FRG: Random matrix models, zeros of L-functions, and arithmetic

本项目涉及数论中的基本问题、L函数的解析性质和随机矩阵理论之间的深层联系。研究人员将进行一系列项目，旨在建立算术和L函数零点的随机矩阵猜想之间的联系。这些结果将使数论中长期存在的问题取得重大进展。相反，这些算术问题的进展将导致随机矩阵理论的新结果。这项建议中的工作将扩展最近发现的数论问题与数学物理结果之间的联系。通过探索数论L函数与物理学家发展的随机矩阵理论技术之间的关系，有望取得重大进展。这项工作将把不同领域的研究人员聚集在一起，并通过研究生和博士后研究员的参与，为这两个研究领域之间更紧密的联系提供机会。它还将向本科生介绍科学研究的性质。最后，将在拟议工作最后一年的讲习班和会议上介绍这一领域的进展情况。这些论坛旨在向研究生和博士后介绍这些领域的新发展，这些论坛将规划出这笔赠款所取得的进展，并为参与者进一步开展这项工作做好准备。

Summary for award DMS-0244660This project concerns deep connections between fundamental questions innumber theory, analytic properties of L-functions, and random matrixtheory. The investigators will undertake a series of projects aimed atestablishing links between arithmetic and the random matrix conjecturesfor zeros of L-functions. These results will lead to significant progresson long-standing questions in number theory. Conversely, progress onthese arithmetic questions will lead to new results in random matrixtheory.The work in this proposal will extend recently discovered connectionsbetween problems in number theory and results in mathematical physics.Significant progress is anticipated by exploring the relationship betweennumber theoretic L-functions and the random matrix theory techniques developed by physicists. This work will bring together researchers in different fields and, through the participation of graduate students and postdoctoral fellows, provide an opportunity for stronger connections between these two research areas. It will also introduce undergraduate students to nature of scientific research. Finally, progress in this area will be presented at a workshop and conference in the final year of the proposed work. Designed to introduce graduate students and postdocs to new developments in these fields, these forums will map out the progress made by this grant and prepare the participants to extend this work.