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Name Qualification Mode Type


The School of Mathematics offers an exceptionally wide range of opportunities for postgraduate studies in mathematics.

PhD, MPhil Full-time, Part-time Programme


The School of Medicine offers research degrees in the medical disciplines such as cancer, immunology, infection, immunity, neurosciences, mental health and population medicine.

PhD, MPhil, MD Full-time, Part-time Programme

Pure Mathematics

Research in this area spans: Ordinary and partial differential equations; Functional analysis; Analytical and computational spectral theory; Quantum mechanics; Number theory and its applications; Mathematical physics; Operator algebras; Algebraic geometry.

PhD, MPhil Full-time, Part-time Area


We offer a 3 year PhD programme, a 4 year integrated PhD programme, an EngD programme, and a 1 year MPhil degree programme.

PhD, MPhil, EngD Full-time, Part-time Programme

Applied Mathematics

Research in this area spans: Wave propagation in inhomogeneous media; Homogenisation; Fluid mechanics; Structural and solid mechanics; Numerical analysis and scientific computing; Applied mathematical modelling; Memory effects; Inverse problems; Integral transforms.

PhD, MPhil Full-time, Part-time Area

Geo-environmental Engineering

Self-healing of plant-stabilised geotechnical structures.


Engineering: Energy and Environment

One of the School’s three research themes is that of Energy and Environment, which aims to advance energy technology and play a key role in addressing the increasing demand for sustainable and low carbon technologies, while reducing environmental impact and ensuring a sustainable environment.

PhD, MPhil, EngD Full-time, Part-time Area


This project will develop knowledge and skills in several general areas of algebraic, geometric and enumerative combinatorics, including polytope theory, poset theory and symmetric function theory.


Engineering: Mechanics, Materials and Advanced Manufacturing

The wide ranging research theme of Mechanics, Materials and Advanced Manufacturing incorporates cutting edge research which fosters innovation and sustainability, supports social and economic development, and contributes to improvements in health and quality of life by ensuring the safety and best performance of materials and structures.

PhD, MPhil, EngD Full-time, Part-time Area

Machine Learning; Data Mining

This project will focus on the interaction between mathematics and neuroscience and applications of deep learning to medical data.


Hawkes processes and financial applications

This project aims to answer novel but cutting edge questions in multivariate Hawkes processes.


Spectral theory of differential operators

Research on this theme is characterised by a combination of functional and harmonic analysis with classical real and complex analysis, special functions and the asymptotic analysis of differential equations.


Nonlinear acoustic-gravity wave theory

This project focuses on the recent finding that acoustic and gravity wave motion could exchange energy via resonant triad nonlinear interactions.


The Mathematics of Conformal Field Theory

The core of this project will explore the mathematical structure of conformal field theory.


Numerical modelling of multiphase flows

This project aims to develop a numerical framework which can be applied to various multiphase flow problems (gas-liquid, gas-liquid-solid, etc) in engineering and scientific research fields such as energy, environment and manufacturing.


Engineering: Health, Technology and the Digital World

The Health, Technology, and the Digital World research theme provides a framework for the research undertaken in the fields of High Frequency Communications Engineering and Medical Engineering, Medical Physics, and Medical Electronics. The combination of these disciplines allows for a truly innovative approach and enables exciting new solutions for the security, healthcare and medical requirements of a modern society.

PhD, MPhil, EngD Full-time, Part-time Area

Early detection of tsunami by acoustic-gravity waves

This project will develop various mathematical techniques and methods, with a focus on perturbation methods, asymptotic analysis, and separation of variables, to solve the general wave equation for a three-dimensional space.


Holomorphic Representations of the Braid Group

The project will deal with certain ‘holomorphic’ representations of braid groups and study the dependence on an underlying ‘R-matrix’.


Metaheuristic methods for probabilistic graphical models

This project will aim to develop approaches for learning probabilistic graphical models that can be used for classification problems and to explore causal relationships between attributes.


Modelling of sporting events using artificial intelligence and statistical methods for big data

This project aims at systematizing and comparing different models and applying them for predicting outcomes of different sporting events


On multi-dimensional continued fractions

This project will establish analytic bounds for the accuracy of the convergents for the multi-dimensional continued fraction algorithm.


Operator algebras and noncommutative geometry

This project focuses on operator algebras and noncommutative geometry.


Interface evolution in random environment

The main goal of this project is to develop mathematical methods for the mathematically rigorous analysis of the properties of interfaces evolving in a heterogeneous, random environment, described on a small scale by nonlinear PDEs with random coefficients.


Radiation of acoustic-gravity waves by an impacting object

This PhD project will focus on developing the computational mathematical model into a three-dimensional space.


Biomedical smart fabric wearable devices

This is a fully-funded EPSRC project in engineering, focusing on energy and environment.


Clustering problems in social networks

The aim of this project is to develop approaches for learning probabilistic graphical models that can be used for classification problems and to explore causal relationships between attributes.


Low rank approximations of matrices with a focus on statistical applications

This project will investigate the structured low-rank approximation (SLRA) problem.


Categorification of generalised braids

This project will work either on further developing the currently in-demand theories of spherical and P-functors, or on computing our first examples of Grassmanian functors.


Design of experiments in regression models with correlated observations

This project is interdisciplinary in nature and will include elements of theoretical probability and applied statistics.


Spectral approximation on metric graphs, on manifolds, and for systems of differential equations

This project will focus on the spectral approximation on metric graphs, on manifolds, and for systems of differential equations.