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SUMMARY:Convergence of the self-dual U(1)-Yang-Mills-Higgs energies to the
  (n - 2)-area functional - Davide Parise (Cambridge)
DTSTART:20220516T130000Z
DTEND:20220516T140000Z
UID:TALK174332@talks.cam.ac.uk
CONTACT:Dr Greg Taujanskas
DESCRIPTION:We overview the recently developed level set approach to the e
 xistence theory of minimal submanifolds and present some joint work with A
 . Pigati and D. Stern. The underlying idea is to construct minimal hypersu
 rfaces as limits of nodal sets of critical points of functionals. After st
 arting with a general overview of the codimension one theory\, we will mov
 e to the higher codimension setting\, and introduce the self-dual Yang-Mil
 ls-Higgs functionals. These are a natural family of energies associated to
  sections and metric connections of Hermitian line bundles\, whose critica
 l points have long been studied in gauge theory. We will explain to what e
 xtent the variational theory of these energies is related to the one of th
 e (n - 2)-area functional and how one can interpret the former as a relaxa
 tion/regularisation of the latter. We will mention some elements of the pr
 oof\, with special emphasis on the role played by the gradient flow. 
LOCATION:CMS\, MR15
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