报告人：李磊博士 

单位：上海交通大学数学科学学院自然科学研究所

    (Institute of Natural Sciences; School of mathematical sciences, Shanghai Jiao Tong University)

时间：2019年6月14日（周五）15:30

地点：数学学院报告厅（8318）

报告摘要：The generalized Langevin equation (GLE) with fraction noise has been used widely by biologists and physists to explain some abnormal diffusion behaviors. We consider the generalized Langevin equation with fractional noise in the overdamped regime, which naturally gives the fractional stochastic differential equations (FSDE). In the FSDE, the Caputo fractional derivative and fractional noise are related by fluctuation dissipation theorem. We first investigate the FSDE in theory and show the well-posedness. In the case the force is linear, we can show that the overdampled GLE converges to Gibbs measure in algebraic rate. Since the ergodicity for general potential is unclear, we then investigate this by designing a fast numerical scheme for sampling the overdamped Langevin equation. This talk is based on joint works with Jian-Guo Liu (Duke), Jianfeng Lu (Duke) and Di Fang (UW-Madison).

报告人简介：李磊，上海交通大学数学科学学院长聘教轨副教授。2010 年毕业于清华大学数理基础科学专业，2015 年在 UW-Madison 获得数学博士学位，在校期间分别获得计算机科学理学硕士学位和数学文学硕士学位。2015-2018 年在 Duke 大学担任助理研究教授，2018年至今在上海交通大学担任终身副教授。李磊教授从事应用数学研究，主要包括微分方程分析（PDE 模型，最优传输等，时间分数微分方程），数值 SDEs 和数值 PDEs 与它们的应用 ，以及流体—结构相互作用。迄今在国际期刊发表并出版论文约 20 篇。

望各位老师和同学积极参加！