Variations of the YangMills Lagrangian in high dimension
Variations of the YangMills Lagrangian in high dimension

Riccardo Caniato, California Institute of Technology
Fine Hall 110
*note location change*
In this talk we will present some analysis aspects of gauge theory in high dimension. First, we will study the completion of the space of arbitrary smooth bundles and connections under L^2control of their curvature. We will start from the classical theory in critical dimension (i.e. n=4) and then move to the supercritical dimension (i.e. n>4), making a digression about the so called “abelian” case and thus showing an analogy between pYangMills fields on abelian bundles and a special class of singular vector fields. In the last part, we will show how the previous analysis can be used in order to build a SchoenUhlenbeck type regularity theory for YangMills fields in supercritical dimension.