Applicable resurgent asymptotics: towards a universal theory
ARA
1 March 2021 to 25 June 2021
Programme theme
Following the outbreak of COVID19, this event has been split into two parts:
- The first part of the programme will be delayed until March 2021. It is planned to run for four months, and in semi virtual mode.
- The second part of the programme will run in 2022. It is planned to run for three months, and (hopefully) more in person, please see programme page here
Asymptotic analysis and perturbation methods can provide approximate solutions and analytical properties to a broad range of problems where an exact solution cannot be found. They are therefore some of the most critically important tools in mathematics and theoretical physics. Nevertheless, the existing approaches to study asymptotic problems are often context specific, varying in rigour or practicality. A key challenge, which this programme will seek to address, is to unify these approaches in asymptotics into techniques of enhanced efficacy and broader applicability.
The role of previously neglected exponentially small terms in asymptotics has been formalised, understood and subsequently exploited to deliver a radical change to the century-old, but ambiguous, approach of Poincaré asymptotic analysis. Significant mathematical breakthroughs have been achieved in a number of areas including rigorous bounds, PDEs, discrete systems and eigenvalue problems. These have wide-ranging applications to, amongst others, fluid dynamics, aero-acoustics, pattern formation, dynamical systems, optics and biomathematics.
Recently, remarkable progress has also been made in theoretical physics in the applications of the comprehensive theory of resurgent asymptotic analysis. This approach has revealed new and deeper insights into the non-perturbative structure and dynamics of quantum field theories, string theory, random matrix and knot theories, as well as computationally efficient techniques for path integral evaluation. Simultaneously this has opened up developments in Riemann Hilbert problems, integrable nonlinear systems and orthogonal polynomials with the potential for applications to wide classes of nonlinear multidimensional problems.
Although overlapping, these advances have developed largely in parallel. However, there is increasing realisation from those working in these distinct areas that there is significant potential for mathematical technology transfer. One ambitious goal of this programme is to bring these communities together to develop a unified set of comprehensive, yet practical, advanced asymptotic approaches, widely applicable not only in mathematics and physics, but also in rapidly emerging areas such as in engineering, data science and systems biology.
The work on unified approaches to asymptotics envisaged during this programme is broad in scope and currently includes transseries and their practical implementation; parametric resurgence and higher order Stokes phenomena for multidimensional systems; analysis of Stokes coefficients; realistic sharp error bounds for highly accurate numerics (e.g., Borel-Padé); complex singularity dynamics in finite and late time phenomena; Riemann-Hilbert methods; exact WKB analysis; practical implementation of Lefschetz thimbles in high-dimensional integrals; nonlinear uniform asymptotics; Painlevé analysis and Picard-Lefschetz theory for novel computational methods.
The applications of these approaches under study during the programme include resurgence and non-perturbative physics in gauge theory, matrix models, string theory, AdS/CFT, supersymmetry, and localizable QFTs; highly correlated systems and relativistic hydrodynamics; metastability, free boundary and late time behaviour of nonlinear PDEs; homogenisation and other multiple scales problems; discrete to continuum limits in biological systems; interplay between integrability and asymptotics.
The programme will bring together applied mathematicians, mathematical analysts, theoretical physicists and subject specialists working on asymptotic analysis to enable significant technology transfer and to inaugurate the next generation of interdisciplinary researchers within these fields. Given the breadth of activity, and the diverse disciplines involved, the stage is set for further major advances and for unforeseen new directions.
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 Applicable resurgent asymptotics: towards a universal theory, where work on this paper was undertaken. This work was supported by EPSRC grant EP/R014604/1.
