the IMG of an expanding Thurston map and prove that it is a branch group, which would imply that it contains Z^n subgroup for any n, which in turn would imply that the group has superpolynomial growth.