ARA
1 March 2021 to 25 June 2021
Following the outbreak of COVID19, this event has been split into two parts:
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.
22 March 2021 to 26 March 2021
14 June 2021 to 18 June 2021
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 | |
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