Analysis and Geometric Analysis Seminar
Riccardo CaniatoETH Zurich
Variations of Yang-Mills lagrangians in high dimension
Monday, April 17, 2023 - 2:40pm
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^p-control of their curvature. We will start from the classical theory in critical dimension (i.e. n=2p) and then move to the super-critical dimension (i.e. n>2p), making a digression about the so called “abelian” case and thus showing an analogy between p-Yang-Mills 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 Schoen-Uhlenbeck type regularity theory for Yang-Mills fields in supercritical dimension.