Discrete harmonic maps between hyperbolic surfaces

Discrete harmonic maps between hyperbolic surfaces

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Jonah Gaster, University of Wisconsin-Milwaukee

Please note that this seminar will take place online via Zoom. You can connect to this seminar via the following link:

https://princeton.zoom.us/j/453512481

Combined work of Eels-Sampson and Hartman asserts the existence of a harmonic diffeomorphism in any homotopy class of maps between a pair of homeomorphic compact hyperbolic surfaces. I'll discuss background, present a suitable discretization, and explore conditions on discretizations that ensure convergence of the discrete maps to the smooth harmonic map.