Limiting vorticities in superconductivity

In analogy with fluid mechanics, to the superconducting current in the model of Ginzburg and Landau can be associated a vorticity, which in the extreme type II limit and under natural hypothesis converges to a measure. Over the years, in joint work with Sylvia Serfaty, we have studied these measures. We describe here some old and recent results, as well as open problems.