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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

Operational Research

Research in this area spans: Modelling of traffic flow; Healthcare modelling; Modelling of the spread of infectious diseases; Queueing theory; Scheduling and timetabling problems; Metaheuristics; Discrete optimisation.

PhD, MPhil Full-time, Part-time Area

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

Accounting and Finance

The Accounting and Finance Section at Cardiff Business School has an established and expanding worldwide reputation for conducting high quality theoretical and empirical research in accounting and finance and related fields.

PhD Full-time, Part-time Area

Physics and Astronomy

The wide range of expertise within the School of Physics and Astronomy enables the School to offer a variety of opportunities for higher degrees by research.

PhD, MPhil Full-time, Part-time Programme

Probability and Statistics

Research in this area spans: Multivariate statistical analysis; Time series analysis; Statistical modelling in market research; Optimal experimental design; Stochastic global optimisation; Change point detection; Probabilistic methods in search and number theory; Fisheries; Medical statistics; Random fields; Mathematical finance.

PhD, MPhil 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.


Game Theory

This project will aim to build on research by exploring novel reinforcement learning algorithms and/or other techniques from machine learning.


Integer Optimisation

The project aims to develop novel algebraic and geometric methods that can be successfully applied to study integer optimisation problems, with a special focus on sparsity of solutions in context of (linear or nonlinear) integer optimisation.


Design of experiments in regression models with correlated observations

This project aims to develop the theoretical and methodological principles for the problem of optimal experimental design in the case of correlated observations.


Adaptive modelling and optimisation of hyperelastic cellular structures

This project will identify mechanical properties amenable to mathematical treatment and produce physically realistic mathematical models for natural cellular structures.


Development of a platform for healthcare operations management underpinning strategic, tactical and operational decisions

This project will develop a platform for healthcare operations management underpinning strategic, tactical and operational decisions.


Spectral element mimetic least squares PGD method

The project will develop new numerical discretisations for solving PDEs that can subsequently be applied to problems in fluid mechanics and will build on current expertise in the School.


Mathematical methods for scale-bridging: From interacting particle systems to differential equations

The focus of the project is on applying two new mathematical developments for the purpose of scale bridging.


Problems in microlocal analysis with an emphasis on spectral asymptotics and scattering theory

In this project, you will gain exposure to a variety of ideas from microlocal analysis and how they are used in problems initiated with the field of quantum mechanics, more specifically quantum chaos.


The Influence of Compressibility on the Dynamics of Encapsulated Microbubbles

The dynamics of EMBs in viscoelastic fluids forced by ultrasound forms the focus of this project.


Vertex algebras and generalisations of Lie theory

This project focuses on symmetric functions and their implications in representation theory, finite dimensional semisimple Lie algebras and their representations, affine Kac-Moody algebras and infinite dimensional Lie algebras.


Superconducting diamond as a bridge to the quantum mechanical world

This project will continue work to explore the fundamental modes of Nano Electro-Mechanical (NEMS) bridges made out of diamond and methods of detection using quantum circuitry.


Optimisation of placement of charging stations for electrical vehicles in road networks

The aim of this PhD project is to develop novel modelling and algorithmic solutions for the charging limitations of electrical vehicles in road networks by drawing from existing research in the fields of optimisation and network theory.


Investigating peroxisome dysregulation in Alzheimer’s disease

In this project you will first determine how peroxisomes respond to the specific pathogenic proteins associated with AD in vivo.


Machine Learning for Dimension Reduction in High‐Dimensional Datasets

This project will focus on the improvement of existing methodology for more accurate and computationally faster estimation algorithms to achieve SDR.


In silico modelling of parasite dynamics

This PhD studentship will bridge this divide by modelling disease transmission at all scales in four WPs.


Operator Algebras and Noncommutative Geometry

The application of Operator Algebras and K-theory to understand structural problems in statistical mechanics and conformal quantum field theory.


Least Squares PGD Mimetic Spectral Element Methods for Systems of First-Order PDEs

The goal of this project is to develop a least squares PGD mimetic spectral element method for the Stokes problem.


Spectral approximation

This project will deal with problems of spectral approximation for operators and operator pencils and try to identify classes of operator for which efficient spectrally inclusive algorithms can be devised.


Sparsity and structures in large-scale machine learning problems

The main objective of this project is to investigate the design of efficient approaches to scale-up and improve state-of-the-art machine learning techniques, while providing theoretical guarantees on their behaviour.


Calcium and mechanics in embryogenesis: continuum and cell-based models

The aim of this project is to extend models to systems of nonlinear partial differential equations to study the rheology of the embryonic epithelial tissue as a viscoelastic medium.


Investigating the childhood neurodevelopmental origins of adult mental illness

This PhD utilises new data generated by a Wellcome Trust Collaborative Award between Cardiff and Bristol Universities to test hypotheses on why child NDDs show links with later adult mental illness.