THEMATIC PROGRAMS

September 19, 2014
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

Thematic Program on Variational Problems in Physics, Economics and Geometry

Coxeter Lecture Series
September 29, 30 and October 1 , 2014 at 3:30 p.m

Fields Institute, Room 230

SYLVIA SERFATY
Université Pierre et Marie Curie Paris 6

Systems with Coulomb interaction: from variational study to statistical
mechanics


Abstract:
Systems of particles with Coulomb and logarithmic interactions arise in various settings: an instance is the classical Coulomb gas which in some cases happens to be a random matrix ensemble, another is vortices in the Ginzburg-Landau model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns, named Abrikosov lattices in physics, a third is the study of Fekete points which arise in approximation theory. I will describe tools to study such systems and derive a next order (beyond mean field limit) "renormalized energy" that governs microscopic patterns of points. I will present the derivation of this limiting problem, and discuss the question of its minimization and its link with the Abrikosov lattice and crystallization questions. I will also discuss generalizations to Riesz interaction energies, and the statistical mechanics of such systems.
This is based on joint works with Etienne Sandier, Nicolas Rougerie, Simona Rota Nodari, Mircea Petrache, and Thomas Leblé.

Speakers in the Distinguished and Coxeter Lecture Series have made outstanding contributions to their field of mathematics. The Lecture Sereies consists of three one-hour lectures.

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