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Graduate Student Geometry-Topology Seminar

Friday, November 1, 2019 - 2:00pm

Artur Saturnino

University of Pennsylvania


University of Pennsylvania

4N30 DRL

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.