ARA programme: interview with organisers Ines Aniceto, Chris Howls and Adri Olde Daalhuis
Workshops
Spring school on asymptotic methods and applications
22 March 2021 to 26 March 2021
Summary meeting
14 June 2021 to 18 June 2021
Seminars
| Thursday 18th March 2021 | |||
|---|---|---|---|
| 15:30 to 16:30 |
Jonathan Chapman University of Oxford |
Room 1 | 
|
| 17:00 to 18:00 |
Sergei Gukov CALTECH (California Institute of Technology) |
Room 1 |
|
| Tuesday 30th March 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Michael Berry University of Bristol |
Room 1 |
|
| Thursday 1st April 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Ovidiu Costin Ohio State University |
Room 2 |
|
| Thursday 8th April 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Gergő Nemes Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences |
Room 1 |
|
| Tuesday 13th April 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Mithat Unsal North Carolina State University |
Room 1 |
|
| Thursday 15th April 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Marcel Vonk Universiteit van Amsterdam |
Room 1 |
|
| Tuesday 20th April 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
John King University of Nottingham |
Room 1 |
|
| Thursday 22nd April 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Christopher Howls University of Southampton |
Room 1 |
|
| Tuesday 27th April 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Sheehan Olver Imperial College London |
Room 1 | |
| Thursday 29th April 2021 | |||
|---|---|---|---|
| 08:00 to 09:00 |
Yoshitsugu Takei Kyoto University |
Room 1 | |
| Monday 3rd May 2021 | |||
|---|---|---|---|
| 08:00 to 09:00 |
Yasuyuki Hatsuda Rikkyo University |
Room 1 |
|
| Tuesday 4th May 2021 | |||
|---|---|---|---|
| 08:00 to 09:00 |
Katsushi Ito Tokyo Institute of Technology |
Room 1 |
|
| Wednesday 5th May 2021 | |||
|---|---|---|---|
| 06:00 to 07:00 |
Exact -WKB vs resurgence in semiclassics -Dr. Naohisa Sueishi |
Room 1 |
|
| 08:00 to 09:00 |
Degenerate Weber Stokes graph and its application - Dr. Syo Kamata |
Room 1 |
|
| Thursday 6th May 2021 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Gergő Nemes Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences |
Room 1 |
|
| 16:00 to 17:00 |
Andrew Neitzke Yale University |
Room 1 |
|
| Tuesday 11th May 2021 | |||
|---|---|---|---|
| 16:15 to 17:15 |
Michal P. Heller Max-Planck-Institut für Gravitationphysik; National Centre for Nuclear Research |
Room 1 |
|
| Thursday 13th May 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Benjamin Withers University of Southampton |
Room 1 |
|
| Tuesday 18th May 2021 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Alba Grassi CERN - European Organisation for Nuclear Research; University of Geneva |
Room 2 |
|
| Thursday 20th May 2021 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Nalini Joshi University of Sydney |
Room 1 |
|
| Tuesday 25th May 2021 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Peter Clarkson University of Kent |
Room 2 |
|
| Thursday 27th May 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Tamara Grava SISSA; University of Bristol |
Room 1 | |
| Tuesday 1st June 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Alexander Its Indiana University-Purdue University Indianapolis |
Room 1 |
|
| Thursday 3rd June 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Traveling waves in diatomic FPUT with small mass-ratio - Professor Douglas Wright |
Room 1 |
|
| Tuesday 8th June 2021 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Scott McCue Queensland University of Technology |
Room 1 |
|
| 16:00 to 17:00 |
Linda Cummings New Jersey Institute of Technology |
Room 1 |
|
Organisers
- Ines Aniceto University of Southampton
- Gerald Dunne University of Connecticut
- Christopher Howls University of Southampton
- John King University of Nottingham
- Christopher Lustri Macquarie University
- Tatsuhiro Misumi Akita University
- Adri Olde Daalhuis University of Edinburgh
- Ricardo Schiappa Instituto Superior Técnico, Lisboa; CERN - European Organisation for Nuclear Research
- Philippe Trinh University of Oxford
- Mithat Unsal North Carolina State University
Speakers
- Michael Berry University of Bristol
- Jonathan Chapman University of Oxford
- Peter Clarkson University of Kent
- Ovidiu Costin Ohio State University
- Linda Cummings New Jersey Institute of Technology
- Alba Grassi CERN - European Organisation for Nuclear Research; University of Geneva
- Tamara Grava SISSA; University of Bristol
- Sergei Gukov CALTECH (California Institute of Technology)
- Yasuyuki Hatsuda Rikkyo University
- Michal P. Heller Max-Planck-Institut für Gravitationphysik; National Centre for Nuclear Research
- Christopher Howls University of Southampton
- Katsushi Ito Tokyo Institute of Technology
- Alexander Its Indiana University-Purdue University Indianapolis
- Nalini Joshi University of Sydney
- John King University of Nottingham
- Scott McCue Queensland University of Technology
- Andrew Neitzke Yale University
- Gergő Nemes Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences
- Sheehan Olver Imperial College London
- Yoshitsugu Takei Doshisha University
- Mithat Unsal North Carolina State University
- Marcel Vonk Universiteit van Amsterdam
- Benjamin Withers University of Southampton
Participants
- Ines Aniceto University of Southampton
