Boundaries, rigidity of representations, and Lyapunov exponents

Abstract

In this paper we discuss some connections between measurable dynamics and rigidity aspects of group representations and group actions. A new ergodic feature of familiar group boundaries is introduced, and is used to obtain rigidity results for group representations and to prove simplicity of Lyapunov exponents for some dynamical systems.

For the Proceedings of the ICM 2014, 27 pages