Speaker: Mitul Islam
Date: April 04, 2024
Affiliation: Max Planck Institute for Mathematics in the Sciences (Leipzig)

Abstract: In this talk, I will explore discrete linear groups from the perspective of their actions on flag varieties. This viewpoint - of much contemporary interest - has led to the discovery of many `flexible’ groups (i.e. discrete groups with nice deformation spaces akin to the Teichmüller space) and close connections have emerged with convex projective geometry and hyperbolic geometry. I will discuss results of two distinct flavors - flexible and rigid. On the one hand, I will discuss recent progress in the study of rank one convex co-compact groups, a class of `flexible’ groups. On the other hand, I will discuss new rigidity results for higher rank lattice actions, that generalize Weil’s local rigidity theorem to homeomorphism groups (joint with Connell-Nguyen-Spatzier).