Israel Michael Sigal: Magnetic Vortices in Superconductivity

The Ginzburg - Landau theory gives a fairly good macroscopic description of superconductors and the effect of magnetic fields on them. This theory is based on the Ginzburg - Landau equations, a pair of coupled nonlinear equations for the macroscopic wave function (order parameter) and magnetic potential (gauge field). In this talk I will review recent results involving key solutions of these equations - the magnetic vortices, their existence, stability and dynamics.