Fifty Years of Number Theory and Random Matrix Theory

该奖项为将于2022年6月21-24日在高等研究院举行的“数论和随机矩阵理论50年会议”的与会者提供部分支持。这次会议将聚集来自两个不同领域的人：数论和随机矩阵理论，讨论与这两个领域相关的想法。在过去的50年里，已经有大量引人注目的工作使用了随机矩阵理论，并深入到了数论中一些最重要的问题的核心。这次会议将提供历史视角，但在强调当代研究方面也将非常具有前瞻性。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群体的成员。50年前，数学家们意识到Riemann Zeta函数的零点的分布就像具有正态分布的大型随机厄米特矩阵的特征值一样。这一发现推动了事情的发展，在过去的20年里，这一发现确实取得了进展。学习如何利用随机矩阵理论作为模型和指南来理解L函数族的有趣的算术统计是当今研究人员不可缺少的。这次会议将突出一些过去的成就，但将集中在当前的工作，如保罗·纳尔逊在L的次凸性方面的开创性工作-附加到GL(N)上的自同构形的函数，这为未来的工作铺平了道路。相关网站是https://www.ias.edu/math/events/50yntrmtThis奖反映了国家科学基金会的法定使命，并已被认为值得支持，通过使用基金会的智力价值和更广泛的影响审查标准进行评估。

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.