Geometry & Topology Seminar: Geometric structures on surfaces

Abstract: Discrete and faithful homomorphisms of the fundamental group of a closed surface into a simple Lie group of non-compact type often provide surfaces with geometric structures, for example using minimal surfaces. On the other hand, an a priori understanding of such geometries helps to understand the space of all such homomorphisms in a given connected component, blending geometry and dynamics. We'll explain how this idea can be used to show that the diameter of quasi-Fuchsian space for the so-called pressure metric is finite. This is largely based on joint work with Elia Fioravanti, Frieder Jaeckel and Yongquan Zhang.

Host: Charles Ouyang