以色列魏兹曼的青年数学家Ronen Eldan

                                                    向开南（湘潭大学数学与计算科学学院）

               2022年9月1日星期四

     Ronen Eldan，https://www.wisdom.weizmann.ac.il/~ronene/，2004年数学本科毕业于以色列Open University，2012年纯数学专业博士毕业于以色列Tel Aviv University，目前是以色列The Weizmann Institute of Science（魏兹曼科学院）数学系的副教授，研究兴趣涉及概率、分析、几何、组合、理论计算机科学和机器学习等，是2022年国际数学家大会（ICM）邀请报告者，获Haim Nessyahu Prize（2013, Israel Mathematical Union）、Paul Erdös Prize（2018, Israel Mathematical Union）、Blavatnik Awards（2022），在Invent. Math.（2篇独著）、Duke Math. J.、GAFA、Ann. Proba.、Proba. Th. Rel. Fields.、J. Funct. Anal.、J. ACM.等上发表论文。其获Blavatnik Awards的介绍如下：

Ronen Eldan Receives 2022 Blavatnik Award for Young Scientists in Israel

Ronen Eldan Receives 2022 Blavatnik Award for Young Scientists in Israel - IAS News | Institute for Advanced Study

https://www.ias.edu/news/2022/ronen-eldan-receives-blavatnik-award

Ronen Eldan, current von Neumann Fellow in the School of Mathematics, has received a 2022 Blavatnik Award for his profound contributions to statistics, machine learning, and theoretical computer science.

Eldan is honored for his work solving conjectures in the mathematical theory of high-dimensional phenomena—in addition to his research on high-dimensional probability, the connection between high-dimensional systems and stochastic calculus, the limitations of neural networks in machine learning, and decision-making in artificial intelligence. At the Institute, Eldan is exploring the phenomena that arise when the dimension of the system tends to infinity, manifested in mathematical domains such as probability, analysis, geometry, combinatorics, theoretical computer science, and machine learning.

The Blavatnik Awards for Young Scientists in Israel was established in 2017 as the honor expanded from the United States to include the scientific community of Israel and the United Kingdom. Past recipients have hailed from 48 countries across six continents, with prizes totaling $13.6 million. Previous Blavatnik Laureates include past Visitor in the School of Mathematics Guy Rothblum (2009–11) and past Visiting Professor June Huh (2014–20) who won in 2017（注：June Huh是ICM2022 Fields奖得主）. 

   Granted by the Blavatnik Family Foundation, the New York Academy of Sciences, and the Israel Academy of Sciences and Humanities, The Blavatnik Awards for Young Scientists in Israel comes with a $100,000 reward and an invitation to join the international community of Blavatnik Science Scholars and the annual Blavatnik Science Symposium.

   The Laureates will be formally honored at a ceremony in Tel Aviv-Jaffa on June 8, 2022.

Read more at Blavatnik Awards.

http://blavatnikawards.org/honorees/profile/ronen-eldan

Research Summary: 

The work of Ronen Eldan, PhD, has led to breakthroughs in solving mathematical conjectures that have profound impacts on the fields of statistics, machine learning, and theoretical computer science. His research spans several fields of mathematics, with a focus on high dimensional probability. This subject area deals with the understanding of random systems in which the datasets have many variables or sources of randomness. It aims to find ways to tame the “curse of dimensionality” which refers to the fact that the number of configutations of a system grows exponentially as the number of variables increases making it difficult to analyze or visualize high-dimensional systems.

One of Eldan’s main research endeavors has been to establish connections between the theory of high dimensional phenomena and stochastic calculus, the theory that explains the motion of diffusing particles. These connections have led to an emerging methodology in the field, referred to as “pathwise analysis”. Eldan first developed a new technique, now coined as “Eldan’s stochastic localization”, which can be used obtain insights regarding the behavior of high dimensional distributions. This technique has proved essential towards solving two central problems in the field of convex geometry that have remained unsolved since the 1980s. These two problems—the hyperplane conjecture by Jean Bourgain and the Kannan-Lovász-Simonovits conjecture—reveal some of the fundamental facts about the geometry of high dimensional convex sets. This progress not only opens the door to solve other questions in high dimensional probability, but also gives important insights in the theoretical foundation of machine learning and data science. By further developing the “pathwise analysis” methodology, Eldan was able to solve two conjectures by prominent mathematician Michel Talagrand, and gain beneficial insights in several fields adjacent to high-dimensional probability such as the theory behind processing of noisy data in statistics, the analysis of Boolean functions—a fundamental object in theoretical computer science —as well as for understanding the behavior of many interacting particles in mathematical physics.

On the applied side, Eldan has utilized the theory of high-dimensional phenomena in two main directions. One of them is to understand the limitations of neural networks in terms of its ability to express functions and fit data, and the role of a network’s depth in those limitations. The other one is to provid the first optimal algorithm for the “convex bandit optimization” problem, a central paradigm for decision-making under uncertainty which combines aspects from optimization and reinforcement learning.

The Weizmann Institute of Science（魏兹曼科学院）

魏兹曼科学院位于以色列中部的Rehovot（雷霍沃特）市，建于1934年（当时叫Daniel Sieff Institute），扩建于1949年（用首任以色列总统、著名化学家Chaim Weizmann的名字命名）。它专注于基础科学（物理、化学、数学、生命科学、计算机科学等）的研究与教育，在世界上很有影响力，是以色列最好同时也是犹太世界里最好的科学研究机构。在2011年，魏兹曼科学院被The Scientist杂志评为非美国院校中学术界最佳工作地方。 魏兹曼科学院资金充足，每年都有世界各地的犹太人的慷慨捐助，亦有自己的工业和科技产业，号称有不低于300亿美元的银行存款。魏兹曼科学院规模不大，科学家、博士后、博士生、硕士生、行政职员共计约2500名左右（科学家约1000名、学生约1000名、行政职员约500名）。

从我的专业（概率论）角度，魏兹曼科学院的数学很牛，值得人打内心尊重。一个例子是犹太概率学者Oded Schramm于1999年在Weizmann开创SLE理论，论文正式发表于2000年。此理论自诞生以来，在11年的时间内，已产生2名菲尔兹（Fields）奖得主[Wendelin Werner（2006年）、Stanislav K. Smirnov（2010年）]；在2019年产生了1名数学Wolf奖得主Gregory F. Lawler。实际上，另一位2019年Wolf数学奖得主 Jean-Francois Le Gall 的最主要成就之一就是发展随机平面地图理论理解Schramm在2006年ICM（国际数学家大会）的1小时大会报告中提的一个与2维量子引力有关的公开问题。目前SLE理论及其衍生topic已产生4名ICM 1小时大会报告者[Oded Schramm（2006年）、 Jean-Francois Le Gall（2014）、Gregory F. Lawler（2018年）、Scott Sheffield（2022年）]以及10名ICM邀请报告者。在前述专家中，无疑Schramm最伟大。

Schramm，1961年12月10日出生于耶路撒冷。一个公开的传言是，若晚生3个星期零1天，则他一定能在ICM2002获菲尔兹奖（此奖只颁发给不超过40岁的数学家）。2008年9月1日，Schramm意外死于一次单独登山。

关于Weizmann的概率，见我2015年的博文“攻读概率论博士的好地方：以色列Weizmann”，它仍有参考价值。其链接如下：https://blog.sciencenet.cn/blog-1687789-934091.html