Sara Maloni (University of Virginia)

The Teichmüller space of a surface S is the deformation space of marked hyperbolic structures. This can be viewed as a component of representations of the fundamental group π1(S) into the isometry group of hyperbolic space. Higher Teichmüller Theory generalizes this idea by studying representations of surface groups into Lie groups of higher rank.

In the first part of the talk, we will introduce key ideas in the theory of deformations of geometric structures, (higher) Teichmüller theory,  and Anosov representations. In the second part of the talk, we will present the work of Guichard-Wienhard and Kapovich-Leeb-Porti that helps relating Anosov representations to deformations of geometric structures. We'll also discuss recent work with Alessandrini, Tholozan, and Wienhard (and independently obtained also by Davalo) and of my PhD student Mason Hart, on the topology of such geometric structures.