Mathematics of highly connected, real-world systems

The scope of this priority is the development of mathematical concepts and tools to understand, predict, design and control systems with many interacting and interdependent components.

Real-world systems are rapidly increasing in scale and connectivity. Examples include the financial and economic systems; infrastructure networks such as electricity and transport; manufacturing systems and social systems. A particular feature in many of these problems is the involvement of diverse human behaviour, which introduces new challenges such as understanding and modelling the resulting uncertainty.

Mathematical sciences provide the tools and techniques to develop a fundamental understanding of the characteristics and behaviour of systems across different length and time scales with differing levels of uncertainty both in the models and in the observable data. The underpinning mathematical areas that need development include network science, agent-based modelling and micro-simulation, control theory, multi-scale modelling, non-linear dynamics, statistics, applied probability, and operational research.

Proposals in this area should be focussed around the mathematical concepts and tools needed to understand, model, control and predict key outcomes in real-world systems at different scales, and should collaborate with other academic disciplines and end-users (including industry) as appropriate, to ensure that the technology that is developed is fit for purpose and delivers maximal impact.

Centres for Doctoral Training graduates will be systems thinkers who are conversant in a broad range of mathematical skills and who are able to interpret mathematical insights in ways that convey meaning to other scientists, engineers and end-users, including policy makers.