First UK-Japan mathematics workshop in nonlinear partial differential equations

Swansea University was pleased to host the first workshop aimed at building new relationships between the mathematics communities in Japan and the UK.

First UK-Japan mathematics

The workshop brought to Swansea a group of leading Japanese and UK nonlinear partial differential equations (PDE) experts to exchange ideas in two closely interconnected fields: travelling wave solutions of reaction-diffusion equations and systems; and nonlinear Schrödinger equations (NLS).

Japan has a longstanding tradition of first-class research in the fundamental analysis of nonlinear PDE and their applications, with particular strength in PDE arising in models from biology and materials science. Swansea has an active Nonlinear PDE group (Crooks, Dancer, Finkelshtein, Mercuri and Moroz), whose research in reaction-diffusion systems and nonlocal nonlinear PDE is particularly highly regarded internationally. Despite having many research interests in common, most of the participants have met in Swansea for the first time. Both communities see a substantial potential for future collaboration.

Bringing together experts on the interconnected areas of travelling waves and NLS was particularly important because they include some of the least understood and most challenging questions in the field of nonlinear PDE. Travelling waves is a traditional area of strength for both the UK and Japan. Despite a long history, this remains a vibrant and fruitful research subject, particularly for systems or problems with nonlocal terms, that is strongly linked to applications in biology and fluid dynamics. Speakers on travelling waves and related reaction-diffusion questions included leading names such as Hilhorst (France), Ninomiya (Japan), as well as Dancer (Swansea), whose talk discussed both themes of the workshop.

The second theme, NLS, is one of the fastest growing areas of nonlinear PDE. A particular emphasis was given to the newly emerging area of NLS with nonlocal interactions, which has its origin in particle physics. Recently, similar ideas were employed in the analysis of large systems of interacting particles of different origin, from materials science and biology to social sciences and models for opinion formation. Speakers in this research area included Del Pino (Bath), Kabeya (Japan), Kawakami (Japan), Musso (Bath) and Ruzhansky (Imperial College London). Together, they presented an overview of the most recent developments in this fast-moving area.

Prof. Vitaly Moroz said: “It was both a pleasure and honour for the Department of Mathematics at Swansea University to host this prestigious workshop. An event of this scale attracted participants from throughout the UK and Europe and highlighted the Swansea Nonlinear PDE group as one of international significance. Bringing together Japanese and UK strengths will enrich Nonlinear PDE study in both countries and enhance both research outputs and prospective grant capture.”

Dr Elaine Crooks said: “It was wonderful to welcome so many excellent mathematicians from around the world to Swansea. The workshop was full of interesting talks on state-of-the-art advances and lively research discussions that will provide a great starting point from which we can develop and grow this exciting new UK-Japan link.”

The meeting was supported by the London Mathematical Society via the Conference Grants – Scheme 1, and attracted 30 established researchers and many early career researchers.