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Mathematics

PhD / MPhil
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 in October or February.

Duration

The duration of this course is generally 3-4 years.

Fees

UK/EU

Full-time: £3,600 per year

Part-time: £1,800 per year

Non-EU

Full-time: £8,100 per year

Part-time: £4,000 per year

Overview

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:

Requirements

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

For applicants whose first language is not English, proof of English language proficiency will be required. We require  a minimum IELTS score of 6.5. Please note that the UK Border Agency currently requires us to confirm that you are at level B2 or above in all components of English before issuing visa documents.

Please note that due to changes in the UKVI's list of SELTs we are no longer able to accept TOEFL as evidence of English language for students who require a CAS as of April 2014.

Visa requirements

If you are not from the European Economic Area / Switzerland and you are coming to study in the UK, you 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:

  • Students on courses of more than six months
  • Students on courses of less than six months
  • Students on a pre-sessional English language course.

If you require a Tier 4 student visa to study in the UK, you cannot undertake any City courses on a part-time basis.

For more information see our main Visa page.

Structure

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: £3,600 per year
  • Part-time EU: £1,800 per year
  • Full-time Non EU: £8,100 per year
  • Part-time Non EU: £4,000 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.

Funding

  • EPSRC Grants
  • City Research Fellowships.

Support

Supervision

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. You are advised to submit your application at least six 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 you through your research, please submit the following documents:

  • PhD application form
  • A three page Research Proposal (See our detailed guidance on writing a research proposal)
  • Copies of your degree transcripts and certificates (originals or certified copies). If your applications is successful, we will need to see the original hard copies before a final offer is made.
  • Two reference letters from at least one academic staff, sent from an office work email (not private) to pgr.smcse.enquire@city.ac.uk.
  • Proof of English language proficiency (minimum 6.5 IELTS) if English is not your first language.

Please note that we will not consider incomplete applications.

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City, University of London is an independent member institution of the University of London. Established by Royal Charter in 1836, the University of London consists of 18 independent member institutions with outstanding global reputations and several prestigious central academic bodies and activities.