Fanny Kassel, CNRS, Institut des Hautes Études Scientifiques

Title: Discrete subgroups of Lie groups and geometric structures.

Abstract: Discrete subgroups of Lie groups play a fundamental role in several areas of mathematics. Discrete subgroups of SL(2,R) are well understood, and classified by the geometry of the corresponding hyperbolic surfaces. On the other hand, discrete subgroups of SL(n,R) for n>2, beyond lattices, remain quite mysterious. While lattices in this setting are rigid, there also exist more flexible "thinner" discrete subgroups, which may have large and interesting deformation spaces (some of them with topological and geometric analogies to the Teichmüller space of a surface, giving rise to so-called "higher Teichmüller theory"). We will survey recent progress in constructing and understanding such discrete subgroups from a geometric and dynamical viewpoint.