Department of Mathematics

Department of Mathematics Seminars and Talks

 

Seminar

Fields Geometric Analysis Colloquium

Talk Information
Title
Nonabelian Yang-Mills-Higgs and Plateau’s problem in Codimension Three
Start date and time
14:00 on Tuesday April 22, 2025
Duration in minutes
60 (until 15:00 on Tuesday April 22, 2025)
Room
FI210, Fields Institute, 222 College St.
Streaming link
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Abstract

In this talk, we will discuss the asymptotic behavior of the SU(2)-Yang-Mills-Higgs energies in the large mass limit, and see how they converge to the codimension three area functional in the sense of De Giorgi’s Gamma-convergence. This is motivated by analogous phenomena in the codimension one (i.e. Allen-Cahn) and codimension two (i.e. Ginzburg-Landau and abelian Yang-Mills-Higgs) settings. To illustrate the geometric content of this convergence result, we will see that area-minimizing (n − 3)-cycles can be approximated locally by minimizers (or minimizing sequences) for the SU(2)-Yang–Mills–Higgs energy; in other words, Plateau’s problem in codimension three can be solved by gauge-theoretic means. These results provide evidence for predictions of Donaldson and Segal in the setting of G2 manifolds and Calabi-Yau 3-folds. The talk is based on joint work with A. Pigati, and D. Stern.

Speaker Information
Full Name
Davide Parise
Personal website
Institution
University of California, San Diego
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