##### Department of Mathematics,

University of California San Diego

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### Math 258: Seminar in Differential Geometry

## Dr. Aria Halavati

#### Courant Institute

## Decay of excess for the abelian Higgs model

##### Abstract:

Entire critical points of the abelian Higgs functional are known to blow down to generalized minimal submanifolds (of codimension 2). In this talk we prove an Allard type large-scale regularity result for the zero set of solutions. In the "multiplicity one" regime, we show the uniqueness of blow-downs and classify entire solutions in low dimensions and minimizers in all dimensions; thus obtaining an analogue of Savin's theorem in codimension two. This is based on a joint work with Guido de Philippis and Alessandro Pigati.

### October 31, 2024

### 1:00 PM

APM 7321

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