Title: Topics in Analysis of Many Particle Systems Abstract: This summer course will present
Speaker: Dr. Zhenfu Wang (University of Pennsylvania)
Time: 9:00-10:30, every Mon.& Wed. between Aug. 17 th and Sep. 2nd
Meeting ID: TBA
Password: TBA

some mathematical tools and concepts for the rigorous derivation and study of nonlinear partial differential equations (PDE's) arising from many-particle limits: (McKean-)Vlasov type equations, the vorticity formulation of the 2D incompressible Euler/Navier-Stokes equations, Boltzmann collision equations, nonlinear diffusion equations, quantum Hartree equations... Depending on time and interest it will include part or all of the following topics: the Liouville/Master equations of N-particle systems, the notion of empirical measures, the BBGKY hierarchy,the Hewitt-Savage theorem, the Dobrushin's stability estimate, the coupling method, the concepts of chaos and entropic chaos, the recent progresses on the mean-_eld limit, in particular, the relative entropy/modulated potential energy/modulated free energy methods as introduced in：
——P.-E. Jabin and Z. Wang, Mean Field Limit and Propagation of Chaos for Vlasov Systems with Bounded Forces. J. Funct. Anal. 271 (2016) 3588{3627.
——P.-E. Jabin and Z. Wang, Quantitative estimates of propagation of chaos for stochastic systems with W-1，∞ kernels. Inventiones mathematicae 214(1) (2018) 523{591.
——S. Serfaty (appendix with M. Duerinckx), Mean Field Limit for Coulomb-Type Flows. To appear in Duke Math. J.
——D. Bresch, P.-E. Jabin and Z. Wang. On mean-_eld limits and quantitative estimates with a large class of singular kernels: Application to the Patlak{Keller{Segel model. Comptes Rendus Mathematique 357(9) (2019) 708{720.