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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

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

Business Studies

Our Business Studies PhD involves one year of research training followed by three years’ work on your PhD topic.

PhD Full-time, Part-time Programme

Marketing and Strategy

The Marketing and Strategy Section at Cardiff Business School undertakes and publishes innovative and original research on the formulation and implementation of effective market strategies at domestic and international levels.

PhD 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

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

Logistics and Operations Management

We aim to be the world's leading interdisciplinary teams of academics in advancing knowledge, theory and practice in logistics and operations management.

PhD Full-time, Part-time Area

Management, Employment and Organisation

As well as promoting research of an international quality, the section aims to deliver research-led teaching of an outstanding quality and to provide a supportive environment for the development of academic researchers and educators.

PhD 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.


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.


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.


Combinatorial optimisation

This project will focus combinatorial optimisation.


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.


Statistical Inference for Entropy, Divergences and Renyl Information

One of the main aims of the project is to develop an asymptotic theory of the nearest neighbour estimates of Shannon and Rényi information.


Unsupervised Dimension Reduction methods for non-Gaussian High‐Dimensional Datasets

This project will extend the work currently being done in our research group for dimension reduction in the exponential families.