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Name	Qualification	Mode	Type
Mathematics The School of Mathematics offers an exceptionally wide range of opportunities for postgraduate studies in mathematics.	PhD, MPhil	Full-time, Part-time	Programme
Medicine 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
Combinatorics 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.			Project
Combinatorial optimisation This project will focus combinatorial optimisation.			Project
Interger Optimisation This project will develop novel algebraic and geometric methods that can be successfully applied to study integer optimisation problems.			Project
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.			Project
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.			Project
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.			Project
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.			Project
Higher order analysis and bifurcation theory You will be expected to extend the current theory to the weakly non-linear regime and beyond.			Project
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.			Project
Metaheuristic methods for probabillistic graphical models This project will focus on metaheuristic methods for probabillistic graphical models.			Project
Operator algebras The aim of this project is to construct subfactors associated to quasi-rational tensor categories and investigate their properties.			Project
Persistent sheaf cohomology This project is about a fairly recent development: the application of sheaf theory to topological data analysis.			Project
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.			Project
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.			Project
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.			Project
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.			Project
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.			Project
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.			Project
Mathematical analysis - Dynamical systems and spectral theory This project will develop cutting edge techniques in the interface between pure mathematics and exciting applications.			Project
Hawkes processes and financial applications This project aims to answer novel but cutting edge questions in multivariate Hawkes processes.			Project
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.			Project
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’.			Project