Mircea Petrache. Max- Planck Institute For Mathematics, Bonn
Sharp Asymptotics And Equidistribution For Large Particle Systems With Long-Range Interactions
Sala 1 de la Facultad de Matemáticas de la P. Universidad Católica de Chile
We consider the asymptotic behaviour of systems of a very large number of particles subject to long-range pairwise repulsive interactions. Such questions appear in several branches of mathematics, such as the study of Fekete points in constructive approximation, Ginzburg-Landau vortex models for superconductors, or in the study of random matrices. Jointly with Sylvia Serfaty we obtained the characterization of the behavior of the system at the microscopic scale: When the temperature tends to zero, our gas "crystallizes" to a minimizer of W, conjectured to be the "Abrikosov" triangular lattice in 2 dimensions.
Steps towards such strong structural results are equidistribution results obtained in joint works with Simona Rota-Nodari and the development of tools for studying minimisation problems on lattices, with Laurent Betermin.
I will also mention the link to the asymptotics for multimarginal optimal transport problems appearing in computational chemistry, as well as other future directions of investigation.