# Research degrees in Mathematical Sciences

## G1ZF

## Introduction

We welcome postgraduate students and visiting research fellows to undertake research in our areas of interest (see below). Research students are registered for University of London degrees (MPhil/PhD) and work under the supervision of members of academic staff.

Students may receive financial support (research studentships) offered by the research councils (including CASE studentships in collaboration with an industrial sponsor). A limited number of College studentships are also available.

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

- School of Mathematical Sciences
- School's research groups:

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

## School of Mathematical Sciences

### Algebra

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.

### Analysis

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.

### Combinatorics

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.

### Logic

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.

### Probability

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.

### Statistics

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.