New connections in number theory and physics

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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.

Timetable

Monday 24th May 2021
14:20 to 14:30	Christie Marr Isaac Newton Institute Welcome Talk	Room 1
14:30 to 15:30	Steve Miller Rutgers, The State University of New Jersey Chair: Daniel Persson D^4 R^4 and D^6 R^4: A 2021 perspective on these automorphic functions	Room 1
15:30 to 16:30	Akshay Venkatesh Institute for Advanced Study, Princeton Chair: Daniel Persson L-functions and Reidemeister torsion modulo squares	Room 1
16:30 to 16:45	Chair: Daniel Persson Break	Room 1
16:45 to 17:45	Jens Funke Durham University Chair: Solomon Friedberg Theta Series and (Singular) Theta Lifts	Room 1
17:45 to 18:45	Discussions	Room 1

Tuesday 25th May 2021
14:30 to 15:30	Boris Pioline Sorbonne Université; CNRS (Centre national de la recherche scientifique) Chair: Katrin Wendland Exact BPS Couplings and Black Hole Counting	Room 1
15:30 to 16:30	Eric D’Hoker University of California, Los Angeles Chair: Katrin Wendland Modular Graph Functions, Forms, and Tensors	Room 1
16:30 to 16:45	Break	Room 1
16:45 to 17:45	Edward Witten Institute for Advanced Study, Princeton Chair: Michael Green Quantization by Branes and Geometric Langlands	Room 1
17:45 to 18:45	Discussions	Room 1

Wednesday 26th May 2021
14:30 to 15:30	Jeff Harvey University of Chicago Chair: Daniel Persson Superconformal Symmetry and Quantum Error Correction	Room 1
15:30 to 16:30	Greg Moore Rutgers, The State University of New Jersey Chair: Daniel Persson N=2* Supersymmetric Yang-Mills Theory, Four-Manifold Invariants, And Mock Modular Forms	Room 1
16:30 to 16:45	Break	Room 1
16:45 to 17:45	Sameer Murthy King's College London Chair: Axel Kleinschmidt 5-Dimensional Black Holes, 4-Dimensional Super Yang-Mills, and 3-Dimensional Chern-Simons Theory	Room 1
17:45 to 18:45	Discussions	Room 1

Thursday 27th May 2021
14:30 to 15:30	Kathrin Bringmann University of Cologne Chair: Katrin Wendland False Theta Functions and Their Modularity Properties	Room 1
15:30 to 16:30	Anne Taormina Durham University Chair: Katrin Wendland Mathieu Moonshine: Quarter BPS States at the Kummer Point and Nearby	Room 1
16:30 to 16:45	Break	Room 1
16:45 to 17:45	Nils Scheithauer Technische Universität Darmstadt Chair: Daniel Bump Holomorphic vertex operator algebras of central charge 24	Room 1
17:45 to 18:45	Amanda Folsom Amherst College Chair: Daniel Bump Eisenstein Series, Cotangent-Zeta Sums, and Quantum Modular Forms	Room 1
18:45 to 19:45	Discussions	Room 1

Friday 28th May 2021
14:30 to 15:30	Miranda Cheng Universiteit van Amsterdam Chair: Axel Kleinschmidt On certain three-manifold invariants	Room 1
15:30 to 16:30	Don Zagier Max-Planck-Institut für Mathematik, Bonn Chair: Axel Kleinschmidt Modular, Mock Modular and Quantum Modular	Room 1
16:30 to 16:45	Break	Room 1
16:45 to 17:45	Yiannis Sakellaridis Johns Hopkins University Chair: Solomon Friedberg Hamiltonian spaces and L-functions	Room 1
17:45 to 18:45	Discussions	Room 1

New connections in number theory and physics

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

Speakers

Eric D'Hoker University of California, Los Angeles
Kathrin Bringmann University of Cologne
Miranda Cheng Universiteit van Amsterdam
Amanda Folsom Amherst College
Jens Funke Durham University
Jeff Harvey University of Chicago
Christie Marr Isaac Newton Institute
Steve Miller Rutgers, The State University of New Jersey
Greg Moore Rutgers, The State University of New Jersey
Sameer Murthy King's College London
Boris Pioline Sorbonne Université; CNRS (Centre national de la recherche scientifique)
Yiannis Sakellaridis Johns Hopkins University
Nils Scheithauer Technische Universität Darmstadt
Anne Taormina Durham University
Akshay Venkatesh Institute for Advanced Study, Princeton
Edward Witten Institute for Advanced Study, Princeton
Don Zagier Max-Planck-Institut für Mathematik, Bonn

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New connections in number theory and physics

Workshop theme

Timetable

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