Mathematical Colloquium

Tuesday, Jul 16, 2013, 06:00 pm

Vortices and the Ginzburg-Landau Functional

Prof. Dr. Stanley Alama (McMaster University)

Abstract:
The Ginzburg-Landau model is a widely used tool for describing the physical state of superconductors, superfluids, or Bose-Einstein condensates. It also appears in particle physics as the Abelian Higgs model. Ginzburg-Landau is a rich source of interesting phenomena in the calculus of variations and in the study of singularities in solutions to partial differential equations. In this talk, I will start with the basics of Ginzburg-Landau vortices, beginning with
the classical results of Bethuel-Brezis-Hélein. Then I will present some theorems on vortex lines for the 3D Ginzburg-Landau model, in the context of Gamma-convergence. Finally, I will present an overview of some recent results on the effect of anisotropy in the mathematical study of superconductors. Anisotropic models are important for the understanding of the high-temperature superconductors, and they present some interesting mathematical results and challenges.

Time: 06:00 pm

Location: Hörsaal III, Hauptgebäude, RWTH Aachen, Templergraben 55, 52062 Aachen