Fifty Years of Number Theory and Random Matrix Theory

数论和随机矩阵论五十年

• 批准号: 2200884
• 负责人: John Conrey
• 金额: $ 5万
• 依托单位: American Institute of Mathematics
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-04-01 至 2023-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2200884&HistoricalAwards=false
• 关键词: Fifty; Years; Number; Theory; Random

This award provides partial support for attendees at "50 Years of Number Theory and Random Matrix Theory Conference," which will take place at the Institute for Advanced Study on June 21-24, 2022. This conference will bring together people from two different areas: Number Theory and Random Matrix theory to discuss the ideas that are relevant to both fields. In the last 50 years there has been a large body of compelling work that uses Random Matrix Theory and gets to the very heart of some of the most important problems in Number Theory. The conference will give a historical perspective but will also be very forward looking in its emphasis on contemporary research. The award will support about 30 participants with an emphasis on supporting early career researchers as well as members of under-represented groups. The talks will be streamed and recorded so that they can be available to a wide audience.Mathematicians realized 50 years ago that the zeros of the Riemann zeta-function are distributed like the eigenvalues of large random Hermitian matrices with normally distributed entries. That discovery set things in motion, which in the past 20 years have really taken off. Learning how to use Random Matrix Theory as a model and guide to understanding the interesting arithmetic statistics of families of L-functions is indispensable for today's researcher. This conference will highlight some of the past achievements but will concentrate on current work, such as Paul Nelson's groundbreaking work on subconvexity for L-functions attached to automorphic forms on GL(n), that is paving the way for future work.The relevant website is https://www.ias.edu/math/events/50yntrmtThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项将在2022年6月21日至24日在高级研究研究所举行的“ 50年的数字理论和随机矩阵理论会议”上为与会者提供部分支持。该会议将使来自两个不同领域的人们聚集在一起：数字理论和随机矩阵理论，讨论与这两个领域相关的想法。在过去的50年中，有大量引人注目的作品使用随机矩阵理论，并成为数字理论中一些最重要问题的核心。该会议将提供历史观点，但在重点是当代研究的重点也将非常前瞻性。 该奖项将支持大约30名参与者，重点是支持早期职业研究人员以及代表性不足的团体成员。演讲将被流式传输和录制，以便可以向广大的观众提供。50年前，我意识到，Riemann Zeta-function的零是像大型随机遗传学矩阵的特征值一样分发的，具有正常分布的条目。这一发现引发了人们的行动，在过去的20年中，这些发现确实脱颖而出。学习如何使用随机矩阵理论作为模型和指南，以理解L功能家族的有趣算术统计数据对于当今的研究人员来说是必不可少的。这次会议将重点介绍过去的一些成就，但将集中在当前的工作上，例如保罗·尼尔森（Paul Nelson）在GL（N）上附带的L型功能的subevexity上的突破性工作，这为将来的工作铺平了道路。认为值得通过基金会的智力优点和更广泛影响的评论标准来评估值得支持。