New connections in number theory and physics
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.
Speakers
- Kathrin Bringmann
- Miranda Cheng
- Eric D’Hoker
- Amanda Folsom
- Jens Funke
- Jeff Harvey
- Greg Moore
- Steve Miller
- Sameer Murthy
- Boris Pioline
- Yiannis Sakellaridis
- Nils Scheithauer
- Anne Taormina
- Akshay Venkatesh
- Edward Witten
- Don Zagier
New connections in number theory and physics
Monday 24th May 2021 to Friday 28th May 2021
| 14:20 to 14:30 | Christie Marr Welcome Talk | INI 1 |
| 14:30 to 15:30 | Steve Miller (Rutgers, The State University of New Jersey) D^4 R^4 and D^6 R^4: A 2021 perspective on these automorphic functions Chair: Daniel Persson | INI 1 |
| 15:30 to 16:30 | Akshay Venkatesh (Institute for Advanced Study, Princeton) L-functions and Reidemeister torsion modulo squares Chair: Daniel Persson | INI 1 |
| 16:30 to 16:45 | Break Chair: Daniel Persson | INI 1 |
| 16:45 to 17:45 | Jens Funke (Durham University) Theta Series and (Singular) Theta Lifts Chair: Solomon Friedberg | INI 1 |
| 17:45 to 18:45 | Discussions | INI 1 |
| 14:30 to 15:30 | Boris Pioline (Sorbonne Université); (CNRS (Centre national de la recherche scientifique)) Exact BPS Couplings and Black Hole Counting Chair: Katrin Wendland | INI 1 |
| 15:30 to 16:30 | Eric D'Hoker (University of California) Modular Graph Functions, Forms, and Tensors Chair: Katrin Wendland | INI 1 |
| 16:30 to 16:45 | Break | INI 1 |
| 16:45 to 17:45 | Edward Witten (Institute for Advanced Study, Princeton) Quantization by Branes and Geometric Langlands Chair: Michael Green | INI 1 |
| 14:30 to 15:30 | Jeff Harvey (University of Chicago) Superconformal Symmetry and Quantum Error Correction Chair: Daniel Persson | INI 1 |
| 15:30 to 16:30 | Greg Moore (Rutgers, The State University of New Jersey) TBA Chair: Daniel Persson | INI 1 |
| 16:30 to 16:45 | Break | INI 1 |
| 16:45 to 17:45 | Sameer Murthy (King's College London) 5-Dimensional Black Holes, 4-Dimensional Super Yang-Mills, and 3-Dimensional Chern-Simons Theory Chair: Axel Kleinschmidt | INI 1 |
| 17:45 to 18:45 | Discussions | INI 1 |
| 14:30 to 15:30 | Kathrin Bringmann (University of Cologne) False Theta Functions and Their Modularity Properties Chair: Katrin Wendland | INI 1 |
| 15:30 to 16:30 | Anne Taormina (Durham University) Mathieu Moonshine: Quarter BPS States at the Kummer Point and Nearby Chair: Katrin Wendland | INI 1 |
| 16:30 to 16:45 | Break | INI 1 |
| 16:45 to 17:45 | Nils Scheithauer (Technische Universität Darmstadt) Holomorphic vertex operator algebras of central charge 24 Chair: Solomon Friedberg | INI 1 |
| 17:45 to 18:45 | Amanda Folsom (Amherst College) Eisenstein Series, Cotangent-Zeta Sums, and Quantum Modular Forms Chair: Solomon Friedberg | INI 1 |
| 14:30 to 15:30 | Miranda Cheng (Universiteit van Amsterdam) TBA Chair: Axel Kleinschmidt | INI 1 |
| 15:30 to 16:30 | Don Zagier (Max-Planck-Institut für Mathematik, Bonn) Modular, Mock Modular and Quantum Modular Chair: Axel Kleinschmidt | INI 1 |
| 16:30 to 16:45 | Break | INI 1 |
| 16:45 to 17:45 | Yiannis Sakellaridis (Johns Hopkins University) Hamiltonian spaces and L-functions Chair: Daniel Bump |
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