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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.


Combinatorial optimisation

This project will focus combinatorial optimisation.


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.


Tunable THz laser source

This project will involve the design, fabrication and characterisation of such a source, based on the non-linear optical process of difference frequency generation in an integrated semiconductor laser structure.


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

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


On multi-dimensional continued fractions

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


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.


Automated Searches for Ultra-Diffuse Emission from Stars

We are particularly interested in the fraction of stars that lie outside of easily recognised galactic structures as a means of tracing the assembly history of dark matter haloes of various masses.


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


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.


Hawkes processes and financial applications

This project aims to answer novel but cutting edge questions, such as convergence of multivariate Hawkes processes, forecasting ability of incorporating Hawkes processes into various risk modelling and calibration of them.


Combinatorial optimisation, operational research, graph theory, algorithms

In this project you will learn about different methods for tackling combinatorial optimisation problems using both exact and approximate (heuristic) algorithms.


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.


Lie groups and twisted K-theory

This project deals with the computation of the characteristic classes of these twists in rational cohomology.


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.


Low rank approximations of matrices with a focus on statistical applications

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


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.


Remote control of gas-liquid flow in horizontal pipelines

This project will further develop existing mathematical models for the co-current gas/liquid flow in horizontal pipes.


Optimal tidal power generation

The aim of this project is to develop a statistical model for the error between the slow but accurate numerical model for water height, and the fast but inaccurate model.


Energy harvesting for autonomous systems

This project will focus on the mechanisms by which communications based on light emission by LEDs or lasers can be powered by energy harvested from the environment.


Problems in semiclassical analysis with an emphasis on quantum chaos

Participants in this PhD project 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.