# Applicable resurgent asymptotics: towards a universal theory

Created: | 2021-03-19 10:36 |
---|---|

Institution: | Isaac Newton Institute for Mathematical Sciences |

Description: | Programme Theme
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. |

# Media items

This collection contains 47 media items.

### Media items

#### The Phenomenon of Dispersive Revivals

Beatrice Pelloni Heriot-Watt University

15 June 2021 – 13:30 to 14:30

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 16 Jun 2021

#### A More Exotic Asymptotic Zoo: New Stokes Lines, Virtual Turning Points and the Higher Order Stokes Phenomenon

Howls, C

Thursday 22nd April 2021 - 16:00 to 17:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 23 Apr 2021

#### Applications of Resurgence Theory to Quantum Theories: ZN Twist, Exact–WKB and Phase Transition

Tatsuhiro Misumi Kindai University

17 June 2021 – 11:00 to 12:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 18 Jun 2021

#### Asymptotics + Functional Equations = Exact Quantisation Conditions ?

Davide Masoero Universidade de Lisboa

14 June 2021 – 11:10 to 12:10

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 16 Jun 2021

#### Borel Summation and Resurgence in PDEs

Ovidiu Costin Ohio State University

18 June 2021 – 16:00 to 17:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 21 Jun 2021

#### Chasing Renormalons in One Dimension

Tomas Reis University of Geneva

17 June 2021 – 13:30 to 14:30

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 18 Jun 2021

#### Differentiations and Diversions

Berry, M

Tuesday 30th March 2021 - 16:00 to 17:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 1 Apr 2021

#### Ecalle’s Theory of Resurgence

Dorigoni, D

Wednesday 24th March 2021 - 16:00 to 17:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 25 Mar 2021

#### Ecalle’s Theory of Resurgence

Dorigoni, D

Thursday 25th March 2021 - 16:00 to 17:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 26 Mar 2021

#### Ecalle’s Theory of Resurgence

Dorigoni, D

Friday 26th March 2021 - 16:00 to 17:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Sat 27 Mar 2021

#### Exact WKB and abelianization of flat connections

Neitzke, A

Thursday 6th May 2021 - 16:00 to 17:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 7 May 2021

#### Exponential Asymptotics for Physical Applications

Chapman, J

Wednesday 24th March 2021 - 14:00 to 15:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 25 Mar 2021

#### Exponential Asymptotics for Physical Applications

Trinh, P

Thursday 25th March 2021 - 14:00 to 15:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 26 Mar 2021

#### Exponential Asymptotics for Physical Applications

King, J

Friday 26th March 2021 - 14:00 to 15:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Sat 27 Mar 2021

#### Exponential asymptotics in applied mathematics

Chapman, J

Thursday 18th March 2021 - 15:30 to 16:30

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 19 Mar 2021

#### From quasinormal modes to constitutive relations

Withers, B

Thursday 13th May 2021 - 16:00 to 17:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 17 May 2021

#### From rainbow to mass gap: Resurgence and Lefschetz thimbles at work

Unsal, M

Tuesday 13th April 2021 - 16:00 to 17:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 14 Apr 2021

#### Generic solution breakdown in Hele-Shaw flow with a point sink: an open selection problem?

Linda Cummings New Jersey Institute of Technology

8 June 2021 – 16:00 to 17:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 9 Jun 2021

#### Global asymptotic analysis of the Painleve equations. The Isomonodromy-Riemann-Hilbert approach.

Its, A

1 June 2021 – 16:00 to 17:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 2 Jun 2021

#### Global study of differential equations via the exact WKB - from Schrödinger and Panlevé

Takei, Y

Thursday 29th April 2021 - 08:00 to 09:00

**Collection**:
Applicable resurgent asymptotics: towards a universal theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 3 May 2021