Mathematics of beyond all-orders phenomena

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Workshop theme

Mathematics beyond all orders involves the inclusion of terms in an asymptotic or perturbative expansion that, due to their, typically exponentially small size, would otherwise be overlooked and neglected. Nevertheless, such terms often either carry important analytical information, or grow in size different sectors to dominate the behaviour. Their exclusion can lead to, for example, apparent non-uniqueness of solutions, and/or significant restrictions on the range of validity of the approximations.

Over the past three decades beyond all order techniques have been widely applied in problems from analysis to fluid mechanics, quantum mechanics to string theory. Often developed from the practical context of the problem, the applied techniques have grown in parallel to the more formal theory of resurgence. Knowledge exchange between the twin track approaches is now highly desirable, on the one hand to extend resurgence techniques in a practical manner to PDE problems, on the other to provide a systematic underpinning of the portfolio of existing applied techniques.

This workshop aims to showcase applications of terms beyond all orders techniques to both resurgence and applied mathematical communities with a view to promoting this dialogue.

Fees

Registration Only

Registration Package: £208
Student Registration Package: £158

The Registration Package includes admission to all seminars, lunches and refreshments on the days that lectures take place (Monday - Friday), wine reception and formal dinner, but does not include other meals or accommodation.

Formal Dinner Only

Formal Dinner: £55

Participants on the Accommodation Package or Registration Package, including organisers and speakers, are automatically included in this event. For all remaining participants who would like to attend, such as programme participants, the above charge will apply.

Accommodation

Unfortunately we do not have any accommodation to offer so all successful applicants will need to source their own accommodation.

Please see the Hotels Combined website for a list of local hotels and guesthouses.

Meals

Lunch

Lunch will be held at Churchill College and timings will be confirmed with timetable.

Evening Meal

Participants are free to make their own arrangements for dinner.

Formal Dinner

The Formal Dinner will be held at Corpus Christi College on Thursday 3rd November at 19:30.

The event is a tradition for INI participants and gives you a chance to socialise with your colleagues on a more personal level. It is not one to miss!

Participants on the Registration Package, including organisers and speakers, are automatically included in this event.

Timetable

Monday 31st October 2022
09:30 to 09:55	Registration and Morning Coffee	No Room Required
09:55 to 10:00	Christie Marr Isaac Newton Institute Welcome Talk	Room 1
10:00 to 10:50	Jonathan Chapman University of Oxford Blowup in the nonlinear Schrodinger equation	Room 1
10:50 to 11:20	Morning Coffee	No Room Required
11:20 to 12:10	Gregory Kozyreff Université Libre de Bruxelles Stokes phenomenon in the propagation of weakly nonlinear wave packets	Room 1
12:10 to 14:00	Lunch	No Room Required
14:00 to 14:50	Saleh Tanveer Ohio State University Dubrovin Conjecture and Singularities of Painleve-I Tritronquee solution	Room 1
14:50 to 15:40	Valery Smyshlyaev University College London Two examples of beyond all-orders asymptotics in diffraction and homogenisation	Room 1
15:00 to 17:00	Discussions Fauvet	Room 2
15:40 to 16:00	Afternoon Tea	No Room Required
16:00 to 17:00	Discussions	Room 1
17:00 to 18:00	Welcome Wine Reception at INI	No Room Required

Tuesday 1st November 2022
09:10 to 10:00	John King University of Nottingham Multiple scales and exponentials	Room 1
10:00 to 10:50	Stephen Griffiths University of Leeds The strange instability of the equatorial Kelvin wave	Room 1
10:50 to 11:20	Group Photo and Morning Coffee	No Room Required
11:20 to 12:10	Scott McCue Queensland University of Technology Singularities of Burgers’ equation in the complex plane	Room 1
12:10 to 14:00	Lunch	No Room Required
14:00 to 14:50	Edgardo Villar-Sepúlveda University of Bristol Homoclinic snaking and the emergence of localised patterns beyond all asymptotic orders	Room 1
14:50 to 15:20	Josh Shelton University of Bath Exponential asymptotics for the equatorial Kelvin wave and the higher-order Stokes phenomenon	Room 1
15:20 to 15:50	Afternoon Tea	No Room Required
15:50 to 17:00	Discussions	Discussion Room
15:50 to 17:00	Discussions	Room 1

Wednesday 2nd November 2022
09:10 to 10:00	David Sauzin CNRS (Centre national de la recherche scientifique) Resurgence and Partial Theta Series	Room 1
10:00 to 10:50	Harini Desiraju University of Sydney The solutions of Painlevé equations and Fredholm determinants: a Riemann-Hilbert approach	Room 1
10:50 to 11:20	Morning Coffee	No Room Required
11:20 to 11:50	Samuel Crew University of Bath Parametric resurgence in practice	Room 1
11:50 to 14:00	Lunch	No Room Required
14:00 to 14:50	Akira Shudo Tokyo Metropolitan University Time-domain semiclassical approach to quantum tunneling in nearly integrable systems	Room 1
14:50 to 15:20	Cecilie Andersen University of Bath Challenges in interfacial selection problems with exponential asymptotics	Room 1
15:20 to 15:50	Afternoon Tea	No Room Required
15:50 to 16:20	Fatih Say Ordu University Late terms of a differential equation and singulants for multi-level asymptotics	Room 1

