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Explore mean-field limits and the derivation of effective evolution equations for systems of N points in singular interaction through this mathematical lecture. Examine joint research with Matt Rosenzweig, Antonin Chodron de Courcel, Hung Q. Nguyen, and Elias Hess-Childs focusing on Coulomb or Riesz interactions evolving by gradient flow or conservative flow, including point vortex systems in 2D with or without noise. Learn how convergence to mean-field limits using the modulated energy method relies on functional inequalities of commutator estimate type. Discover various approaches to proving commutator estimates and recent progress providing sharp and localizable estimates. Investigate the question of obtaining global-in-time convergence and its connection with modulated log-Sobolev inequalities, gaining insights into advanced mathematical techniques for analyzing complex dynamical systems.
