Discrete groups, Lyapunov exponents, and Hodge theory

Families of algebraic manifolds give interesting examples of discrete subgroups of Lie groups, via their monodromy. They also lead to differential equations, such as the hypergeometric ones, whose solutions have an arithmetic significance. After providing the necessary background Iwill explain a connection to dynamical invariants called Lyapunov exponents, which reveals special geometric features of the discrete groups andthe corresponding differential equations.