Mirimanoff Lecture 2015 : Magnetic Vortices, vortex lattices and automorphic functions (Israel Michael Sigal, University of Toronto and ETHZ)

10.12.2015 14:30

The Ginzburg - Landau theory was first developed to understand behaviour of superconductors, but has had a profound influence on physics well beyond its original area. It had the first demonstration of the Higgs mechanism and it became a fundamental part of the standard model in the elementary particle physics. The theory is based on a pair of coupled nonlinear equations for a complex function (called order parameter or Higgs field) and a vector field (magnetic potential or gauge field). They are the simplest representatives of a large family of equations appearing in physics and mathematics.

Besides of their importance in physics, the equations contain beautiful mathematics (some of the mathematics was discovered independently by A. Turing in his explanation of patterns of animal coats). In this talk I will review recent results involving key solutions of these equations - the magnetic vortices (called Nielsen-Olesen or Nambu strings in the particle physics) and vortex lattices, their existence and stability and how they relate to the modified theta functions appearing in number theory and algebraic geometry. Certain automorphic functions play a key role in the theory described in the talk.

Lieu

Bâtiment: Ecole de Physique

Stueckelberg Auditorium (Att. unusual time and place)
24 Quai E.-Ansermet
1205 Genève

entrée libre