PhD in mathematics in the UK | doctorate in applied mathematics and statistics

You will be part of a small group of mathematics and statistics PhD students, but part of a wider school and university base that includes, for example, staff and student researchers in computing and engineering, facilitating further potential for interdisciplinary interactions. To help you build your academic network, you will be aligned with the Computing and Mathematical Science Research Excellence Group. Other groups and centres at the university are also open to PGR members from the maths department. 

This drives and informs the research through a wide range of topics based around three research areas:

• Computational methods
• Discrete mathematics
• Statistics and operational mathematics. 

We also welcome mathematics and statistics PhD students whose original research is developed through interdisciplinary projects, offering a wealth of close interaction with the university's science departments. We have had many successful PhDs that connect with areas such as biology (eg big data analysis) and computing (eg visualisation) or financial mathematics. 

We have a strong reputation in a range of topics in mathematics, which is strengthened by collaborations with many UK and international academic institutes (eg University of Liverpool; Durham University; Royal Holloway, UK; University of Rome, Italy; University of Montepellier, France) and industrial partners (for example, Hurstwood Park Neurosciences Centre, Haywards Heath, UK;  Southern Water, UK; and Poste Italiane, Napoli, Italy).

The focus of mathematics research at the University of Brighton is into the use of applied numerical methods, with close relationships with research progressing biomedical sciences, computing and engineering.

We would be particularly interested in projects that aligned to one or more of these long-standing strengths at the university: 

• Computational methods focuses on the development of numerical methods for solving problems in applied mathematics and engineering. Avenues of interest include finite element methods, boundary element methods and the machinery which underpins these, such as numerical methods of linear algebra. These methods have been applied to problems as diverse as modelling the sound field radiated from a loudspeaker to modelling the formation and growth of cavities in the spinal cord.
• Discrete mathematics is interested in the development and application of discrete mathematical techniques, particularly as applied within computer science. Areas of interest include logic, formal languages, algebraic structures, algorithms, graph theory, combinatorial and computational geometry and topology. These methods have been applied to the development of visual logics to assist human reasoning, the development of information visualisation algorithms which automatically generate diagrams, and efficient knot detection with biological applications.
• Statistics and operational research has a wide range of research interests from theoretical probability to applied statistics and rigorous machine learning. Examples of current work are the application of financial and operational research methods for pricing financial and energy instruments and analysing investment incentives, the development of statistical methodologies for analysing big data studies, the development of marginal regression models with correlated discrete response variables, the theoretical analysis of online prediction models and the application of topological data analysis methods.

Research supervisors for your PhD research programme

As a mathematics postgraduate you will benefit from research supervision comprising two or maximum three members of academic staff. Depending on your research specialism one of those supervisors may be from another school, another research institution, or could include an external partner. 

You will identify your potential mathematics research supervisor from the early stages of application and they will usually then support you throughout your programme of study, helping you carry out your research interests, guiding your learning of rigorous research methods and preparing you for the next stage of your career.

You should consider the staff listed below and create a short draft research proposal identifying your suitability for supervision from that person's research specialism. If you discuss your research with a potential supervisor it is likely to improve your opportunity to study with us. 

Research training and support

The independent research programme for mathematical research is balanced and enhanced with a range of support from your supervisors and the extended academic community. You and your fellow postgraduate research students will have the opportunity to attend and present at research seminar sessions at the Computing and Mathematical Science Research Excellence Group with guests from professional and academic spheres. The PhD programme will give you the opportunity to build research skills as well as developing transferable skills essential for employment and practice within mathematics and its related fields.

As a member of the Brighton Doctoral College, you will benefit from regular opportunities on a training programme designed to support postgraduate researchers at all stages of the PhD and help them achieve their career goals. Attendance at appropriate workshops within this programme is encouraged, as is involvement with the annual Festival of Postgraduate Research. Academic and technical staff also provide more subject-specific training. 

You will benefit from access to all necessary research resources, including a contemporary range of electronic resources via the university’s Online Library, as well as the physical book and journal collections housed within campus libraries. The library services are connected to national and international collections and students also have the option of inter-library loans.

We strongly recommend that you apply with the support of one of our academics. By establishing your supervisor from the early stages of application, you will be supported through the application process and can make the best start to your programme of study.

You should consider the staff listed below and create a short draft research proposal identifying your suitability for supervision from that person's research specialism and your place in the wider context of the department's research ambitions. Their contact details are available on their full profile.

Our primary staff supervising in the discipline are listed. For further information on university supervisory staff, including cross-disciplinary options, please visit research staff on our research website.

Dr Alexey Chernov

I am interested in supervising postgraduate research projects related to mathematically intensive methods of machine learning. My main area is sequential online forecasting, particularly prediction with expert advice. I am also interested in reinforcement learning (especially as a generalisation of online forecasting), kernel methods and topological data analysis.

Dr Paul Harris

I supervise PhD students who use numerical methods (such the boundary element method and finite element method) to solve problems in applied mathematics.

PhD projects that I am interested in supervising include using combined boundary element and finite element methods for modelling the motion of biological cells due to chemotaxis, the use of the finite element method to model deformations of the spinal cord (in relation to the medical condition syringomyelia) and the use of the finite element method in image analysis (such denoising images and segmenting images).

Dr Barbara S. Lancho Barrantes

My area of expertise is Bibliometrics and Scientometrics. I would be interested in supervising PhD/Master/Undergraduate students at any angle of Bibliometrics and Scientometrics and linking them with data analytics and data science. Some examples of specific potential topics (but are not limited to):

• Analyse and examine the relation between economic factors and the amount of scientific productivity within countries, academic institutions, geographic regions and subject areas.
• Examine the citation flows between countries or organisations that collaborate.
• Analysis of Scientific Research Collaborations (institutional, national, international)
• Research on Sustainable Development Goals (SDGs)
• Cyber Security, theoretical and practical aspects
• Bibliometric horizon scanning methodology for identifying emerging topics.
• Analyse the relationship between international collaborations and the mobility of researchers.
• Conduct gender analyses based on publication data, especially in the context of the SDGs.
• Creation and implementation of new scientometric indicators in open research infrastructures.
• Examine the open-access citation advantage.
• Analysis of predatory publishing as a threat to research integrity.
• Understand the research profiles of Higher Education Institutions and their connection with scientific productivity.
• Bibliometric mappings of countries, institutions, disciplines, etc.

These topics are general and can be more detailed once the students show an interest in any of them. I will consider any new proposals and discuss any ideas that come up.

In my papers, I analyse the citation increment among collaborating countries. I have also examined how citation patterns of disciplines and bibliographic database coverage may influence the citation flows between subject areas.

The impact of economic factors on countries' research productivity has been the subject of my recent publications. I used data from citation databases, UNESCO, and the OECD for this purpose. I confirmed the relationship between investment in research and scientific results using multiple linear regression.

As well as understanding the scientific contribution to Sustainable Development Goals (SDGs), I focus my research on the mechanisms to interpret this data, since different databases can produce different results.

Dr Anestis Touloumis

I am interested in supervising postgraduate research students in machine learning methods, categorical data analysis, multivariate analysis and high-dimensional statistics. Projects are likely to involve development of open-source software to support and disseminate the findings of the research.