Mathematics PhD

Our research-active academics are involved in cutting-edge research covering a range of topics including applied analysis, computational mathematics, continuum mechanics and mathematical physics, financial mathematics, operational research and applied statistics.

We address problems of real biological or engineering importance and investigate the underlying mathematical and phenomenological processes. There is a strong emphasis on the development of innovative analytic, asymptotic, computational and hybrid methods. Our research also focuses on random matrix theory, quantum information theory, mathematical foundations of quantum mechanics, mesoscopic disordered systems, statistical mechanics, graph theory, matroid theory, and infinite-dimensional Riemannian geometry, algebraic geometry and orthogonal polynomials. 

Find out about the exciting research we do in this area. Browse profiles of our experts, discover the research groups and their inspirational research activities you too could be part of. We’ve also made available extensive reading materials published by our academics and PhD students.  

Learn more about research in this area.

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Our researchers create knowledge and advance understanding, and equip versatile doctoral researchers with the confidence to apply what they have learnt for the benefit of society. Find out more about working with the Supervisory Team.

You are welcome to approach your potential supervisor directly to discuss your research interests. Search for expert supervisors for your chosen field of research.

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Applied and Numerical Analysis:

• Analysis of partial differential equations, including nonlinear PDEs of fluid mechanics and mathematical biology (S. Mikhailov, M. Winter)
• Analysis and numerical implementation of boundary-domain integral and integro-differential equations (S. Mikhailov)
• Computational modelling of problems in solid mechanics, as well as acoustic, elastic and electromagnetic wave propagation, by Finite Element and Boundary Element methods (S. Langdon, M. Maischak, S. Shaw, M. Warby, J. Whiteman)
• Approximation of orthogonal polynomials and special functions (I. Krasikov)
• Abstract bifurcation and singularity theory (J. Furter)
• Fast solvers and preconditioners, error estimators and adaptive algorithms, high performance and scientific computing, software development (S. Langdon, M. Maischak, S. Shaw)
• Theoretical and computational modelling of fatigue, damage, durability, and fracture (S. Mikhailov)

Financial Mathematics and Operational Research:

• Financial modelling; in particular, forecasting of spreads in commodity futures prices using latent state based models/ MCMC filters (P. Date, J.W. Lim)
• Applications of machine learning in financial models. (P. Date, E. Boguslavskaya)
• Optimisation problems in power system transmission networks (P. Date, C. Lucas)
• Modelling paradigms and stochastic optimisation applied to (financial) decision making under uncertainty and risk (P. Date, D. Roman, C. Lucas)
• Meta heuristics for solving large combinatorial problems. (C. Lucas)
• Preventative maintenance modelling in the face of uncertainty (P. Date, C. Lucas)
• Stochastic optimal control, with applications in finance (D. Roman, C. Lucas)
• Efficient simulation of Levy processes (E. Boguslavskaya, J.W. Lim)

Mathematical Physics and Applied Mathematics:

• Random matrix theory and its applications (D. Savin, I. Smolyarenko)
• Resonances and transport in open wave chaotic systems (D. Savin)
• Quantum information and quantum computing (S. Virmani)
• Algebraic geometry, birational geometry (A.-S. Kaloghiros)
• Complex networks (G. Rodgers, I. Smolyarenko)
• Statistical mechanics of complex systems and econophysics (G. Rodgers)
• Waves in solids and fluids (M. Greenhow, J. Lawrie, E. Nolde, A. Pichugin)
• Structural acoustics and diffraction theory (M. Greenhow, J. Lawrie)
• Asymptotic theory of thin elastic structures (E. Nolde , A. Pichugin)
• Layout optimization of structures (A. Pichugin)

Statistics and Data Science:

• High-dimensional Bayesian Learning (D. Chakrabarty)
• Learning in the Absence of Training Data (D. Chakrabarty)
• Applications of Statistics in Astronomy, Materials Science, etc. using MCMC-based inference (D. Chakrabarty, C. Spire, K. Yu)
• Random Geometric Graphs & Networks (D. Chakrabarty, B. Parker)
• Design of Experiments for Network Science (B. Parker)
• Algorithms for Experimental Design (B. Parker)
• Bayesian regression beyond the mean (K. Yu)
• Weibull analysis for lifetime data analysis (K. Yu)
• Quantile regression for big data (K. Yu)
• Machine learning methods and application (K. Yu, B. Parker)
• Nonparametric smoothing (K. Yu)
• Advanced regression analysis of carbon emissions (K. Yu)
• Applications of Statistics in Health Science, Biology and Genomics (K. Yu)

This course can be studied undefined undefined, starting in undefined.

Find out about what progress might look like at each stage of study here: Research degree progress structure.

Research support

Excellent research support and training

The Graduate School provides a range of personal, professional and career development opportunities. This includes workshops, online training, coaching and events, to enable you to enhance your professional profile, refine your skills, and plan your next career steps as part of the Researcher Development Programme. The researcher development programme (RDP) offers workshops and seminars in a range of areas including progression, research management, research dissemination, and careers and personal development. You will also be offered a number of online, self-study courses on BBL, including Research Integrity, Research Skills Toolkit, Research Methods in Literature Review and Principles of Research Methods.

Library services

Brunel's Library is open 24 hours a day, has 400,000 books and 250,000 ebooks, and an annual budget of almost £2m. Subject information Specialists train students in the latest technology, digital literacy, and digital dissemination of scholarly outputs. As well as the physical resources available in the Library, we also provide access to a wealth of electronic resources. These include databases, journals and e-books. Access to these resources has been bought by the Library through subscription and is limited to current staff and students.

Dedicated research support staff provide guidance and training on open access, research data management, copyright and other research integrity issues.

Find out more: Brunel Library

You will receive tailored careers support during your PhD and for up to three years after you complete your research at Brunel. We encourage you to actively engage in career planning and managing your personal development right from the start of your research, even (or perhaps especially) if you don't yet have a career path in mind. Our careers provision includes online information and advice, one-to-one consultations and a range of events and workshops. The Professional Development Centre runs a varied programme of careers events throughout the academic year. These include industry insight sessions, recruitment fairs, employer pop-ups and skills workshops.

In addition, where available, you may be able to undertake some paid work as we recognise that teaching and learning support duties represent an important professional and career development opportunity.

Find out more.

Following the completion of the course students may follow several career paths:

• Career path within academia starting as a Post-doc or Lecturer/Assistant Professor at a university
• Career progression within research institutions commencing as a Researcher and progressing to Senior Researcher.
• Career path within the industry as a Research Scientist, Senior Research Scientists, Financial Analyst, etc.
• Career path in secondary education as Maths teacher, Maths Subject Leader