Anosov representations, Lyapunov exponents, and Hodge theory

Group Actions and Dynamics
Event time: 
Monday, November 15, 2021 - 4:00pm
Simion Filip
Speaker affiliation: 
University of Chicago
Event description: 

Discrete subgroups of semisimple Lie groups arise in a variety of contexts, sometimes “in nature” as monodromy groups of families of manifolds, and other times in relation to geometric structures and associated dynamical systems. I will discuss a class of such discrete subgroups that come from certain variations of Hodge structure and give rise to Anosov representations. Among many consequences, this leads to uniformization results for certain domains of discontinuity of the discrete group, and also yields a proof of a conjecture of Eskin, Kontsevich, Moller, and Zorich on Lyapunov exponents. The necessary background will be explained.