Conference: Arithmetic quantum field theory

Harvard University, Cambridge MA

Investigators

Abstract

The conference Arithmetic Quantum Field Theory will be held at the Harvard Center of Mathematical Sciences and Applications (CMSA) on March 25-29 2024. This will be an in-person gathering of approximately 70 researchers - graduate students, postdocs, and faculty in mathematics and physics, available in hybrid mode to an unlimited number of outside participants. A central focus of the conference - and the dedicated aim of its first day - is to encourage a high level of participation by women in math and physics. The first day is designed to encourage junior researchers to come and network, give talks in a friendly environment, and participate without concern over the precise fit of their research to the narrow theme of the workshop. The conference Arithmetic Quantum Field Theory, and the two-month program of the same title it concludes, are aimed at catalyzing interactions between mathematicians and physicists by disseminating exciting new connections emerging between quantum field theory and algebraic number theory, and in particular between the fundamental invariants of each: partition functions and L-functions. On one hand, there has been tremendous progress in the past decade in our understanding of the algebraic structures underlying quantum field theory as expressed in terms of the geometry and topology of low-dimensional manifolds. On the other hand, the arithmetic topology dictionary provides a sturdy bridge between the topology of manifolds and the arithmetic of number fields. Thus, one can now port over quantum field theoretic ideas to number theory. The program will bring together a wide range of mathematicians and physicists working on adjacent areas to explore the emerging notion of arithmetic quantum field theory as a tool to bring quantum physics to bear on questions of interest for the theory of automorphic forms, harmonic analysis and L-functions, and conversely to explore potential geometric and physical consequences of arithmetic ideas. The conference website is https://cmsa.fas.harvard.edu/event/aqftconf/ where recordings of the talks and notes from lectures will be made widely available. 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.