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Simons Foundation

Beyond Gaussians emerging from independence, for many correlated systems, new types of universal distributions have emerged in the past sixty years, which appear to effectively describe a wide range of statistical physics phenomena. Surprisingly, numerical and theoretical evidence has shown that these new, intricate statistics also reflect several aspects of the distribution of prime numbers, and of arithmetic objects in general. This question is relevant for all arithmetic topics covered in this meeting: conjectures from random matrix theory, distributions of multiplicative functions, limit theorems for L-functions, and the anatomy of integers.

In 1998, number theorists at Université Laval and the University of Maine founded the "Maine/Québec Conference on Number Theory and Related Topics." Since then it has taken place annually on a weekend in early Fall (except 2001, when it was cancelled due to the terrorist attacks that September). We invite number theorists and mathematicians in adjacent fields from New England, eastern Canada, and beyond to speak about their research and discuss ideas for future work. Each year there is a change in venue: odd years at UMaine, even years at U. Laval.

On the occasion of 40+ years after the seminar paper of Gross--Zagier, we bring together experts to deliver lectures on a broad range of topics connected with the Gross-Zagier formula, its generalizations, related future directions, and other works that it has inspired.

The program will unite researchers from a number of areas: algebraic and complex geometry, arithmetic geometry, Hodge theory, and mathematical physics. It will bring theoretically and computationally oriented researchers together, expecting that computations will illuminate conjectures made by the theorists and that theory will enlarge the range of what can be computed. We intend to develop databases of certain types of K3 surfaces for the L-Functions and Modular Forms Database and promote the development of software for computations on K3 surfaces in Magma, SageMath, or other systems for public release.

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