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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.


Data mining at the South Galactic Pole

Automated methods of extracting the properties of millions of galaxies from survey data and identifying new classes of rare objects.


Machine learning to extract gravitatonal wave transients

Identifying astrophysical gravitational wave transients from events such as supernovae.


Combinatorial optimisation

This project will focus combinatorial optimisation.


Interger Optimisation

This project will develop novel algebraic and geometric methods that can be successfully applied to study integer optimisation problems.


Machine learning to maximise the impact of ALMA

Development of new, automated methods for identifying sources in data from the Atacama Large Millimeter/submillimeter Array (ALMA).


Game Theory

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


Machine learning and data mining

On this project, you'll learn several areas of IT and mathematics, including data mining, machine learning and analysis on graphs.


Extracting weak Gravitional Wave events

Use of machine learning techniques to identify and classify weak gravitational wave events in data from the LIGO and Virgo detectors.


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.


Vertex algebras and lie theory

This is a pure mathematics project related to Lie theory and vertex algebras as well as their connection to the mathematics of conformal field theory.


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.


Searching for Cosmic Anomalies

This project will involve developing, testing and applying innovative statistical analysis techniques to real and simulated data sets.


Nonlinear acoustic-gravity wave theory

This project will use multiple scale analysis along with other standard mathematical techniques to derive the general solution in a three-dimensional space.


Dynamics of bubbles rising in viscoelastic fluids

This project will develop new numerical discretisations for solving PDEs that can subsequently be applied to problems in fluid mechanics.


Metaheuristic methods for probabillistic graphical models

This project will focus on metaheuristic methods for probabillistic graphical models.


Operator algebras

The aim of this project is to construct subfactors associated to quasi-rational tensor categories and investigate their properties.


Studying human neuropsychiatric disease in DLG2 deficient human neurons

This PhD project in Medicine tries to understand DLG2’s role during neural development and in mature neurons using variety of techniques.


Persistent sheaf cohomology

This project is about a fairly recent development: the application of sheaf theory to topological data analysis.


Homogenisation of periodic problems in linear PDEs and non-linear elasticity

This project will explore ideas from mathematical analysis and differential equations which exploit modern techniques of analysis of periodic problems and deal with multi-scale analysis, dimension reduction, asymptotic approximation.


Higher order analysis of chiral chasing populations

This project will extend the current theory to the weakly non-linear regime, and beyond.


The influence of compressibility on the dynamics of encapsulated microbubbles

This project will develop new numerical discretizations for solving PDEs that can subsequently be applied to problems in fluid mechanics.