Mean-Field Limits for Singular Flows

Explore a comprehensive lecture on mean-field limits for singular flows presented by Sylvia Serfaty from New York University at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the analysis of N-point systems with Coulomb or Riesz type singular interactions, evolving through gradient flow or conservative flow, including the point vortex system in 2D, with or without noise. Discover the convergence to mean-field limits using the modulated energy method and its reliance on commutator estimates. Learn about the method's application in achieving global-in-time convergence. Throughout the 57-minute talk, examine key topics such as general interaction kernels, modulated energy and free energy, functional inequalities, Coulomb proofs, and global time conversions, providing a comprehensive overview of this complex mathematical subject.

Introduction
Motivations
General Interaction Kernel
Methods
Modulated Energy
Extensions
Modulated Free Energy
Functional Inequality
Coulomb Proof
Global Time Conversions