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All colloquia (unless otherwise stated) will take place on Tuesdays at 3.00pm in Room 505 in the Mathematics Department (25 Gordon Street). See see how to find us for further details. There will be refreshments afterwards in Maths Room 502. If you require any more information on the Departmental Colloquia please contact Prof Dima Vassiliev e-mail: d.vassiliev AT ucl.ac.uk or tel: 020-7679-2442.
10 March 2015
Prof Sylvia Serfaty - Université Pierre et Marie Curie
Title: Crystallization questions for large systems with Coulomb and Riesz interactions
This is based on joint works with Etienne Sandier, Nicolas Rougerie, Simona Rota Nodari, Mircea Petrache, and Thomas Leblé.
Abstract:
Systems of particles with Coulomb, Riesz and logarithmic interactions arise in various settings : one 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. We will describe tools to study such systems and derive a next order (beyond mean field limit) "renormalized energy" that governs microscopic patterns of points and discuss its link with the Abrikosov lattice and crystallization questions. We will also address the statistical mechanics of such systems and how the temperature influences the disorder of the system.