Geb. 20.30, SR 2.058

23.01.2025

Eduard Schesler

15:45 Uhr

Abstract: Since its first appearance in the 1960’s the class of (finite state) automata groups re-mained a constant source of groups with exotic and interesting properties. Coarsely speaking, an automaton group consists of homeomorphisms of the Cantor set (thought of as the set of infinite words over a finite alphabet) that is given by a finite set of rules that determines how to process a word letter by letter. In the talk I will give an introduction to the world of automata groups and present some the classical examples of them. Moreover, I will discuss the role of automata groups in the solution of some classical problems in group theory: The construction of finitely generated infinite torsion groups (Burnside’s problem), groups of intermediate growth (Milnor’s problem), groups with non-uniform exponential growth (Gromov’s problem), and finitely presented amenable groups that are non-elementary amenable (Day’s problem). Finally, I will survey on the state of the art of the notoriously open question whether polynomial automata groups are amenable.