Thursday 3rd November 2022
09:10 to 10:00	Nalini Joshi University of Sydney Asymptotics of discrete Painlevé equations	Room 1
10:00 to 10:50	Peter Clarkson University of Kent Classical solutions of the fifth Painlev\'e equation	Room 1
10:50 to 11:20	Morning Coffee	No Room Required
11:20 to 12:10	Gergő Nemes Tokyo Metropolitan University; Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences Dingle's final main rule, Berry's transition, and Howls' conjecture	Room 1
12:10 to 14:00	Lunch	No Room Required
14:00 to 14:50	Alfredo Deaño Universidad Carlos III de Madrid The Riemann-Hilbert approach to exponentially small asymptotics in Painlevé I	Room 1
14:50 to 15:20	Aaron Moston-duggan Macquarie University Generalized Solitary Waves In Karpman Equations: Effects Of Discretization	Room 1
15:20 to 15:50	Afternoon Tea	No Room Required
15:50 to 16:20	Tomas Lasic latimer University of Sydney Asymptotic analysis of Riemann Hilbert Problems using q calculus	Room 1
19:30 to 22:00	Formal Dinner at Corpus Christi College	No Room Required

Friday 4th November 2022
09:10 to 10:00	Sheehan Olver Imperial College London Uniform numerical-asymptotics for integrable systems via Riemann–Hilbert problems	Room 1
10:00 to 10:50	Dan Dai City University of Hong Kong Asymptotics of Fredholm determinants associated with higher dimensional kernels	Room 1
10:50 to 11:20	Morning Coffee	No Room Required
11:20 to 12:10	Ana Loureiro University of Kent On special function positive solutions of the first discrete Painlevé hierarchy	Room 1
12:10 to 14:00	Lunch	No Room Required
14:00 to 14:30	Claudia Rella University of Geneva Stokes constants in topological string theory	Room 1
14:30 to 15:20	Diego Dominici Johannes Kepler Universität; State University of New York Asymptotic analysis of discrete semi-classical orthogonal polynomials	Room 1
15:20 to 16:00	Afternoon Tea	No Room Required

Applicable resurgent asymptotics: towards a universal theory

Mathematics of beyond all-orders phenomena

Organisers

Christopher Howls University of Southampton
Philippe Trinh University of Oxford

Speakers

Cecilie Andersen University of Bath
Jonathan Chapman University of Oxford
Peter Clarkson University of Kent
Samuel Crew University of Cambridge
Dan Dai City University of Hong Kong
Alfredo Deaño University of Kent
Harini Desiraju University of Birmingham
Diego Dominici State University of New York; Johannes Kepler Universität
Stephen Griffiths University of Leeds
Nalini Joshi University of Sydney
John King University of Nottingham
Gregory Kozyreff Université Libre de Bruxelles
Tomas Lasic latimer University of Sydney
Ana Loureiro University of Kent
Scott McCue Queensland University of Technology
Aaron Moston-duggan Macquarie University
Gergő Nemes Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences
Sheehan Olver Imperial College London
Claudia Rella University of Geneva
David Sauzin CNRS (Centre national de la recherche scientifique)
Fatih Say None / Other
Josh Shelton University of Bath
Akira Shudo Tokyo Metropolitan University
Valery Smyshlyaev University College London
Saleh Tanveer Ohio State University
Edgardo Villar-Sepúlveda University of Bristol

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Participants

Cecilie Andersen University of Bath
Ines Aniceto University of Southampton
Matteo Baggioli Shanghai Jiao Tong University
Zoltan Bajnok WIGNER Research Centre for Physics; Eotvos Lorand University
Kemal Gokce Basar University of North Carolina
Michael Berry University of Bristol
Alan Champneys University of Bristol
Jonathan Chapman University of Oxford
Peter Clarkson University of Kent
Ovidiu Costin Ohio State University
Samuel Crew University of Bath
Dan Dai City University of Hong Kong
Jonathan Dawes University of Bath
Alfredo Deaño Universidad Carlos III de Madrid
Fabrizio Del Monte Université de Montréal; Concordia University
Harini Desiraju University of Sydney
Diego Dominici Johannes Kepler Universität; State University of New York
Patrick Dorey University of Durham; Durham University
Frederic Fauvet University of Strasbourg
Stephen Griffiths University of Leeds
David Gross University of California, Santa Barbara
Qianyu Hao University of Geneva
Daniel Hasenbichler University of Southampton
Christopher Howls University of Southampton
Alexander Its Indiana University-Purdue University Indianapolis
Nalini Joshi University of Sydney
Shingo Kamimoto Hiroshima University
Omar Kidwai University of Tokyo
John King University of Nottingham
Gregory Kozyreff Université Libre de Bruxelles
Tomas Lasic latimer University of Sydney
Kimyeong Lee Korea Institute for Advanced Study (KIAS)
Ana Loureiro University of Kent
Christopher Lustri Macquarie University
Scott McCue Queensland University of Technology
Aaron Moston-duggan Macquarie University
Gergő Nemes Tokyo Metropolitan University; Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences
Adri Olde Daalhuis University of Edinburgh
Sheehan Olver Imperial College London
Pavel Putrov Abdus Salam International Centre for Theoretical Physics
Claudia Rella University of Geneva
Shinji Sasaki Shibaura Institute of Technology
David Sauzin CNRS (Centre national de la recherche scientifique)
Fatih Say Ordu University
Ricardo Schiappa Instituto Superior Técnico, Lisboa
Maximilian Schwick Instituto Superior Técnico, Lisboa
Alexandre Serantes National Centre for Nuclear Research
Didina Serban CEA/Saclay
Josh Shelton University of Bath
Akira Shudo Tokyo Metropolitan University
Kostas Skenderis University of Southampton
Mikael Slevinsky University of Manitoba
Valery Smyshlyaev University College London
Michal Spalinski National Centre for Nuclear Research; Uniwersytet w Bialymstoku
Noam Tamarin Instituto Superior Técnico, Lisboa
Saleh Tanveer Ohio State University
Philippe Trinh University of Bath
Mithat Unsal North Carolina State University
Edgardo Villar-Sepúlveda University of Bristol
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