##### 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****************************