Dick Canary, University of Michigan

An invitation to Anosov representations

Fuchsian groups arise naturally as groups of covering transformations of hyperbolic surfaces. One may view them as images of discrete faithful representation of free groups and surface groups into PSL(2,R). The study of hyperbolic surfaces and deformation spaces of Fuchsian groups is a rich and classical subject. One may naturally generalize this to the study of groups of covering transformations of hyperbolic manifolds and this also has a beautiful, well-developed theory especially in dimension three.

Introduced in 2006, the theory of Anosov representations into semi-simple Lie groups (e.g. PSL(d,R)) has emerged as a higher rank analogue of the theory of Fuchsian groups. Our talk will begin by recalling some of the classical facts about Fuchsian groups. We will then gently introduce the subject of Anosov representations and their emerging theory. We will focus on the subject of representations into PSL(3,R) whose images arise as covering transformations of convex projective structures on surfaces.