Computational and Applied Mathematics seminar

Abstract: In this talk I will present ongoing work on finite element discretization of Yang–Mills connections on principal bundles. To approximate Yang–Mills connections numerically, we first choose local sections and partition the base manifold. This allows us to represent connections as piecewise 1-forms with trace jumps across interfaces prescribed by the sections. For bundles with abelian structure group, enforcing these jumps via Lagrange multipliers leads to a well-posed saddle-point problem that can be solved using finite element methods. We illustrate the method on the Hopf bundle.