[math-ias] Analysis seminar on Friday, November 30 at 3:15pm

[Aynur Bulut]

Dear All,

This is a reminder that Israel M. Sigal (of University of Toronto)  
will give a talk at the Analysis seminar tomorrow.

Please find enclosed below the details.

Best, Aynur


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Analysis Seminar

Day: Friday, November 30, 2012
Time: 3:15pm - 4:15pm
Room: S-101
Speaker: Israel M. Sigal
Title: Magnetic Vortices, Nielsen-Olesen-Nambu Strings and Theta Functions

Abstract:



The Ginzburg-Landau theory was first developed to explain magnetic and  
other properties of superconductors, but 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.  
Geometrically, these are equations for the section of the principal  
bundle and the connection on this bundle. (The latest variant of these  
equations is the Seiberg-Witten equations.) Besides of importance in  
physics, they 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  
and vortex lattices, their existence, stability and dynamics, and how  
they relate to the modified theta functions appearing in number theory.