Geometric Analysis and Topology Seminar

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Decay of excess for the abelian Higgs model

Speaker: Aria Halavati, Courant Institute

Location: Warren Weaver Hall 512

Date: Friday, September 6, 2024, 11 a.m.

Synopsis:

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 a joint work with Guido de Philippis and Alessandro Pigati.