EPSRC and MRC Centre for Doctoral Training in Mathematics for Real-World Systems

MathSys addresses two of EPSRC's CDT priority areas in Mathematical Sciences: "Mathematics of Highly Connected Real-World Systems" and "New Mathematics in Biology and Medicine". We will train the next generation of skilled applied mathematical researchers to use and develop cutting-edge techniques enabling them to address a range of challenges faced by science, industry and modern society. Our Centre for Doctoral Training will build on the experience and successes of the Complexity Science DTC at Warwick, while refining the scope of problems addressed. It will provide a supportive and stimulating environment for the students in which the common mathematical challenges underpinning problems from a variety of disciplines can be tackled.

The need for mathematically skilled researchers, trained in an interdisciplinary environment, has never been greater and is viewed as a major barrier in both industry and government. This is supported by quotes from reports and business leaders: "Systems research needs more potential future leaders, both in academia and industry" (EPSRC workshop on Systems science towards Engineering, Feb 2011); Andrew Haldane (Bank of England, 2012) said "The financial crisis has taught us the importance of modelling and regulating finance as a complex, adaptive system. That will require skills currently rare or missing in the regulatory community - including, importantly, in the area of complexity science"; Paul Matthews (GlaxoSmithKline) stated "Scientists trained in statistical and computational approaches who have a sophisticated understanding of biologically relevant models are in short supply. They will be major contributors in the task of translating insights on human biology and disease into treatments and cures."

Our CDT will address this need by training PhD students in the development and innovation of mathematics in the context of real-world systems and will operate in close collaboration with stakeholders from outside academia who will provide motivating problems and real-world experience. Common mathematical themes will include statistical behaviour of complex systems, tipping points, novel methods in control and resilience, hierarchical aggregation methods, model selection and sufficiency, implications of network structure, response to aperiodic forcing and shocks, and methods for handling complex data. Applications will be driven by local and external partner expertise in Epidemiology, Systems Biology, Crop Science, Healthcare, Operational Research, Systems Engineering, Network Science, Financial Regulation, Data Analysis and Social Behaviour. We believe that the merging of real-world applications with development of novel mathematics will have great synergy; applications will motivate and drive mathematical advances while novel mathematics will allow students to solve challenging real-world problems.

The doctoral training programme will follow a 1+3 year MSc+PhD model that has proved successful in the Complexity Science DTC. The first year will consist of six months of taught training, followed by 3-month group research projects on problems set by external partners and a 3-month individual research project, leading to an MSc qualification. This preparation will enable the students to make rapid progress tackling their 3-year PhD research project, under the guidance of one mathematical and one application-oriented supervisor, alongside general skills training and group research projects. We have over 50 suitable supervisors with relevant mathematical expertise, all enthusiastic to contribute; they will be supported by a similar number of application-oriented supervisors from across campus and from external partners.

The CDT seeks the equivalent of 7 full studentships per year from EPSRC and has commitment from non-RCUK sources for the equivalent of 3 full studentships per year.

Impact from the MathSys CDT will arise from three separate mechanisms, each of which will generate a spectrum of academic, economic and societal impacts.

1) Most prominently, this CDT will create the next generation of quantitative researchers that are trained in the necessary skills and techniques to make substantial impact in academia, industry and government agencies. Creation of skilled researchers with a broad scientific outlook will have a number of beneficiaries. We expect that our students will be in high demand within academia and will be the researcher leaders of tomorrow. In addition, many of our brightest students post-PhD are now moving out of academia to research positions within industry or government agencies; such students are likely to generate substantial financial impact within industry and societal benefits within government agencies. By encouraging strong collaboration with our external partner organisations throughout their training, our PhD students will have a broad insight into the impact that mathematics can bring, and the routes through which academic excellence can be translated into meaningful applied outputs with impact. The assembled team of supervisors has an excellent track-record of supporting and training high calibre PhD students with skills that are in demand both within and outside of academia.

2) More immediate economic and societal benefits will accrue from the direct interaction of our students with external partners that is an integral part of their training. We anticipate that 4-6 students per cohort will undertake a PhD that is co-supervised by one of our external partner organisations; in addition all students during their MSc year will partake in one of several group projects led and supported by one of our external partners. In both cases, research will be focused towards real-world problems that are of current concern to the partners. It is anticipated that through these close interactions our students will develop methodologies and results that will address real-world problems. These new solutions to particular challenging real-world problems from external partners are likely to have substantial industrial, economic or societal benefits as they directly tackle prominent and pressing issues set by those with the greatest knowledge of the real-world challenges. Impact will therefore be generated through direct problem-solving research with a number of the UK's leading organisations.

3) Finally, we envisage that the mathematical techniques that are developed in the context of one real-world problem will have wider benefit to other academic fields. Although the immediate beneficiaries are likely to be other academics who will gain from an increased repertoire of tools and techniques, in the longer term these insights are likely to lead to new applications that feed back into industry, finance and society in general. The transdisciplinary nature of our MathSys CDT will facilitate such interactions, promoting the exchange of ideas between diverse subject areas. We firmly believe that such cross-fertilisation of ideas will be a feature of the MathSys CDT, where students are united by common goals of quantitative understanding and prediction and a common language of mathematics. We therefore expect rapid impact in a variety of applied areas, as novel techniques are introduced.