50 Years of Number Theory and Random Matrix Theory Conference
Organizers:
Brian Conrey, American Institute of Mathematics
Jon Keating, University of Oxford
Hugh Montgomery, University of Michigan
Kannan Soundararajan, Stanford University
Summary:
On April 6, 1972 a young graduate student named Hugh Montgomery and the world-renowned mathematical physicist Freeman Dyson had a conversation in the tearoom at the Institute for Advanced Study which led to a fusion of two disparate fields and an intellectual revolution that is stronger than ever today. Montgomery and Dyson discovered that the zeros of the Riemann zeta-function, important for understanding prime numbers, seem to obey the same distribution patterns as the eigenvalues of large random unitary (or hermitian) matrices, which had been extensively studied by physicists, especially to model the interactions within large atomic nuclei. This stunning connection has held up to extensive numerical and theoretical tests over the intervening years and has been extended to give random matrix models for the low lying zeros of families of L-functions and for the moments and distribution of values of the L-functions in these families and to analogous families over function fields. This conference brought together 130 mathematical scientists to a meeting that highlighted the progress and the state of the art of results at the nexus of these two fields and underlined the questions most pertinent for further research.
Speakers:
Louis-Pierre Arguin, City University of New York
Emma Bailey, City University of New York
Sieg Baluyot, American Institute of Mathematics
Vorrapan Chandee, Kansas State University
Alexandra Florea, University of California at Irvine
Yan Fyodorov, King's College London
Adam Harper, University of Warwick
Nina Holden, ETH Zurich
Matilde Lalin, Universite de Montreal
Paul Nelson, Institute for Advanced Study
Kyle Pratt, University of Oxford
Zeev Rudnick, Tel Aviv University
Tom Spencer, Institute for Advanced Study
Matt Young, Texas A &M University
Sponsors: NSF, AIM, Heilbronn Institute for Mathematical Research
Agenda:
Tuesday, June 21 2022
Topic: Opening Remarks and History of the math talks
Speakers: Peter Sarnak, Hugh Montgomery and Jon Keating
Time/Room: 10:00 am - 11:30 am/Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-the…
Topic: Statistical mechanics arising from random matrix theory
Speaker: Thomas Spencer - Institute for Advanced Study
Time/Room: 12:00 PM - 1:00 PM / Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-the…
Topic: The distribution of values of zeta and L-functions
Speaker: Kannan Soundararajan - Stanford University
Time/Room: 2:30 PM - 3:30 PM / Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-the…
Topic: Large sieve inequalities for families of L-functions
Speaker: Matt Young -Texas A&M Unviersity
Time/Room: 4:00 PM - 5:00 PM / Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-the…
Wednesday, June 22 2022
Topic: Number theoretic aspects of multiplicative chaos
Speaker: Adam Harper - University of Warwick
Time/Room: 9:00 AM - 10:00 AM / Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-theory-conference-14
Topic: Gaussian multiplicative chaos: applications and recent developments
Speaker: Nina Holden - ETH Zurich
Time/Room: 10:30 AM - 11:30 AM / Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-the…
Topic: A few results and conjectures on some product-ratio correlation functions of characteristic polynomials of beta-Hermite ensembles
Speaker: Yan Fyodorov - King's College London
Time/Room: 12:00 PM - 1:00 PM / Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-theory-conference-2
Topic: The Fyodorov-Hiary-Keating Conjecture
Speaker: Louis-Pierre Arguin - City University of New York
Time/Room: 2:30 PM - 3:30 PM / Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-the…
Topic: Large deviation estimates for Selberg’s central limit theorem, applications, and numerics
Speaker: Emma Bailey - City University of New York
Time/Room: 4:00 PM - 5:00 PM / Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-the…
Thursday, June 23 2022
Topic: RMT statistics in number theory and in quantum chaos
Speaker: Zeev Rudnick - Tel Aviv University
Time/Room: 9:00 AM - 10:00 AM / Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-theory-conference-9
Topic: Negative moments of the Riemann zeta function
Speaker: Alexandra Florea -University of California, Irvine
Time/Room: 10:30 AM - 11:30 AM / Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-theory-conference-4
Topic: Half-Isolated Zeros and Zero-Density Estimates
Speaker: Kyle Pratt -University of Oxford
Time/Room: 12:00 PM - 1:00 PM / Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-theory-conference-6
Topic: The recipe for moments of LL-functions and characteristic polynomials of random matrices
Speaker: Sieg Baluyot -American Institute of Mathematics
Time/Room: 2:30 PM - 3:30 PM / Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-theory-conference-5
Topic: Problem Session
Time/Room: 4:00 pm - 5:00 pm/Wolfensohn Hall and Remote Access
Friday, June 24 2022
Topic: Sums of certain arithmetic functions over Fq[T]Fq[T] and non-unitary distributions
Speaker: Matilde Lalin -University of Montreal
Time/Room: 9:00 AM - 10:00 AM / Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-theory-conference-8
Topic: Moments of large families of Dirichlet L-functions
Speaker: Vorrapan Chandee - Kansas State University
Time/Room: 10:30 AM - 11:30 AM / Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-the…
Topic: Moments and bounds for L-functions of large degree
Speaker: Paul Nelson -Institute for Advanced Study
Time/Room: 12:00 PM - 1:00 PM / Wolfensohn Hall and Remote Access
Abstract URL: https://www.ias.edu/events/50-years-number-theory-and-random-matrix-the…
Limited funding from the National Science Foundation was available to attend the workshop. *All funding has been allocated.