Modul: MAT772 Geometrie-Seminar

## On the existence of free subsemigroups in automata groups

Vortrag von Dominik Francoeur

**Datum:** 10.10.18 **Zeit:** 15.45 - 16.45 **Raum:** ETH HG G 43

Groups generated by automata have attracted a lot of attention since their introduction, partly because despite their simple combinatorial description, they can possess many interesting properties. For instance, one can find among this class finitely generated infinite torsion groups, just infinite groups and groups of intermediate growth. There is also a connection, discovered by Glasner and Mozes, between these groups and square complexes. An important question in the study of automata groups is how the properties of the automaton are reflected in the properties of the group that it generates. We will discuss one such connection, namely the link between reversibility of the automaton and the existence of free subsemigroups. This is joint work with Ivan Mitrofanov.