Department of Mathematics,
University of California San Diego
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Math 258 - Differential Geometry Seminar
Dr. Riccardo Caniato
California Institute of Technology
Variations of the Yang-Mills Lagrangian in high dimension
Abstract:
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^2-control of their curvature. We will start from the classical theory in critical dimension and then move to the supercritical dimension, 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.
Hosts: Davide Parise and Luca Spolaor
May 30, 2024
11:00 AM
APM 7321
Research Areas
Differential Equations Geometric Analysis Geometry and Topology****************************
