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# ONLINE PDE LECTURE SERIES

Updated: Jan 17

### Organizer: Quoc-Hung Nguyen, the Academy of Mathematics and Systems Science, Chinese Academy of Sciences.

Speaker: Prof. Sylvia Serfaty, Courant Institute, New York University

Title：Mean-Field limits for systems with singular interactions

Abstract：This course will be concerned with recent developments in the derivation of mean-field evolution PDEs from discrete systems of particles with pair interaction potentials, with or without noise terms. Motivations are numerous and come from physics, biology and social sciences, convergence of particle methods and stochastic gradient descent, neural networks, etc. We will discuss the relative entropy based methods and the modulated energy approach for singular interactions.

References: • Didier Bresch, Pierre-Emmanuel Jabin, and Zhenfu Wang, On mean-field limits and quantitative estimates with a large class of singular kernels: application to the Patlak-Keller-Segel model, C. R. Math. Acad. Sci. Paris, 357(9):708--720, 2019. • Pierre-Emmanuel Jabin and Zhenfu Wang. Quantitative estimates of propagation of chaos for stochastic systems with $W^{-1,\infty}$ kernels, Invent. Math., 214(1):523--591, 2018. • Daniel Lacker, Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions, arXiv preprint arXiv:2105.02983, 2021. • Quoc-Hung Nguyen, Matthew Rosenzweig, and Sylvia Serfaty, Mean-field limits of Riesz-type singular flows with possible multiplicative transport noise, arXiv preprint arXiv:2107.02592, 2021. • Matthew Rosenzweig and Sylvia Serfaty, Global-in-time mean-field convergence for singular Riesz-type diffusive flows. arXiv:2108.09878 • Sylvia Serfaty, Mean field limit for Coulomb-type flows, Duke Math. J., 169(15):2887--2935, 10 2020, Appendix with Mitia Duerinckx.

Time

• Monday, January 10th 2022 , 16:00-17:00 and 21:00-22:00 in Beijing time/ 9:00-10:00 and 14:00-15:00 in Paris time.

• Tuesday, January 11th 2022 , 16:00-17:00 and 21:00-22:00 in Beijing time/ 9:00-10:00 and 14:00-15:00 in Paris time.

• Wednesday, January 12th 2022, 16:00-17:00 and 21:00-22:00 in Beijing time/ 9:00-10:00 and 14:00-15:00 in Paris time.

• Monday, January 17th 2022 , 16:00-17:00 and 21:00-22:00 in Beijing time/ 9:00-10:00 and 14:00-15:00 in Paris time.

Zoom ID924 888 5804 Password：AMSS2022

Brief biography: Professor Sylvia Serfaty is the Silver Professor of Mathematics at the Courant Institute, New York University. She earned her PhD from Université Paris-Sud. Her previous positions include appointments at Université Pierre et Marie Curie and the École Normale Supérieure de Cachan. A large part of her work has focused on the Ginzburg-Landau model of superconductivity and on understanding why and when vortices form triangular lattices. She has more recently turned her attention to questions of statistical mechanics of systems with Coulomb-type repulsion, also arising in approximation theory and random matrices, and which turn out to be generalizations of the questions addressed for the behavior vortices in superconductors. She was a plenary speaker at the ICM Rio in 2018, and is the recipient of the EMS and Henri Poincaré prizes and of the Mergier-Bourdeix prize of the French Academy of Sciences.