The equations of the Ginzburg-Landau theory of superconductivity retain
their mathematical fascination. The talk will discuss various results
concerning the vortex solutions in two dimensions at the critical point
between the Type I and Type II regime. Here vortices neither attract
nor repel, so there are many static vortex and multi-vortex solutions.
These also exist in curved background geometries. In a model where the
vortices can move ballistically, one can study the effective mass of one
vortex, what happens in vortex collisions, and the properties of an
interacting gas of many vortices. There are some precise but surprising
mathematical results here. Whether they have physical relevance is (at
least for the speaker) an open issue.