New connections in number theory and physics - Cancelled
NCN
4 May 2021 to 25 June 2021
Programme theme
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Following the outbreak of COVID19, this event has been postponed. The Institute is working with the organisers to find a suitable date in the calendar for its resumption; further information will be made available in due course. Please visit the new programme webpage here.
There are also plans to hold a virtual workshop 24th - 28th May 2021. Please see the workshop webpage for more details
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During the 20th century, interactions between geometers and theoretical physicists were revolutionary in both areas, leading to such unexpected developments as mirror symmetry and the impact of topological field theory on invariants of 4-manifolds. Another momentum is now developing around new connections between number theory and physics, mainly but not exclusively through the theory of automorphic forms. We have reached a time when contacts between number theorists and physicists have the potential to generate another surge of developments. The purpose of this interdisciplinary programme is to investigate connections between various fields of theoretical physics, in particular string theory and statistical models of crystals, and the theory of automorphic forms, mock modular forms and beyond. The non-perturbative structure of string theory has led to new uses of automorphic forms that have already appeared in number theory, as well as new exotic automorphic objects that have not yet been encountered. This is an emergent research area with a lot of potential for cross-disciplinary collaborations with great benefit to both areas. Recent work has revealed, on the one hand, a profound significance of automorphic forms and automorphic representations for string scattering amplitudes and, on the other hand, an unexpected appearance of mock theta functions in answering key questions pertaining to quantum properties of black holes. In addition, solvable lattice models have recently appeared in connection with Eisenstein series on metaplectic groups, calling for some underlying structure that remains to be understood. The program will begin with a one-week school, with the purpose of bridging the gap between physicists and mathematicians and to ignite the seeds for collaborations and discussions during the remainder of the program. Following the school, there will be on-going lecture series and research talks, focusing on developing the core themes of the program. There will also be a second workshop in the middle of the program period to highlight recent research developments and to describe potential future research directions. This workshop will provide a foundation for the second half of the program. The core themes of the program are: - String amplitudes and automorphic representations - Modular graph functions and multiple zeta values - Mock modular forms, moonshine and black holes - Metaplectic Eisenstein series and quantum groups - Automorphic forms on Kac-Moody groups
Organisers
- Daniel Bump Stanford University
- Solomon Friedberg Boston College
- Michael Green University of Cambridge
- Axel Kleinschmidt Max-Planck-Institut für Gravitationphysik
- Daniel Persson Chalmers University of Technology
- Katrin Wendland Albert-Ludwigs-Universität Freiburg
Participants
- Terry Gannon University of Alberta
- Sameer Murthy King's College London
- Daniel Persson Chalmers University of Technology
Supported By
