Warwick EPSRC Symposium 2016-17 on Partial Differential Equations and their Applications

The Warwick EPSRC Mathematics Symposium is organised annually by the University of Warwick with the support of the EPSRC for the benefit of the mathematical sciences community in the UK. It brings leading national and international experts together with UK researchers in a year-long programme of research activities focused on an emerging theme in the mathematical sciences. The proposed symposium for the 2016-17 academic year will concentrate on the theme of "Partial Differential Equations and Their Applications".

Partial differential equations provide the fundamental objects which are used to model the world around us. Classically they are used in geometry, mathematical physics, fluids, mechanics in general and biology, and increasingly they are employed in social sciences. In very general terms, the symposium will constitute a forum for the leading resarchers to discuss and propose solutions of emerging problems in theory and applications and to develop techniques for the analysis and numerical approximation of PDEs.

The fundamental aim of Warwick EPSRC Symposia in terms of impact is to increase the ability of UK universities to generate top quality research in mathematics and its applications. We ensure this happens by identifying and exploring promising new research directions, fostering international links, facilitating the formation of new collaborations, positioning the UK at the forefront of research in active and emerging areas of mathematics, showcasing and disseminating recent results and promoting the interest of PhD students, postdocs and early career researchers in upcoming areas of research. The proposed 2016/17 Symposium will benefit many researchers working in PDEs and their applications and we envisage the following impacts will be delivered.

- Strengthening the UK knowledge base in Partial Differential Equations and links with applications and related areas.
- Bringing the top world specialists to the UK to promote collaboration with UK researchers, including postgraduate students and recent postdocs, and to enhance our research basis.
- Supporting and also building links between several leading UK groups in this active and vibrant area and enhancing their position at the cutting edge of research.
- Focusing attention and developing areas identified by the International Review of Mathematics 2010 where specific recommendations for development were made.
- Fostering the development of home-grown talent by engaging the PhD and young postdoctoral community working in the area, providing them with exposure to the cutting edge research in the area, and the environment in which to develop career opportunities and research connections and collaboration.

The quality and cutting-edge nature of this proposal will ultimately have wide significant implications beyond academic research over the longer term. The ubiquitousness and relevance of PDE in the modelling of real-life scenarios is reflected in the proposed speakers for the workshops, which include researchers from other disciplines such as Statistics, Scientific Computing, Physics, Engineering and Materials. Several workshops feature and actively engage real-life applications and practitioners.

Pedestrian motion modelling, identification of clusters in social networks, opinion formation and criminal and terrorist activity are socioeconomic examples for which the workshop Emerging PDE models in Socio-Economic Sciences will have significance beyond the analysis of PDEs. The workshop Density Functional Theory: Analysis and computation will invite participants who are actively involved in industrial research. The workshop Numerical analysis of PDEs will not only have the generic impact enjoyed by the development of computational methods for PDEs but also will address the wider need for efficient and reliable open source software packages and will invite as participants core developers of widely used open source software packages, (DUNE, Nektar++, Featflow).

The symposium will benefit researchers working in all areas of PDEs and their applications. The programme will be advertised widely as possible through the website of the symposium and through our contacts at UK universities thus maximising the impact on the community. Young researchers in the UK will draw immense profit from a year of sustained research activities in this broad area. The programme will be of particular interest to the PhD students and researchers affiliated to several EPSRC-funded CDTs at Warwick and beyond.

We will provide a top-quality internationally renowned speaker to give a talk in this area aimed at the general public, to raise public awareness and stimulate interest in this important and exciting area of mathematics. This will form part of the ongoing series of Warwick Public Lectures in Mathematics and Statistics.