Lipschitz Lectures

The renormalized energy, the Ginzburg-Landau functional, and log gases

Sylvia Serfaty

Date: June 8, 10, 15, 17 and July 6, 8, 2011
Time: 09:00 - 11:00
Location: Lipschitz Lecture Hall, Bonn University, Endenicher Allee 60, Bonn

The lecture at July 8 takes place in kleiner Hörsaal, Wegelerstr. 10, Bonn!


The Ginzburg-Landau model is a famous model for superconductivity. In superconductors submitted to a magnetic field, and in certain regimes, hexagonal lattices of "vortices" appear. They are called Abrikosov lattices. In joint work with Etienne Sandier, we introduced the "renormalized energy" W, a Coulombian interaction between points in the plane, which we derived as a limit of the Ginzburg-Landau functional. I will introduce both the Ginzburg-Landau model and the function W, as well as explain the derivation. I will then discuss the question of minimization of W and its link with the "Abrikosov lattices" in superconductivity. I will finally present the one-dimensional version of W that we introduced, and the relevance of W, both an 1 and 2 dimensions, for the study of the statistical mechanics of "log gases" and random matrix models.