Michael Loss: Some results for functionals of Aharanov-Bohm type

Abstract: In this talk I present some variational problems of Aharanov-Bohm type, i.e., they include a magnetic flux that is entirely concentrated at a point. This is maybe the simplest example of a variational problem for systems, the wave function being necessarily complex. The functional is rotationally invariant and the issue to be discussed is whether the optimizer have this symmetry or whether it is broken.