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New connections in number theory and physics


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24th May 2021 to 28th May 2021
Daniel Persson Chalmers University of Technology
Daniel Bump Stanford University, Stanford University
Solomon Friedberg Boston College
Michael Green University of Cambridge, Queen Mary University of London
Axel Kleinschmidt Max-Planck-Institut für Gravitationphysik
Katrin Wendland Albert-Ludwigs-Universität Freiburg

Workshop theme

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.


Given the current restrictions on movement, due to the ongoing pandemic, the INI intends to run this workshop virtually across 5 days. All talks and discussion sessions will be available virtually.


Deadline for applications: 2nd May 2021

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons