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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

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

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.


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 and data mining

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


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.


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.


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.


Persistent sheaf cohomology

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


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.


Coordinated movement of random fish schooling

This project aims to develop a theoretical model for three-dimensional random movement in fish schools, with the absence of a centralised coordination.


Proper general decomposition for convection-diffusion equations

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


Connectivity of group C*-algebras

The goal of the project is to identify examples and counter example among the group C*-algebras of discrete torsion free amenable groups.


Mathematical analysis - Dynamical systems and spectral theory

This project will develop cutting edge techniques in the interface between pure mathematics and exciting applications.


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.


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.


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.


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


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.