Monday

In this talk we illustrate the most salient features of boundary value problems for non-abelian gauge theories over Riemannian manifolds with boundary, and their applications and implications in connection to the fields of geometric analysis and mathematical physics. We define a range of well-posed boundary value problems for the Yang-Mills/ Yang-Mills-Higgs equations, analyzed in comparison to other contexts, such as that of harmonic maps, H-surface equations, and, possibly, the nonlinear sigma model. A Morse theory for the Yang-Mills Dirichlet problem is outlined. This talk includes results derived by the author, individually and collaboratively, over the course of many years [with Isobe, on the existence of non-absolute minimizers and min-max-type solutions, with Moncrief and Maitra, for applications to QFT, with Otway, to frame those results in the context of a nonlinear Hodge-de Rham theory].