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2D Coulomb gases, Abrikosov lattices and the Renormalized energy

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If you have a question about this talk, please contact Prof. Clément Mouhot .

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.

This talk is part of the Geometric Analysis & Partial Differential Equations seminar series.

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Engineering Department - Lecture Room 3A Roger Needham Room, Wolfson College, Cambridge, UK, CB3 9BB Divinity School Lecture Theatre, St John's College All Saint's Passage Cambridge CB2 1TP

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