Abstract: We are interested in systems of points in the plane with Coulomb interaction. An instance is the classical 2D Coulomb gas, 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. In joint work with Etienne Sandier, we studied both systems and derived a “Coulombian renormalized energy”. I will present it, examine the question of its minimization and its link with the Abrikosov lattice and weighted Fekete points. I will describe its relation with the statistical mechanics models mentioned above and show how it leads to expecting crystallisation in the low temperature limit.
Sylvia Serfaty is a Professor of Mathematics at the Université Pierre et Marie Curie – Paris 6, and a Global Distinguished Professor at the Courant Institute of Mathematical Sciences, New York University. She studied at the Ecole Normale Supérieure in Paris and earned her PhD in mathematics in 1999 at the University of Paris Sud-Orsay. She then was a CNRS researcher, and was on the faculty at the Courant Institute of New York University from 2001 to 2008.
She was an Invited Speaker at the International Congress of Mathematicians in 2006. She received an NSF Career award in 2003, a European Mathematical Society Prize in 2004, a EURYI award in 2007, and the Henri Poincaré Prize of the IAMP in 2012. Her work has addressed PDE and variational models coming mostly from physics, and particularly vortices and phase transitions in the Ginzburg-Landau model of superconductivity. More recently she has gotten interested in Coulomb systems.