Informal Group Action Seminar

Thin groups are finitely generated, infinite index subgroups of arithmetic lattices in Lie groups. Interesting examples come from monodromies of families of algebraic manifolds and in these cases, the "thinness" of monodromy is explained by special dynamical properties of the group. In particular, the thin group acts properly discontinuously on domains where the ambient lattice acts with dense orbits. I will explain these constructions and their relations to Hodge theory, Anosov representations, and their applications to questions of uniformization. I will also explain an application to a conjecture of Eskin-Kontsevich-Moller-Zorich about Lyapunov exponents.