Geb. 20.30, SR 2.058

06.02.2025

Eduard Schesler

15:45 Uhr

Abstract: In the third part of my introduction to automata groups, we conclude our considerations of the current state of the amenability conjecture of polynomial automata groups. We use the opportunity to use the methods we have learned so far to outline the proof of the amenability of interval exchange transformation groups of small rank, which is based on the concept of extensive amenability. We then turn to the concept of self-similarity, which can be understood as a natural generalization of automata. After dealing with some examples of self-similar groups, we will discuss their role in the context of the Boone-Higman conjecture. If time permits, we will talk about another generalization of (synchronous) automata groups: asynchronous automata groups. These allows us to transform the Cantor set using homeomorphisms that do not necessarily arise from automorphisms of a regular tree. We will see that the class of groups of asynchronous automata is huge. It contains all hyperbolic groups, Thomspon's groups F,T,V, and most of the classical branch groups such as Grigorchuk's group.