Onset of vorticity and interaction between vortex lines in the 3D Ginzburg-Landau model of superconductivity

The Ginzburg-Landau model is a phenomenological description of superconductivity. A crucial feature in type II superconductors is the occurrence of vortex lines, which appear above a certain value of the strength of the applied magnetic field called the first critical field. In this talk I will present a sharp estimate of this value and report on a joint work with Etienne Sandier and Sylvia Serfaty in which we study the onset of vortex lines and derive an interaction energy for them. In particular, we will show that this onset of vorticity is directly related to an "isoflux problem" on curves (finding a curve that maximizes the ratio of a magnetic flux by its length).