- Takashi Aoki Kindai University
- Claude Baesens University of Warwick
- Matteo Baggioli Shanghai Jiao Tong University
- Zoltan Bajnok WIGNER Research Centre for Physics; Eotvos Lorand University
- Salvatore Baldino Instituto Superior Técnico, Lisboa
- Kemal Gokce Basar University of North Carolina
- Marc Bellon Sorbonne Université; CNRS - Ecole Normale Superieure Paris
- Carl Bender Washington University in St. Louis
- Tom Bennett University of Kent
- Michael Berry University of Bristol
- Michael Borinsky National Institute for Subatomic Physics (Nikhef)
- David Broadhurst The Open University
- Alex Buchel University of Western Ontario; Perimeter Institute for Theoretical Physics
- Jonathan Chapman University of Oxford
- Victor Eduardo Chavez heredia University of Bristol; SISSA
- Aleksey Cherman University of Minnesota
- Peter Clarkson University of Kent
- Ovidiu Costin Ohio State University
- Rodica Costin Ohio State University
- Samuel Crew University of Cambridge
- Linda Cummings New Jersey Institute of Technology
- Dan Dai City University of Hong Kong
- Bryn Davies ETH Zürich
- Jonathan Dawes University of Bath
- Alfredo Deaño Universidad Carlos III de Madrid
- Fabrizio Del Monte Université de Montréal; Concordia University
- Harini Desiraju University of Birmingham
- Oscar Dias University of Southampton
- Diego Dominici State University of New York; Johannes Kepler Universität
- Daniele Dorigoni Durham University
- Gerald Dunne University of Connecticut
- Clare Dunning University of Kent
- Jean Ecalle Université Paris-Saclay
- Frederic Fauvet University of Strasbourg
- Valentina Forini City University, London
- Vassili Gelfreich University of Warwick
- Alexander Gorsky Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences
- Tamara Grava SISSA; University of Bristol
- Sergei Gukov CALTECH (California Institute of Technology)
- Hal Haggard Bard College; Perimeter Institute for Theoretical Physics
- Zachary Harris University of Connecticut
- Daniel Hasenbichler University of Southampton
- Yasuyuki Hatsuda Rikkyo University
- Michal P. Heller Max-Planck-Institut für Gravitationphysik; National Centre for Nuclear Research
- Masazumi Honda Kyoto University
- Andrew Hone University of Kent
- Christopher Howls University of Southampton
- Katsushi Ito Tokyo Institute of Technology
- Alexander Its Indiana University-Purdue University Indianapolis
- Kohei Iwaki University of Tokyo
- Romuald Janik Uniwersytet Jagiellonski
- Omar Kidwai University of Tokyo
- John King University of Nottingham
- Alisa Knizel University of Chicago
- Shota Komatsu CERN - European Organisation for Nuclear Research; Institute for Advanced Study, Princeton
- Gregory Korchemsky CEA/Saclay
- Ivan Kostov CEA/Saclay; CNRS (Centre national de la recherche scientifique)
- Dirk Kreimer Humboldt-Universität zu Berlin
- Oleg Lisovyi Université François-Rabelais Tours
- Ana Loureiro University of Kent
- Sergei Lukyanov Rutgers, The State University of New Jersey
- Christopher Lustri Macquarie University
- Kirone Mallick CEA/Saclay; École Polytechnique
- Marcos Marino University of Geneva
- Davide Masoero Universidade de Lisboa
- Scott McCue Queensland University of Technology
- Ben Meiring University of Oxford
- Tatsuhiro Misumi Kindai University
- Akane Nakamura None / Other
- Andrew Neitzke Yale University
- Gergő Nemes Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences
- Nikita Nikolaev University of Sheffield
- Adri Olde Daalhuis University of Edinburgh
- Sheehan Olver Imperial College London
- Christiana Pantelidou Trinity College Dublin
- Erik Panzer University of Oxford
- Beatrice Pelloni Heriot-Watt University
- Veronika Pillwein Johannes Kepler Universität
- Pavel Putrov Abdus Salam International Centre for Theoretical Physics
- Jean-Pierre Ramis Université Paul Sabatier Toulouse III
- Tomas Reis University of Geneva
- Enrico Russo Sorbonne Université
- Shinji Sasaki Shibaura Institute of Technology
- David Sauzin CNRS (Centre national de la recherche scientifique)
- Fatih Say Ordu University
- Thomas Schaefer North Carolina State University
- Ricardo Schiappa Instituto Superior Técnico, Lisboa; CERN - European Organisation for Nuclear Research
- Maximilian Schwick Instituto Superior Técnico, Lisboa
- Alexandre Serantes National Centre for Nuclear Research
- Didina Serban CEA/Saclay
- Josh Shelton University of Bath
- Mikhail Shifman University of Minnesota
- Akira Shudo Tokyo Metropolitan University
- Kostas Skenderis University of Southampton
- Michal Spalinski National Centre for Nuclear Research; Uniwersytet w Bialymstoku
- Andrei Starinets University of Oxford
- Jonathan Stone University of Southampton
- Tin Sulejmanpasic Durham University
- Yoshitsugu Takei Doshisha University
- Saleh Tanveer Ohio State University
- Alessandro Tanzini SISSA
- Marika Taylor University of Southampton
- Daniel Thompson University of Wales, Swansea; Vrije Universiteit Brussel
- Philippe Trinh University of Bath
- Mithat Unsal North Carolina State University
- Arkady Vainshtein University of Minnesota
- Jacques Vanneste University of Edinburgh
- Marcel Vonk Universiteit van Amsterdam
- André Voros CEA/Saclay
- Edwin Watson-Miller University of Bath
- Benjamin Withers University of Southampton
- Roderick Wong City University of Hong Kong
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