7. John von Neumann Lecture: Prof. Dr. Sylvia Serfaty (Laboratoire Jacques-Louis Lions
Université Pierre et Marie Curie Paris 6, Courant Institute, New York): Questions of crystallization in systems with Coulomb and Riesz interactions
Donnerstag, 13.11.2014 16:30 im Raum M5
We are interested in systems of points with Coulomb, logarithmic or more generally Riesz interactions (i.e. inverse powers of the distance). They 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, a third is the study of Fekete points which arise
in approximation theory. We describe tools to study such systems and
derive a next order (beyond mean field limit) ``renormalized energy"
that governs microscopic patterns of points. We present the
derivation of the limiting problem and the question of its
minimization and its link with the Abrikosov lattice and
crystallization questions, and also discuss the statistical mechanics
of such systems.