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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
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.			Project
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.			Project
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.			Project
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’.			Project
Spectral Theory of Differential Operators Spectral Theory of Differential Operators 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
On multi-dimensional continued fractions This project will establish analytic bounds for the accuracy of the convergents for the multi-dimensional continued fraction algorithm.			Project
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.			Project
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			Project
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.			Project
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.			Project
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.			Project
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.			Project
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.			Project
Lie groups and twisted K-theory This project deals with the computation of the characteristic classes of these twists in rational cohomology.			Project
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.			Project
Low rank approximations of matrices with a focus on statistical applications This project will investigate the structured low-rank approximation (SLRA) problem.			Project
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.			Project
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.			Project
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.			Project
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.			Project