# CAIMS Prize Award

Department of Mathematics and Statistics, University of Toronto

Supervisor: I. Sigal

Thesis title: Some Mathematical Problems in The Ginzburg-Landau Theory of Superconductivity

Abstract:

The thesis studies the Ginzburg-Landau equation describing superconductors. It proves that for superconductors of the first kind, the magnetic vortices are stable for any vorticity n and for superconductors of the second kind, the magnetic vortices with |n|=1 are stable and |n|>1 are unstable. This result proves a conjecture by A. Jaffe and C. Taubs, implicitly assumed in the physics literature since the foundational paper of A. Abrakosov of more than 40 years ago.