Research profile
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.
Browse the work of subject-relevant research groups
Find a supervisor
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.
View supervisors by research area
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)
PhD topics
While we welcome applications from students with a clear direction for their research, we are providing you with some ideas for your chosen field of research:
- Ambient Vibration-Based Calibration of Finite Element Models of Bridges, supervised by Michael Rustell
- Automatic computational fluid-dynamics, supervised by James Tyacke
- Autonomous Drone Surveys and Convolutional Neural Networks for Bridge Maintenance: A Predictive Approach Using Finite Element Analysis, supervised by Michael Rustell
- Bridging the Gap: Integrating Neural Radiance Fields and Micro-drones for Enhanced 3D Volumetric Finite Element Analysis, supervised by Michael Rustell
- Decision making for stratified medicine life cycle, supervised by Yang Yang
- Decision making for stratified medicine life cycle, supervised by Yang Yang
Research journey
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
Careers and your future
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.
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
UK entry requirements
The general University entrance requirement for registration for a research degree is normally a First or Upper Second Class Honours degree (1st or 2:1).
An interview will be required as part of the admissions process and will be conducted by at least two academic staff members remotely via MS Teams, Zoom, or face to face.
Applicants will be required to submit a personal statement and a research statement.
Please contact your proposed supervisor, where possible, to receive feedback and guidance on your research statement before submitting it. Learn how to prepare a research statement here.
EU and International entry requirements
English language requirements
- IELTS: 6.5 (min 6 in all areas)
- Pearson: 59 (59 in all subscores)
- BrunELT: 63% (min 58% in all areas)
- TOEFL: 90 (min 20 in all)
You can find out more about the qualifications we accept on our English Language Requirements page.
Should you wish to take a pre-sessional English course to improve your English prior to starting your degree course, you must sit the test at an approved SELT provider for the same reason. We offer our own BrunELT English test and have pre-sessional English language courses for students who do not meet requirements or who wish to improve their English. You can find out more information on English courses and test options through our Brunel Language Centre.
Please check our Admissions pages for more information on other factors we use to assess applicants. This information is for guidance only and each application is assessed on a case-by-case basis. Entry requirements are subject to review, and may change.
Fees and funding
2024/5 entry
International
£23,615 full-time
£11,805 part-time
UK
£4,786 full-time
£2,393 part-time
Fees quoted are per year and are subject to an annual increase.
Some courses incur additional course related costs. You can also check our on-campus accommodation costs for more information on living expenses.
Brunel offers a number of funding options to research students that help cover the cost of their tuition fees, contribute to living expenses or both. Recently the UK Government made available the Doctoral Student Loans of up to £25,000 for UK and EU students and there is some funding available through the Research Councils. Many of our international students benefit from funding provided by their governments or employers. Brunel alumni enjoy tuition fee discounts of 15%.