Fifty Years of Number Theory and Random Matrix Theory

American Institute Of Mathematics, Pasadena CA

Investigators

Abstract

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/50yntrmt This 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.