"Geometry and Analysis on Groups" Research Seminar
Solved and unsolved problems in automaton (semi-)groups.
Daniele D'Angeli (TU Graz)
Automaton groups have became very popular in the decades for their exotic behavior: important examples of groups with intermediate growth, amenable groups, Burnside groups belong to this class. Such groups naturally act by automorphisms on a rooted regular tree. The first part of this talk consists of a very gentle introduction to the theory of automaton groups (and semigroups). I will show some classical examples and some combinatorial properties of such structures.
In the second part I am going discuss some recent results regarding the structure and some algorithmic problems for automaton (semi-)groups. In particular, I will focus on the finiteness and freeness problem and their connection the dynamics of these (semi-)groups on the boundary of the corresponding tree.
The talk presents a collection of results obtained with D. Francoeur, E. Rodaro and J-F. Waechter.