**Abstract:**

We first develop random batch methods for classical interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the computational cost is reduced from O(N^2) per time step to O(N), for a system with N particles with binary interactions. For one of the methods, we give a particle number independent error estimate under some special interactions.

This method is also extended to molecular dynamics with Coulomb interactions, in the framework of Ewald summation. We will show its superior performance compared to the current state-of-the-art methods (for example PPPM) for the corresponding problems, in the computational efficiency and parallelizability.

**Biography:**

Shi Jin is the Director of Institute of Natural Sciences, and Chair Professor of Mathematics, at Shanghai Jiao Tong University. He obtained his BS degree from Peking University and his Ph.D. from University of Arizona. He was a postdoc at Courant Institute, New York University,

an assistant and associate professor at Georgia Institute of Technology, and full professor, department chair and Vilas Distinguished Achievement Professor at University of Wisconsin-Madison, Chair of Department of Mathematics at Shanghai Jiao Tong University.

He also serves as a co-director of the Shanghai National Center for Applied Mathematics, director of Ministry of Education Key Lab on Scientific and Engineering Computing, and director of Center for Mathematical Foundation of Artificial Intelligence at Shanghai Jiao Tong University.

He received a Feng Kang Prize of Scientific Computing in 2001. He is an inaugural Fellow of the American Mathematical Society (AMS) (2012), a Fellow of Society of Industrial and Applied Mathematics (SIAM) (2013), an inaugural Fellow of the Chinese Society of Industrial and Applied Mathematics (CSIAM) (2020), and an Invited Speaker at the International Congress of Mathematicians in 2018. In 2021 he was elected a Foreign Member of Academia Europaea and a Fellow of European Academy of Sciences.

His research interests include kinetic theory, hyperbolic conservation laws, quantum dynamics, uncertainty quantification, interacting particle systems and computational fluid dynamics, etc. He has published over 170 research papers.

*Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai*