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

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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.