Abstract:
The theory of the Furstenberg-Poisson boundary provides a "boundary theory" for general groups. In a somewhat similar fashion to the action on the Gromov boundary hyperbolic groups, with the advantage of working for general group, without any geometric assumptions on the group. We will motivate and discuss this theory, its connection to rigidity theory, and will focus on the question of the triviality of this boundary.
Based on joint work with Frisch, Tamuz and Vahidi Ferdowsi.