Geometry and Topology Seminar

Given a closed oriented surface S of genus at least 2, the notion of maximal representations in SO(2,3) naturally generalizes the Teichmueller space of S. In this talk, I will explain how to construct a unique maximal surface into the pseudo-hyperbolic space H^{2,2} which is preserved by the action of a maximal representation. It generalizes in particular a recent result of Labourie. If time permits, I will explain how to extend the construction for maximal representations in SO(2,n). This is a joint work with Brian Collier and Nicolas Tholozan.