The UK needs more mathematicians who can tackle messy, real-world problems—and this centre will train them. The problem is a persistent skills gap. Industry and government repeatedly report that too few researchers can apply advanced mathematics to complex systems like financial networks, disease outbreaks, or crop science. The centre addresses this by training PhD students in both mathematical theory and direct collaboration with external partners—banks, drug companies, engineering firms—who supply the real problems. If successful, the centre will produce a steady pipeline of mathematically skilled leaders for academia, industry, and regulation. These researchers could help model financial contagion to prevent future crises, improve how we predict tipping points in ecosystems or epidemics, and translate biological data into new treatments. The work also advances fundamental mathematics itself—developing new methods for handling complex data, network structures, and system resilience—which in turn enables better solutions to the practical challenges that keep society running.
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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.
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