Speaker: Yair Hartman (Weizmann Institute, Israel)

Title: The Furstenberg entropy realization problem

Abstract: Stationary actions are a generalization of measure preserving actions, in the context of a random walk on a group. The Furstenberg entropy of a stationary action is an important invariant which measures its “distance from invariance”. The realization problem is to determine the possible entropy values realizable for a given random walk. In this talk we will see a new characterization of Kazhdan’s property (T) in terms of this problem (for non-singular actions) and will use Invariant Random Subgroups (IRSs) in order to describe a full solution of the problem for lamplighter groups.

Based of several joint works with Lewis Bowen, Omer Tamuz and Ariel Yadin