About

The theory of boundaries of groups lies at the intersection of ergodic theory, geometry, and analysis.

On the one hand, the notion of Poisson boundary devised by Furstenberg proved to be an essential tool in the ergodic theory of group actions, leading to the celebrated rigidity results. On the other hand, in a purely geometric setting, the introduction of boundaries of groups has since the work of Gromov opened the road to modern geometric group theory. Moreover, the notion of Poisson boundary also appears as a central object in the theory of operator algebras. In the last decades, the interplay between these three fields has brought about several breakthroughs, providing solutions to some conjectures and the invention of new tools.

The goal of this NSF funded workshop is to bring together experts in the theory of random walks and group actions, so as to develop further the interaction between probability, ergodic theory, geometry, and operator algebras.