Sylvia Serfaty, University Pierre et Marie Curie Paris VI and Courant Institute

TITLE AND ABSTRACT:

Crystallisation in 2D Coulomb systems.
We are interested in the classical two-dimensional Coulomb gas. 
Zero temperature states correspond to "weighted Fekete sets", 
and certain particular temperature states correspond 
to some random matrix ensembles. We connect the problem to the 
"renormalized energy"  W, a Coulombian interaction for an infinite set 
of points in the plane that we introduced with Etienne Sandier 
in connection to the Ginzburg-Landau model, and whose minimum 
is expected to be achieved by the "Abrikosov" 
triangular lattice. Results include a next order asymptotic expansion of the 
partition function, and various characterizations of the behavior 
of the system at the microscopic scale. When the temperature tends to zero 
we show that the system tends to "crystallize" 
to a minimizer of W. This is based on joint works with Etienne Sandier, 
and some with Simona Rota Nodari.