Magnetic vortex lattices

Speaker: 

Israel Michael Sigal

Institution: 

University of Toronto

Time: 

Monday, January 8, 2018 - 2:00pm

Host: 

Location: 

RH 340N

 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. These turned out to have a beautiful structure of (magnetic) vortex lattices discovered by A.A. Abrikosov. (Their discovery was recognized a Nobel prize. Finite energy excitations are magnetic vortices, called Nielsen-Olesen or Nambu strings, in the 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.

Spectral gaps for quasi-periodic Schrodinger operators with Liouville frequencies II

Speaker: 

Yunfeng Shi

Institution: 

Fudan University

Time: 

Thursday, November 16, 2017 - 12:00am

Location: 

rh 340P

We consider the spectral gaps of quasi-periodic Schrodinger operators with Liouville frequencies. By establishing quantitative reducibility of the associated Schrodinger cocycle,  we show that the size of the spectral gaps decays exponentially. This is a joint work with Wencai Liu. 

Combinatorial properties of simple Toeplitz subshifts

Speaker: 

Daniel Sell

Institution: 

Friedrich-Schiller-Universität Jena

Time: 

Thursday, October 26, 2017 - 2:00pm

Location: 

RH 340P

Toeplitz sequences are constructed from periodic sequences with undetermined positions by successively filling these positions with the letters of other periodic sequences. In this talk we will consider  the class of so called simple Toeplitz sequences. We will describe combinatorial properties, such as the word complexity, of the subshifts that are associated with them. The relation between combinatorial properties of the coding sequences and the Boshernitzan condition will be also discussed.

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