# The parabolic U(1)-Higgs equations and codimension-two mean curvature flows

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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.