01/08/2020: L^p-bounded curvatures in high dimensions

January 8, 2020
TITLE: L^p-bounded curvatures in high dimensions

ABSTRACT: In this talk we shall be presenting some analysis aspects of gauge theory in high dimension. In the first part we will study the completion of the space of arbitrary smooth bundles and connections under L^p-control of their curvature. We will first recall the classical theory in critical dimension (i.e. p=n/2) and then move to the super-critical dimension (i.e. p<n/2). In a second part we will explain how the previous analysis can be used to study the variations of Yang-Mills lagrangian as well as the weak closure of smooth Yang-Mills Fields in arbitrary dimension. If time permits, in the last part of the talk, we will study the space of weak unitary connections over complex manifolds with 1-1 curvatures.