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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.

Geometrie und Topologie,    Kurse und Veranstaltungen für Studenten der Mathematik

Institute for Computational and Experimental Research in Mathematics (ICERM)

The ongoing development of machine learning as a research tool, the rapid expansion of formalization efforts in mathematics, and recent advances in computer algebra systems are leading to a major transition in the research methods used in mathematics. This transition will be of particular significance to number theory, a field which has long had an algorithmic focus and a tradition of tabulating data. These characteristics are both embodied in the L-functions and Modular Forms Database (LMFDB), an online catalog of mathematical objects associated with the Langlands program, which has become the premier online resource for researchers in this area and a rich source of experimental data. The semester program will bring together leading researchers in computational number theory to explore the capabilities of these new tools and apply them to the vast repository of data that has been accumulated in the LMFDB, and beyond, in the hope of shedding new light on old problems, and formulating new ones. Specific focus areas of the program will include the nascent use of machine learning in number theory; the development of computer algebra systems widely used in number theory, highlighting their capabilities and future plans, and comparing their speed, correctness, and utility; and various approaches to computing with L-functions. In addition, there will be numerous opportunities for collaboration throughout the semester beginning with the opening event.

Tel.: [4018635030];     Email: info@icerm.brown.edu