Geometry Seminar: A. Tamburelli (Rice U)

Geometry Seminar (Geometric Analysis)

Speaker: Andrea Tamburelli (Rice U)

Title: Thurston boundary for higher Teichmüller spaces

Abstract: Higher Teichmüller theory studies representations of surface groups into Lie groups of higher rank, in contrast with the classical Teichmüller 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.