Nearly parallel vortex filaments in 3D Ginzburg-Landau theory
DateTuesday, December 4, 2018 - 12:30pm
In this talk I present the derivation of a reduced model for nearly parallel vortex filaments in Ginzburg-Landau theory. The reduced energy of the filaments had been formally derived in many contexts in soft condensed matter (Aftalion-Riviere, del Pino-Kowalczyk) and it was known that its validity would constitute a fundamental step towards solving several open problems in the field. Our main theorem gives the first rigorous proof of this phenomenon. The analysis relies on an improved characterization of the vorticity region and a more precise asymptotic expansion of the energy, valid in this context. This is joint work with Robert L. Jerrard.