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2018菲尔兹奖获得者Alessio Figalli教授做客线上“自然科学杰出演讲系列讲座”“Distinguished Lecture in Natural Sciences” by Chair Professor Alessio Figalli,2018 Fields Medalist

6月19日下午,2018菲尔兹奖获得者、苏黎世联邦理工学院讲席教授Alessio Figalli做客第11期“自然科学杰出演讲系列讲座”,以“障碍问题的一般正则性”为题,为海内外师生带来一场妙趣横生的学术报告。本次报告由自然科学研究院院长金石教授主持,来自数学科学学院、物理与天文学院、致远学院以及海内外其他高校的近500名师生在线聆听。

讲座伊始,Figalli教授回忆了2011年来访上海交大的难忘经历。

本次报告中,Figalli教授指出,一个重要的问题是研究自由边界奇点集的大小与结构等。他首先由经典的自由边界问题——Stefan问题讲起,对Laplace方程障碍问题的重要进展进行回顾,随后展示了他与合作者关于自由边界奇点集大小的估计及奇点集结构的重要结果,由此解决Schaffer猜想。最后,分享了关于原始Stefan问题的最新研究进展。

Figalli教授热情洋溢的报告感染了听众,引发师生深入思考。在问答环节中,Figalli教授就高阶方程的障碍问题,一般椭圆型方程的障碍问题奇点集的估计,Bernoulli型自由边界问题正则性等方面与参会者展开了热烈的讨论。

嘉宾介绍

Alessio Figalli,2018 菲尔兹奖获得者,苏黎世联邦理工学院讲席教授、FIM数学研究所负责人。 Alessio Figalli教授一直致力于最优运输理论,利用最优的技术来获得各向异性不均匀性的改进版本,并在最优运输理论及其在偏微分方程、度量几何和概率方面的应用做出了突破性贡献。2018年,34岁的Alessio Figalli教授获菲尔兹奖。 此前,Alessio Figalli教授曾获2011 Peccot-Vimont奖,2012 EMS奖,2012 法兰西学院Peccot奖,2015 Stampacchia奖章以及2017 Feltrinelli数学奖。2014年,Alessio Figalli教授在第27届国际数学家大会作45分钟邀请报告。


Alessio Figalli, 2018 Fields Medalist and Chair Professor of ETH Zurich was invited to deliver the 11th “Distinguished Lecture in Natural Sciences” at INS. The lecture “Generic Regularity in Obstacle Problems” has amazed faculty and students from home and abroad. This lecture was chaired by Professor Shi Jin, Director of the Institute of Natural Sciences. About 500 professors and students from the School of Mathematical Sciences, the School of Physics and Astronomy and Zhiyuan College from SJTU, and other domestic and overseas universities participated in the online conference.

At the beginning of the talk, Prof. Figalli recalled his unforgettable experience of visiting Shanghai Jiao Tong University in 2011. In the talk, Prof. Figalli drew attention to the importance of studying problems related to the size and structure of singular sets of the free boundary. He started from the classical free boundary problem, the Stefan problem, and reviewed important progress in obstacle problems of the Laplace equation. Then he presented their significant progress on the structure for the singular sets of the free boundary. This helped to solve the Schaffer conjecture. Finally, he shared the very recent progress on the original Stefan problem.

The enthusiastic lecture by Prof. Figalli inspired listeners and encouraged them to think more deeply about the important problems he raised. In the Q & A session of the lecture, Prof. Figalli had an in-depth discussion with the participants on many topics including obstacle problems for higher-order equations, estimates for the singular sets of obstacle problems for general elliptic equations and regularity theory for the Bernoulli-type free problems.

Bio

Alessio Figalli,2018 Fields Medalist,Chair Professor and the director of the “FIM-Institute for Mathematical Research” at ETH Zurich. Prof. Figalli has been devoted to the theory of optimal transportation and uses the most cutting-edge techniques to obtain an improved version of anisotropic inhomogeneity. He made breakthrough contributions in the theory of optimal transportation and its application to partial differential equations, metric geometry and probability. In 2018, Prof. Figalli won the Fields Medal at the age of 34. Prof. Figalli has won an EMS Prize in 2012, the Peccot-Vimont Prize 2011, the Peccot 2012 of the Collège de France, the 2015 edition of the Stampacchia Medal, and the 2017 edition of the Feltrinelli Prize for mathematics. He was an invited speaker at the 27th International Congress of Mathematicians in 2014.