Description:

Title: Thin surface group embeddings and deformation theory in higher rank

Abstract: The subgroup structure of lattices, particularly that of their thin subgroups, is in general poorly understood. Through the Tits alternative and tools like the ping pong lemma, there are a wealth of ways in which we understand these aspects for free subgroups. However, for groups which are not freely generated, essentially nothing is known in general. In this talk, I’ll outline some aspects in which we can understand questions along these lines for surface groups, the first interesting case after free groups. In particular, for higher-rank Lie groups, we can use geometric and dynamical tools coming from the world of Anosov representations to study arithmetic properties of character varieties via “bending deformations” which, in turn, provide a wealth of thin surface subgroups of arithmetic groups. This is based partially on work joint with Jacques Audibert.