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  1. Research degrees
Study at City

PhD / MPhil Mathematics

Candidates carry out original research within the Department of Mathematics in the areas of representation theory, mathematical physics and mathematical biology.

Key information

Start date

Research students may commence their degree studies on 1st October.


Full-time: 2 - 4 years

Part-time: 3 - 7 years



Full-time: £4,500 per year

Part-time: £2,250 per year


Full-time: £15,000 per year

External Candidate: £785 per year

Part-time: £7,500 per year


Candidates carry out original research within the Department of Mathematics specific areas of expertise:

  • Representation theory
  • Mathematical physics
  • Mathematical biology

Recent publications from the Department of Mathematics.

Examples of recent PhD theses:


Entry requirements

A good first class degree in Mathematics or Physics from a UK university or a recognised equivalent from an overseas institution. Some subjects also require an appropriate Masters qualification.

English requirements

Proof of English language proficiency is required for applicants whose first language is not English. We require a minimum IELTS overall score of 6.5 with a minimum of 6.0 in each of the four components; or, a minimum TOEFL overall score of 92 with a minimum of 22 in Writing and 20 in Listening, Speaking and Reading.

Please note that the UKVI currently requires us to confirm that you are at level B2 or above in all components of English before issuing visa documents.

Find out more about English language proficiency requirements at City.

Visa requirements

International Students (EEA and Non EEA) coming to study in the UK, may need to apply for a visa or entry clearance to come to the UK to study. The way that you apply may vary depending on the length of your course. There are different rules for:

  • EEA nationals joining the programme in 2020 and EEA nationals joining from January 2021
  • Students on courses of more than six months
  • Students on courses of less than six months
  • Students on a pre-sessional English language course.

For more information see our main Visa page.


The Department carries out world class research in the areas of representation theory, mathematical physics and mathematical biology.

The Representation Theory Group has a broad range of expertise in mainstream modern representation theory. The research focus is on gaining deep conceptual understanding of algebraic, combinatorial, geometric and topological structure. The main areas of expertise are: finite dimensional algebras, symmetric groups and Hecke algebras, representations of finite and algebraic groups, Brauer and other diagram algebras, triangulated categories and dg categories, fusion systems, operads and homotopy algebras.

The Mathematical Physics Group's research activities are concentrated on topics in quantum field theory, quantum mechanics and string theory. Extensive expertise in various techniques and methods, developed originally in the context of integrable systems, creates a unique cohesive and vigorous environment. The main research focus is on: the form factor programme, non-Hermitian systems with antilinear symmetry, non-commutative spacetime structures, string and M-theory, gauge/string correspondences with less than maximal supersymmetry, Calabi-Yau manifolds, spintronic systems, graphene nanostructures, fluid mechanics and magnetohydrodynamics.

The Mathematical Biology Group applies mathematical methods to increase our understanding of the biological world. The central focus is on the mathematical modelling of evolution. The main research focus is on: applications of Evolutionarily Stable Strategy, evolution of specific animal behaviour such as kleptoparasitism and biological signalling, modelling of processes of cultural evolution, evolutionary modelling on networks/graphs.

Funding options

  • Full-time EU: £4,500 per year
  • Part-time EU: £2,250 per year
  • Full-time Non EU: £15,000 per year
  • Part-time Non EU: £7,500 per year

Fees for doctoral candidates are charged annually and cover registration, supervision and examination. Fees are subject to review each year and may vary during your period of registration.

External Candidate study of this course costs £785 per year either as a part-time or full-time option.


  • EPSRC Grants
  • City Research Fellowships.

Doctoral studentships

Find out about our fourteen full-time, three-year doctoral studentships for 2019/20 entry.

Postgraduate Doctoral Loans

The Government has introduced a new Postgraduate Doctoral Loans scheme which can provide a loan of up to £25,000 over three years to support study for a doctoral degree. A Postgraduate Doctoral Loan can help with course fees and living costs while you study and can be used alongside any other forms of support you may be able to receive, for example from industry or business or through your PhD supervisor.

Find out more about Postgraduate Doctoral Loans



Students are assigned to a lead and second supervisor within a Research Group. They are strongly encouraged to widen their horizons by attending our weekly research seminars in-house and at institutions in London, such as the London triangle seminars focusing mainly on aspects of string theory and the

London Algebra Colloquium. Specialised courses are delivered by theLondon Taught Course Centre

(LTCC), which offers 14 basic courses and 15 advanced courses, each with a typical length of ten hours. Students are expected to attend 3-4 courses per year, ensuring a minimum of 100 hours training during their studies, and are required to take an examination at the end of the year. In-house, students may attend relevant lectures provided as part of the MMath programme and the MSc in Decision Sciences. Students participate in theme-oriented study groups and present their own work in a seminar after the first year. They are also strongly encouraged to present their work at national and internal schools, workshops and conferences. Support is provided by research grants and the Department's travel budget. After the first year the Department offers the opportunity for PhD students to gain teaching experience and improve their communication skills by tutoring undergraduate students. Assignments depend on progression and are co-ordinated by the Head of Department in liaison with supervisors.

Research Environment

City provides broad training on research methods and communication and presentation skills, along with an introduction to the research degree framework and online research skills support, two researcher development days per year and an annual research symposium. Further support for the development of generic research skills and personal transferable skills is provided by the City Graduate School, founded in August 2012, which among other objectives aims to facilitate cross-School collaboration and improve skills training provision and employability.

Student progression is closely monitored by the School's senior tutor for research through annual progress reports and by means of a recently introduced software system (the Research and Progress platform), whose use is mandatory for both supervisors and students. The system involves PhD students in the management of their own research projects with a flexible approach according to individual student needs. Key milestones are recorded, with required reporting on at least four meetings per term, an initial six-month report, an annual progress report, details of progression from MPhil to PhD status, intention to submit and transfer to writing-up status no later than year four.

How to apply

We accept applications on an ongoing basis for entry in October, January and April. Please see the requirements section above for eligibility criteria.

It is essential that you contact a member of staff in the department you are interested in, to discuss your ideas for research (research proposal). Unfortunately, we will not be able to consider your application without this pre-requisite.

Details of relevant academic staff can be found on our department pages.

You are advised to submit your application at least 10 weeks before your proposed start date in order for us to consider and process your application. Once you have identified a supervisor who will accept to guide through your research, please submit an application online using the link below:

Supporting documents

To apply online, an applicant will need to submit the following supporting documents:

  • Research proposal: The Research Proposal should be a maximum of 3 sides A4. See guidance on writing your research proposal
  • Copies of degree certificates and transcripts – original will be requested before an offer is made;
  • Official work e-mail addresses (not private ones) for two referees (one of which must be an academic);
  • Proof of English language proficiency (if applicable).
  • Evidence of sponsorship (if applicable).