Z/2 harmonic differential forms and S1(2;C)-like gauge theories

Abstract:  Z/2 harmonic forms are closed and coclosed 1-forms with values in a real line bundle that is defined on the complement of a cxdimension 2 subvariety of a Riemannian manifold with their norms being zero on this same subvariety. These objects are now known to appear (in dimensions 2-4) in diverse contexts involving SL(2,C) gauge theories. I hope to tell you a story about these objects and the role that they might be playing with regards to the differential topology of low dimensional manifolds.

You can learn more about Professor Cliff Taubes at https://www.math.harvard.edu/people/taubes-cliff/