【开课说明】

  课程日期：2022年12月20/23/27/30日

  授课时间：09:00 - 12:00

  课时数：4 课时/天，共16课时

  腾讯会议ID： 505 7333 4304  密码：654321

  授课老师：王振富 研究员  北京大学

  主办单位：国家天元数学中部中心、武汉大学数学与统计学院

  欢迎参加课程交流学习！联系人：杨老师 电话：027-68788932   Email:  tmcc@whu.edu.cn

【Abstract】

    This short course will focus on recent progress in the derivation of mean field PDEs from large systems of interacting particles with singular kernels, with or without noise. Motivations are ubiquitous and arise from physics, biology and social sciences, numerical analysis of particle method and stochastic gradient descent, neural networks, etc. We will first review classical methods and results of mean field limit/propagation of chaos and then focus on the recent developed relative entropy/modulated energy based method and BBGKY hierarchy approach for systems with singular interactions.

    Reference:

    1. 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.

    2. S. Serfaty (appendix with M. Duerinckx), Mean Field Limit for Coulomb-Type Flows. Duke Math. J. 169(15) (2020) 2887-2935.

    3. D. Bresch, P.-E. Jabin and Z. Wang, Modulated Free Energy and Mean Field Limit. In S´eminaire Laurent Schwartz — EDP et applications. (2019-2020), Talk no.2, 22 p.

    4. D. Bresch, P.-E. Jabin, and Z.Wang, Mean-field limit and quantitative estimates with singular attractive kernels. arXiv preprint arXiv:2011.08022 (2020).

    5. D. Lacker, Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions, arXiv preprint arXiv:2105.02983 (2021).

    6. D. Bresch, P.-E. Jabin and J. Soler, A new approach to the mean-field limit of Vlasov-Fokker-Planck equations,  arXiv preprint arXiv:2203.15747. (2022).