Geometry & Topology Seminar: "Hybrid methods for gauge theory"

Abstract: In Maxwell's equations, charge conservation is deeply tied to gauge symmetry. Numerical methods that preserve this gauge symmetry (and therefore the conservation law) have been well-understood since the 1980s. A similar "charge conservation" law arises from the gauge symmetry in Yang-Mills theory. However, the numerical approach that works for Maxwell's equations does not easily generalize, due to the fact that, in the nonabelian case, gauge transformations no longer preserve polynomials of a given degree. I will discuss a new approach (joint with Yasha Berchenko-Kogan) which uses "hybrid" finite element methods to get around this obstacle.

Host: Xiang Tang