We consider a system of N particles evolving according to the gradient flow of their Coulomb or Riesz interaction, or a similar conservative flow, and possible added random diffusion. By Riesz interaction, we mean inverse power s of the distance with s between d-2 and d where d denotes the dimension. We present a convergence result as N tends to infinity to the expected limiting mean field evolution equation. We also discuss the derivation of Vlasov-Poisson from newtonian dynamics in the monokinetic case, as well as related results for Ginzburg-Landau vortex dynamics.

Bio: Sylvia Serfaty is Silver Professor of Mathematics at the Courant Institute of Mathematical Sciences of New York University. She earned her PhD in 1999 from the Université Paris Sud Orsay, and has held positions at New York University and Université Pierre et Marie Curie (now Sorbonne Université). Recipient of the EMS and Henri Poincaré prizes, plenary speaker at the ICM, she is also a member of the American Academy of Sciences.