Miklós Abért: Sofic entropy and factor maps

Speaker: Miklós Abért

Title: Sofic entropy and factor maps

Abstract: I will talk about new results with Benjy Weiss that say that for a process mu over a sofic group (or vertex transitive graph), and a factor map F, we have h(mu) <= h(Im F) + h(Ker F). (Or course one has to define the entropy notion h so that this makes sense). Equality never holds for nonamenable groups or graphs because of Ornstein-Weiss type counterexamples. This implies the following strengthening of Gromov's original theorem that made him introduce sofic groups: Let A be a finite automata over a sofic group such that the preimage of every point is countable. Then A is surjective.