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.
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Ort: Hörsaal V Hauptgebäude, Templergraben 55, 52062 Aachen