The APDE seminar on Monday, 11/03, will be given by Robert Jerrard (Toronto) in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PDT. To participate, please email Adam Black (adamblack@berkeley.edu).

Title: Vortex reconnection in 3d near-critical Abelian Higgs models

Abstract: The critical Abelian Higgs model (AHM) is a system of nonlinear wave equations arising in particle physics. We construct solutions of this system in 3+1 dimensions that exhibit a number of slowly-moving nearly parallel vortex filaments. The leading-order dynamics of this ensemble of filaments are described by a wave map into the modulo space, a manifold carrying a natural Riemannian structure that parametrizes stationary 2D solutions of the AHM. These results allow for the study of the poorly-understood phenomenon of vortex reconnection in this setting. In particular, it is shown that in the regime studied, reconnection is the generic outcome of collisions of pairs of vortex filaments. Extremely similar results are also proved for the critical Abelian Higgs heat flow, modeling certain superconductors, near-critical versions of these equations, and in higher dimensions. This work is joint with Masoud Geevechi.