Mathematical Colloquium

Friday, April 20, 2018, 2:15pm

Magnetic vortex lattices

Israel Michael Sigal (University of Toronto)

The Ginzburg - Landau equations play a fundamental role in various areas of physics, from superconductivity to elementary particles. They present the natural and simplest extension of the Laplace equation to line bundles. Their non-abelian generalizations - Yang-Mills-Higgs and Seiberg-Witten equations have applications in geometry and topology.

Of a special interest are the least energy (per unit volume) solutions of the Ginzburg - Landau equations. Though the equations are translation invariant, these turned out to have a beautiful structure of (magnetic) vortex lattices discovered by A.A. Abrikosov. (Their discovery was recognized by a Nobel prize. Finite energy excitations are magnetic vortices, called Nielsen-Olesen or Nambu strings, in particle physics.)

I will review recent results about the vortex lattice solutions and their relation to the energy minimizing solutions on Riemann surfaces and, if time permits, to the microscopic (BCS) theory.

Wir laden herzlich alle Interessierten zu diesem Vortrag ein.

Ort: Hörsaal V Hauptgebäude, Templergraben 55, 52062 Aachen