Combined work of Eells–Sampson and Hartman asserts the existence of a unique smooth harmonic map in the homotopy class of a map of nonzero degree between a pair of 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.
Please email Anton Bernshteyn (abernsht ~at~ math.cmu.edu) for a password.
The ACO Seminar (2019–2020)