Robert Jerrard: Vortex reconnection in the 3d critical Abelian Higgs model

The critical Abelian Higgs model (AHM) is a nonlinear system of wave equations arising in particle physics. We construct solutions of this system in 3+1 dimensions that exhibit $N\ge 2$ slowly-moving nearly parallel vortex filaments, with the leading-order dynamics of this ensemble of filaments described by a wave map into the moduli space, a manifold carrying a natural Riemannian structure that parametrizes stationary 2d solutions of the AHM. These results allow us to study the poorly-understood phenomenon of vortex reconnection in this setting. In particular, we show that in the regime we study, reconnection is the generic outcome of collisions of pairs of vortex filaments. This is joint work with Amirmasoud Geevechi.