Abstract: Many classical fractals, such as the Sierpinski gasket, and Julia sets of polynomials can be described through groups generated by finite automata. Automaton groups also provide a rich source of examples (such as Grigorchuk group of intermediate growth) and play an important role in geometric group theory. In this talk we will show a phase transition in the Liouville property of automaton groups, and deduce that all automaton groups with activity growth of degree up to 1 are amenable. A key ingredient is the analysis of random walks on the Schreier graphs of these groups.

This talk is based on joint works with O. Angel and B. Virag. No prior knowledge on automatons, the Liouville property or amenability is required.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006