More than 100 academics took part in the Applicable Resurgent Asymptotic research programme, organised by Dr Ines Aniceto, Principal Research Fellow and EPSRC Early Career Fellow, and Professor Christopher Howls, from Mathematical Sciences.
The programme was held at the Isaac Newton Institute (INI) for Mathematical Sciences, in Cambridge, and enabled the next generation of early career researchers to exchange knowledge and set up a network of collaborative opportunities for the future.
They had the opportunity to integrate recent significant, but parallel, advances in mathematics and physics into a more systematic approach to asymptotic analysis of more complicated, complex and multidimensional problems.
Addressing a complex challenge
Asymptotic analysis provides approximate, accurate and analytical solutions to a broad range of problems where an exact solution cannot be found.
Despite the ready availability of computing power, and the rise of data science and artificial intelligence (AI), asymptotic analysis is still one of the most important tools used in mathematics and theoretical physics.
It helps to gain a comparatively quick numerical result and an understanding of the underpinning drivers of a complicated quantitative system.
The modern approach to asymptotic analysis involves incorporating exponentially small quantities, which over time and space can grow to be exponentially large, and understanding these potentially explosive quantities. It is essential in all sorts of areas beyond maths: from jet engine noise pollution, to submarine wakes, from rainbows to stealth technology, from black holes to Bose-Einstein Condensates and from quantum field theory to quark-gluon plasmas.
Existing asymptotic approaches have been in use for nearly two centuries, with a very interesting history of its development, but still usually remain context specific. Recently great advances and significant breakthroughs have been made by mathematicians and physicists by blending a numerical approach with a theory called resurgence.
The Southampton-led programme addressed how to unify these asymptotic approaches into techniques that enhance efficiency and have broader applications.
Ines said "Although overlapping, these advances have developed largely in parallel. One ambitious goal of this INI programme was to bring these communities together to develop a common understanding of these advanced asymptotic approaches for future applications, not only in mathematics and physics, but also in rapidly emerging areas such as in engineering, data science and systems biology."
It built on a previous INI programme run 30 years ago that forged career-building collaborative links between an earlier generation of mathematicians and physicists who developed and applied the then radical approach of exponential asymptotics. They worked with the next generation to contribute to the most recent advances both at the levels of methodology and applications.
The impact
The INI programme provided the opportunity to bring academics at all levels of experience together to establish cross-generational and interdisciplinary collaborative links. These have developed a novel unified approach to the practical applications of asymptotics, which combine the best exponential asymptotics techniques with the extensive theory of resurgence.
No other previous meeting has been able to bring these fields together for so long and in such numbers and scope to advance the common benefits. The interviews with the organisers of this meeting show their own perpectives and these common benefits.
Ines added: “By combining the knowledge between the different approaches that knowledge will be stronger and more unified. I have already been working with applied mathematicians on physics problems using methods that I hadn’t thought possible.”
As well as the problems that were solved during the Isaac Newton Institute programme, the lasting impact will be the fostering of a new generation of collaborations that will attack a wider range of future challenges with more advanced and capable asymptotic techniques.
