Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Anosov representations, Hodge theory, and Lyapunov exponents
Speaker: Simion Filip, University of Chicago
Date: November 29, 2021
Time: 19:00:00 Hours
Venue: via Zoom
Abstract: Discrete subgroups of semisimple Lie groups arise in a variety of contexts, sometimes "in nature" as monodromy groups of families of algebraic manifolds, and other times in relation to geometric structures and associated dynamical systems. I will discuss a class of such discrete subgroups that arise from certain variations of Hodge structure and lead to Anosov representations, thus relating algebraic and dynamical situations. Among many consequences of these relations, I will explain Torelli theorems for certain families of Calabi-Yau manifolds, uniformization results for domains of discontinuity of the associated discrete groups, and also a proof of a conjecture of Eskin, Kontsevich, Moller, and Zorich on Lyapunov exponents. The necessary context and background will be explained.
Title of Talk: Anosov representations, Hodge theory, and Lyapunov exponents
Speaker: Simion Filip, University of Chicago
Date: November 29, 2021
Time: 19:00:00 Hours
Venue: via Zoom
Abstract: Discrete subgroups of semisimple Lie groups arise in a variety of contexts, sometimes "in nature" as monodromy groups of families of algebraic manifolds, and other times in relation to geometric structures and associated dynamical systems. I will discuss a class of such discrete subgroups that arise from certain variations of Hodge structure and lead to Anosov representations, thus relating algebraic and dynamical situations. Among many consequences of these relations, I will explain Torelli theorems for certain families of Calabi-Yau manifolds, uniformization results for domains of discontinuity of the associated discrete groups, and also a proof of a conjecture of Eskin, Kontsevich, Moller, and Zorich on Lyapunov exponents. The necessary context and background will be explained.