Research degree opportunities in Mathematics

A PhD in mathematics can be the first step into an academic career or a passport to some of the most interesting technology jobs in the world. We are welcoming students for study towards a PhD or MPhil degree in data science, artificial intelligence and other areas of mathematics.

We have a limited number of funded places each year, and these are advertised on FindAPhD.

We also welcome students from the UK and abroad who have their own funding or who wish to develop a proposal to apply for a scholarship. We will help you develop your research question and your proposal with a view to you studying at Stirling. You may have your own ideas for a research question and we would be happy to help you shape them into a high quality PhD proposal. Alternatively, you may find one of our existing research projects the perfect fit for your own interests. We also offer a professional doctorate programme, in which you can work on a project for your employer (who covers the costs) and earn a PhD at the same time.

The list below describes some PhD opportunities that are available right now. If you have a scholarship opportunity or private funding, please contact the supervisor listed for the project that interests you.

Topic: Sports statistics using generalized Bradley-Terry likelihood methods

Supervisor: Dr Robin Hankin

Many sports such as football, test cricket, and chess have the possibility of a draw and dealing with this statistically is not straightforward. This project will compare and contrast different methods of addressing draws in the context of sports statistics including reified Bradley-Terry and weighted likelihood functions.

Topic: Born rigidity

Supervisor: Dr Robin Hankin

In classical mechanics, an object's being "rigid" has a very clear definition. This definition needs to be altered when relativistic considerations become important, the relevant concept being 'Born rigidity'. This project will generalize Born rigidity to cover inelastic string under various kinematic scenarios. One application of these ideas might be to understand the behaviour of light inelastic string in the Kerr metric.

Topic: Stability in eco-evolutionary meta-community models

Supervisor: Dr Gavin Abernethy

In theoretical ecology, meta-community models simulate the interactions between several discrete populations of multiple species in different patches on a spatial environment. We can study how the spatial patterns of species occurrence depend on the physical environment and dispersal behaviour, and how interactions by competitors or predators and prey can enable co-existence or lead to extinctions. Simulated experiments predict the biodiversity impact of habitat destruction, climate change or habitat fragmentation to reveal principles for conservation and landscape management. Eco-evolutionary modelling further incorporates rules for speciation, so that in this project you will explore how evolutionary, ecological, and spatial mechanisms inform each other to shape the emergent ecosystem and influence its stability against perturbation.

Topic: Optimising disease control measures for novel outbreaks

Supervisor: Dr Anthony O'Hare

This project will use census, demographic, and travel network data to model a disease outbreak in a country given some high-level input such as incubation period and R0 value and use Artificial Intelligence to determine the optimal disease control measures, e.g. closing schools, closing rail lines etc. Also, for a given amount of vaccine, you will determine the optimal distribution of the use of the vaccine.

Title: Modelling Pathologies in Cardiac Cells

Supervisor: Dr Anya Kirpichnikova

Cardiac modelling serves as a crucial tool in comprehending the mechanisms of pathophysiology in both healthy and afflicted hearts. The prospective PhD project centres around cardiac modelling, specifically focusing on creating and examining models of both healthy and diseased ventricular cells. As part of this project, the candidate will acquire proficiency in sophisticated techniques for model development and analysis. These techniques will encompass virtual population methodology and sensitivity analysis, aimed at identifying cardinal cellular attributes influencing disease manifestation.

Title: Designing obstacles for the Network Simulator 3

Supervisor: Dr Anya Kirpichnikova

In the realm of network simulation, the process of integrating obstacles plays a pivotal role in achieving realistic and reliable results. This project is a combination of various methods of wave propagation techniques in the presence of obstacles together with the implementation of the results in coding, i.e. implementing obstacles within Network Simulator 3 (NS-3), a popular tool utilized extensively for network research and development. The approach considers the physical characteristics of real-world barriers and their impact on signal propagation, effectively enabling more accurate simulations of varied environmental conditions. By incorporating variables such as material type, size, and location of obstacles, the model should emulate their interference in signal strength, reflection, refraction, diffraction, and absorption.

Title: Novel methods for ECG classification

Supervisor: Dr Anya Kirpichnikova

Electrocardiogram (ECG) classification is critical in diagnosing cardiac abnormalities, offering an essential tool in preventative health measures. Despite advancements in this field, there remain significant opportunities for improving the accuracy and reliability of ECG classification methods. This research proposal aims to explore novel mathematical and signal processing techniques to enhance ECG classification and support timely intervention for cardiac patients.

Topic: How to avoid tipping points in the food system

Supervisor: Prof Rachel Norman

The way we produce, distribute and purchase food is referred to as the food system and has many non-linearities in it. In this project we will look at the role of tipping points, and in particular ways in which we could avoid them. The project will use mathematical models to describe aspects of the food system and we will take a theoretical approach to the analysis alongside considering particular case studies of previous tipping points, for example the collapse of some cod populations.

Topic: When does a new infectious disease outbreak occur and when does it die out?

Supervisor: Prof Rachel Norman

There have been a significant number of emerging infections which are either diseases which we have not seen before or ones which enter a new region. For example, Covid-19 had not been seen until the end of 2019 and it seems to have come from wildlife. However, we are challenged with these new infections more frequently as the way we interact with our environment changes. This project will use mathematical models to look at what features cause an outbreak to occur or the disease to die out. This project will use stochastic SIR type models which are coupled non-linear differential equations to understand what happens at the start of an outbreak. If a small number of individuals get infected (for example if a pathogen passes from wildlife into humans), what pathogen characteristics are more likely to result in an outbreak? The approach will be a combination of theoretical exploration of parameter space for different models and consideration of specific diseases.

Topic: Sparse multidimensional exponential analysis in computational science and engineering

Supervisor: Dr Wen-shin Lee

Exponential analysis might sound remote, but it touches our lives in many surprising ways, even if most people are unaware of just how important it is. For example, a substantial amount of effort in the field of signal processing is essentially dedicated to the analysis of exponential functions of which the exponents are complex. The analysis of exponential functions whose exponents are very near each other is directly linked to super-resolution imaging. As for exponential functions with real exponents, they are used to portray relaxation, chemical reactions, radioactivity, heat transfer, and fluid dynamics.

Since exponential models are vital to being able to describe physical as well as biological phenomena, their analysis plays a crucial role in advancing science and engineering. The proposal investigates several multidimensional uses of exponential analysis in practice.

Topic: Exponential analysis meets Wavelet theory

Supervisor: Dr Wen-shin Lee

In the past years, sparse representations have been realised as linear combinations of several trigonometric functions, Chebyshev polynomials, spherical harmonics, Gaussian distributions and more. Recently also the paradigm of dilation and translation was introduced for use with these basis functions in sparse exponential analysis or sparse interpolation. As a result, high-resolution models can be constructed from sparse and coarsely sampled data, and several series expansions (Fourier, Chebyshev, ...) can be compactified. The above are available in one as well as higher dimensions. The similarity with wavelet theory remains largely unexplored.

Topic: Improving Antibiotic Dosage Regimens: Mitigating for risks associated with Varying Patient Compliance

Supervisor: Dr Andy Hoyle

The rise of antibiotic resistance is putting increasing pressure on our health service, and it is estimated that over 30,000 deaths per year across the EU are associated with resistant bacteria. Yet, there is little movement away from conventional antibiotic regimens, whereby we apply a constant daily dosage, e.g. X mg (or 1 tablet) per day for N days. This project will combine mathematical modelling and Artificial Intelligence, and aims to find optimal antibiotic regimens which maximise host survival, minimise the emergence of resistance and mitigate against uncertain patient compliance.