Distinguished Lecture Series in Mathematics 系列数学前沿学术讲座  

   报告题目：PDEs for neural assemblies; analysis, simulations and behavior but it could also be on tumor growth

    报告人：Prof. Benoit Perthame（Laboratoire J.-L. Lions, Sorbonne Universit'e）

    报告时间：2024年 9月2日（周一）10:30-11:30 

    报告地点：校本部教二727

    报告人简介：Benoit Perthame教授是法国科学院院士、欧洲科学院院士（Member of European Academy of Sciences）、欧洲人文和自然科学院院士（Member of Europaea Academia）、法国巴黎第六大学(UMPC)终身教授和巴黎第六大学Jacques-Louis Lions实验室主任，他是法国国家信息与自动化研究所（INRIA）合作者和风暴团队（Team Bang）创始人、欧洲科学院数学部主任。Benoit Perthame教授从事非线性偏微分方程及其应用的研究，包括双曲守恒律方程组、动理学方程、Hamilton-Jacob方程等，作出了多项有重要国际影响的创新成果，被国际顶尖期刊Journal of the American Mathematical Society，Inventiones Mathematicae，Communications on Pure & Applied Mathematics等接受发表。Benoit Perthame教授2023年依托yl9193永利官网申报获北京科学技术奖国际合作中关村奖，曾先后应邀在国际数学家大会(ICM)上做1小时大会邀请报告（2014年）和45分钟邀请报告（1994年）、在国际工业与应用数学联合会(ICIAM)上做大会邀请报告（2011年），曾获“法国科学院INRIA大奖”（2015年）和“欧洲科学院Blaise Pascal奖”（2013年）。此外，他曾担任多个国际知名杂志（如SIAM J. Analysis, CPDE等）的编委，也是Springer、Birkhauser 图书系列等的主编。

    摘要：Neurons exchange information via discharges propagated by membrane potential which trigger firing of the many connected neurons. How to describe large assemblies of such neurons? How can such a network generate a collective activity?

Such questions can be tackled using nonlinear partial-integro-differential equations which are classically used to describe neuronal assemblies. Among them, the Wilson-Cowan equations are the best known and describe globally brain spiking rates. Another classical model is the integrate-and-fire equation based on Fokker-Planck equations. The spike times distribution, which encodes more directly the neuronal information, can also be described directly thanks to structured population.

We will compare and analyze these models. A striking observation is that solutions to the I\&F can blow-up in finite time, a form of synchronization that can be regularized with a refractory stage. We can also show that for small or large connectivities the 'elapsed time model' leads to desynchronization. For intermediate regimes, sustained periodic activity occurs compatible with observations. A common tool is the use of the relative entropy method.

举办单位：yl9193永利官网、交叉科学研究院

          北京国家应用数学中心、北京成像理论与技术高精尖创新中心  

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