##### Department of Mathematics,

University of California San Diego

****************************

### Math 258

## Davide Parise

#### UCSD

## A gauge-theoretic construction of codimension-two mean curvature flows

##### Abstract:

Mean curvature flow is the negative gradient flow of the area functional, and it has attracted a lot of interest in the past few years. In this talk, we will discuss a PDE-based, gauge theoretic, construction of codimension-two mean curvature flows based on the Yang-Mills-Higgs functionals, a natural family of energies associated to sections and metric connections of Hermitian line bundles. The underlying idea is to approximate the flow by the solution of a parabolic system of equations and study the corresponding *singular limit* of these solutions as the scaling parameter goes to zero. This is based on joint work with A. Pigati and D. Stern.

### June 8, 2023

### 1:00 PM

APM 5829

****************************