New connections in number theory and physics
NCN2
1 August 2022 to 23 September 2022
Programme 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.
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
The Institute kindly requests that any papers published as a result of this programme’s activities are credited as such. Please acknowledge the support of the Institute in your paper using the following text:
The author(s) would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme New connections in number theory and physics, where work on this paper was undertaken. This work was supported by EPSRC grant EP/R014604/1.
NCN programme: interview with organisers D Persson, A Kleinschmidt, K Wendland, and S Friedberg
Workshops
New connections in number theory and physics
24 May 2021 to 28 May 2021
Making the bridge: Exploring new connections between number theory and physics
1 August 2022 to 5 August 2022
Crossing the bridge: New connections in number theory and physics
22 August 2022 to 26 August 2022
Seminars
| Tuesday 9th August 2022 | |||
|---|---|---|---|
| 18:00 to 19:00 |
Terry Gannon University of Alberta |
No Room Required | |
| Wednesday 10th August 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Anne Taormina Durham University |
Room 1 | 
|
| Thursday 11th August 2022 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Jeff Harvey University of Chicago |
Room 2 |
|
| Monday 15th August 2022 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Marcus Berg Karlstad University |
Room 2 |
|
| Tuesday 16th August 2022 | |||
|---|---|---|---|
| 18:00 to 19:00 |
Philip Candelas University of Oxford ; Xenia de la Ossa University of Oxford |
No Room Required | |
| Wednesday 17th August 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Jeff Harvey University of Chicago |
Room 1 |
|
| Thursday 18th August 2022 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Marcus Berg Karlstad University |
No Room Required | |
| 14:00 to 15:00 |
Jeff Harvey University of Chicago |
Room 2 | |
| Friday 19th August 2022 | |||
|---|---|---|---|
| 14:00 to 15:00 |
David Evans Cardiff University |
Room 2 | |
| Tuesday 30th August 2022 | |||
|---|---|---|---|
| 18:00 to 19:00 |
Jens Funke Durham University |
No Room Required | |
| Thursday 1st September 2022 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Erik Panzer University of Oxford |
Room 2 |
|
| Tuesday 6th September 2022 | |||
|---|---|---|---|
| 18:00 to 19:00 |
David Ginzburg Tel Aviv University |
No Room Required | |
| Wednesday 7th September 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Nils Scheithauer Technische Universität Darmstadt |
Room 2 |
|
| Thursday 8th September 2022 | |||
|---|---|---|---|
| 10:30 to 11:30 |
Daniele Dorigoni Durham University |
No Room Required | |
| 14:00 to 15:00 |
Federico Zerbini CEA/Saclay |
Room 2 |
|
| Thursday 15th September 2022 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Claire Frechette Boston College |
Room 2 | |
| Tuesday 20th September 2022 | |||
|---|---|---|---|
| 10:30 to 11:30 |
Andrew Hone University of Kent |
No Room Required | |
| 18:00 to 19:00 |
Marcela Hanzer University of Zagreb |
No Room Required |
|
| Thursday 22nd September 2022 | |||
|---|---|---|---|
| 11:00 to 14:00 |
Siddharth Mahendraker Boston College |
Discussion Room | |
| 14:00 to 15:00 |
Erez Lapid Weizmann Institute of Science |
Room 2 |
|
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
- Marcus Berg Karlstad University
- Philip Candelas University of Oxford
- Xenia de la Ossa University of Oxford
- Daniele Dorigoni Durham University
- David Evans Cardiff University
- Claire Frechette Boston College
- Jens Funke Durham University
- Terry Gannon University of Alberta
- David Ginzburg Tel Aviv University
- Marcela Hanzer University of Zagreb
- Jeff Harvey University of Chicago
- Andrew Hone University of Kent
- Erez Lapid Weizmann Institute of Science
- Siddharth Mahendraker Boston College
- Erik Panzer University of Oxford
- Nils Scheithauer Technische Universität Darmstadt
- Anne Taormina Durham University
- Federico Zerbini CEA/Saclay
Supported By
