Harmonic maps between negatively curved surfaces have very nice analytic properties that can be used to show geometric and topological properties. We will introduce the notion of a harmonic map between two surfaces and the Hopf differentials of such maps. Using a few equations, some basic PDE principles (and some hand waving) we will be able to see that the space of Hopf differentials of a surface is diffeomorphic to it's Teichmuller space.

### Graduate Student Geometry-Topology Seminar

Friday, November 1, 2019 - 2:00pm

#### Artur Saturnino

University of Pennsylvania