Research degrees in Mathematics

Welcome to the Postgraduate Research webpage for prospective new PhD students of the School of Mathematical Sciences. Our School offers PhD opportunities in a wide range of areas in Mathematical Sciences: see here for details about our research activities. We have a large and thriving community of postgraduate research students, currently numbering approximately 70 students.

Research students are assigned a PhD supervisor who has closely related mathematical interests, and with whom they agree on a programme of study and research. That programme includes advanced courses provided by the London Taught Course Centre (LTCC)(link is external), which is a joint initiative of several London Colleges. The School furthermore provides opportunities for acquiring skills through short courses such as, e.g., on Mathematical Writing. Students will also have the opportunity to gain experience in teaching, for example through leading exercise classes for undergraduate students, while at the same time supplementing their income.

Funding, usually for a period of 3.5 years, is available on an annual basis from both EPSRC and from the College, designed to cover the fees and living expenses of suitably qualified applicants. See here for current PhD studentship offers and for a list of sample PhD projects.

Please note that the internal deadline for fully-funded positions is the 31st of January 2018.

We accept applications for self-funded full or part-time projects all year round.

If you are interested to do a PhD with us, we recommend that you first study the admissions information which you can find under the links of the menu on the left. For detailed information about what it means to do a PhD at our School please explore the information under Current Students - PhD Maths/Stats that you can also find in the menu on the left.

For more information about the School and the research programmes please see:

If you are interested in PhD in Statistics please also check Research degrees in Statistics.

School of Mathematical Sciences


The world-leading algebra section includes research in linear groups and algebraic groups, topological and combinatorial aspects of group theory, finite p-groups and computational group theory. We also research in representation theory, quantum algebras, and algebraic geometry, including non-commutative geometry, model theory, and higher or categorical algebra.


Research work centres on harmonic and functional analysis, especially harmonic analysis on groups, operator algebras, infinite dimensional manifolds and holomorphy. We also research in Jordan algebras and analysis on infinite-dimensional manifolds; operator algebras and functional analysis; and non-commutative geometry.


A very active group that works both on topics within combinatorics (especially finite geometry and design theory) and on links with algebra (permutation groups), logic (model theory), information and coding theory, and design of experiments.

Geometry and Topology

Research includes algebraic topology, Riemannian geometry, noncommutative and algebraic geometry. There are connections with other areas such as in group theory, relativity and dynamical systems.


Research is mainly in model theory, particularly connections with algebraic geometry, model theory of the Frobenius map, geometry of fields with measure, (nonstandard) cohomology theories and motivic integration.

Number Theory

Areas being pursued include algebraic number theory and Diophantine approximation. Number Theory also features in connection with research in other areas in the School including in group theory, logic and dynamical systems.


Areas on the pure mathematics side include randomised algorithms, Markov chains (especially mixing time of combinatorially or geometrically defined Markov chains), probabilistic existence proofs of combinatorial structures, and use of random combinatorial structures.

Relativity and Computation

The Relativity Group interacts with the Astronomy Group in the Physics Department. Research interests include: exact solutions of Einstein's equations and applications of algebraic computing, topological questions, alternative theories of gravity, black holes, and gravitational radiation.

Statistical Mechanics

Research interests of this group include generalised statistical mechanics methods applied to a variety of complex systems (hydrodynamic turbulence, econophysics, traffic flow, biological and medical applications). The group uses tools from large deviation theory, nonequilibrium statistical mechanics and the theory of stochastic processes. The group also works on complex networks, in particular their dynamical evolution and chracterization.


The Statistics group works on the design of experiments, on Bayesian statistics, on algebraic statistics, and on sequential analysis. In the design of experiments there is particular emphasis on applications in the pharmaceutical industry, agriculture, the food industry and chemistry, but the underlying algebraic theory and combinatorial structure are also explored. Members of the group are also regularly involved in applied statistics projects with researchers from other disciplines.

Entry requirements

Candidates for the PhD or MPhil programmes in mathematics or statistics should normally have a first or good upper second-class honours BSc in mathematics or statistics, or a more advanced qualification such as MSci, MMath, or MSc.

For international students, please refer to the International students section.

Find out more

For more information please contact:

PhD Programmes Officer

Dr Reto Buzano
PhD Programme Director

Apply online