# Dr. Ben Mares: "Eigenfunctions of the Laplacian on S^2 with two Z/2 branch points"

Oct 26, 2017 from 04:15 PM to 05:45 PM

Abstract:

This relatively elementary problem is motivated by the study of a particular broad class of limiting configurations which arise in the compactification of gauge-theoretic moduli spaces.  Just like the holomorphic function $\sqrt{z}$, such configurations are harmonic, have a sign ambiguity, and a codimension 2 branch locus.  In dimensions bigger than two, it's unknown whether or not the branch locus is a smooth manifold.  We tackle the problem of branched harmonic functions on R^3 which are homogeneous and explain what this suggests about gauge theory.