Higher Teichmuller theory studies representations of surface groups into Lie groups of higher rank, in contrast with the classical Teichmuller theory that concerns PSL(2,R). In this talk we will describe a scheme to find the analog of Thurston compactification for generalizations of Teichmuller space in the case where the Lie group is real split of rank 2 (SL(3,R), Sp(4,R), G2). For concreteness, we will mostly focus on SL(3,R), where the theory involves the study of convex real projective structures on surfaces, which in some sense extend the notion of hyperbolic structures.

Marcel Bökstedt marcel@math.au.dk, for Zoom details.