时间：2026.3.27（周五）9：00-10：00

地点：数学楼423

报告人：周珍楠，研究员, 西湖大学

报告题目：Fokker-Planck equations of neuron ensembles: numerical simulation and dilating the blowup solution

报告摘要：In this talk, we consider the Fokker-Planck equations associated with the Nonlinear Noisy Leaky Integrate-and-Fire model for neuron networks. Due to the jump mechanism at the microscopic level, these equations feature an unconventional structure: transporting the boundary flux to a specific interior point.

In the first part, we present a conservative and positivity-preserving finite difference scheme for these equations. For the linear case, the semi-discrete scheme satisfies a discrete relative entropy estimate that captures the correct long-time asymptotic behavior, and extensive numerical tests demonstrate its capability in resolving finite-time blowup, equilibrium convergence, and time-periodic solutions in variant models.

In the second part, we address the challenge of solution breakdown by introducing a new notion of generalized solutions via dynamical time rescaling. This approach systematically dilates the time variable near singularities, allowing the extension of physical solutions beyond finite-time blowups and providing a consistent framework to continue the dynamics after the firing threshold collapses.

报告人简介：周珍楠，西湖大学数学副教授。2014 年在美国威斯康辛大学麦迪逊分校获得博士学位，2014-2017 年在美国杜克大学担任助理研究教授，2017 年加入北京大学北京国际数学研究中心担任助理教授，2024年加入西湖大学理论科学研究院和交叉科学中心。主要研究领域为微分方程的应用分析，微分方程数值解，应用随机分析，随机模拟等，特别是关注来源于自然科学的应用数学问题。入选国家级人才项目，目前担任Studies in Applied Mathematics，Communications in Mathematical Sciences，Mathematical Medicine and Biology: A Journal of the IMA等国际著名期刊的编委。