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Explore two mathematical methods for deriving singular mean-field limits in this 54-minute lecture by Sylvia Serfaty from Sorbonne Université, presented at the Institut des Hautes Etudes Scientifiques (IHES). Examine the fundamental question of mean-field limits and learn how to derive effective evolution equations of PDE type for systems of N points in singular interaction, particularly those of Coulomb or Riesz nature, evolving through first-order dynamics. Discover the modulated energy method, which proves effective for gradient flows or conservative flows of Coulomb/Riesz type energies, and understand a novel approach based on multiscale mollification metric that works well for interactions up to Coulomb singularity without requiring extensive structural assumptions. Gain insights into advanced mathematical techniques for handling singular interactions in many-particle systems and their applications to partial differential equations.
