PhD projects

We welcome applications to study for a PhD in our group. For details about the areas of research, look at our staff members' websites. If you have further questions, please contact the staff member you are interested in working with.

Typically a small number of fully funded places in the School are available each year and decisions on these are made between January and April for an October start. Other start dates during the year are possible, but PhD funding is only allocated once a year.

Do not send applications or CVs directly to us by email; you need to apply through the University system. We also recommend reading the page How to apply for your PhD as it explains the process of how we select candidates for PhD places and funding, which may be different from how it works in other universities and countries.

PhD funding: As is standard in the UK, your application to the University is for a place to study, which does not automatically come with funding. Our main source of PhD funding is EPSRC:

To apply for one of our projects, please select the application code S3.5-MPS-Open. (This is a generic code for any project in Mathematics, so it would apply to any of our projects.)

To apply for a PhD place without EPSRC funding (for instance, because there are other sources of funding available to you) please see

Apply online for PhD study

The deadline to apply for EPSRC funding will be 29th January 2025. Your application should be complete before any deadline. Since we usually receive a large number of applications just before the deadline, we encourage you to apply even earlier if possible. In particular, please include either your Master's dissertation (or equivalent) or an example of written project work.

We usually await the first deadline for PhD studentships before selecting some applicants for an online interview. We might ask applicants to prepare a short presentation as part of the interview. After a successful interview applicants will be put forward for funding, which is then decided at the level of the School of Mathematical and Physical Sciences in a complicated process.

Below are some examples of projects we could supervise in 2025, organised by general research area. In general, finding a suitable project can be part of the discussions around a PhD interview. Given how our PhD funding works, in a particular year we may or may not find funding for any of these projects.

Projects in Black Holes and Gravitational Waves

Black hole perturbation theory for gravitational-wave source modelling (Sam Dolan)

Orbiting black holes generate distinctive 'chirp' signals, which have been successfully detected at gravitational-wave observatories such as LIGO since 2015. A key aim of the forthcoming LISA mission (a space-based interferometer) is to detect signals from supermassive black holes, such as the one at the centre of our galaxy.

In this project, we will aim to model the final ~100,000 orbital cycles of a stellar-mass black hole orbiting a supermassive black hole, by applying gravitational self-force theory. In particular, we will extend recent work by Dolan, Kavanagh and Wardell (arXiv:2108.06344) to construct Lorenz-gauge metric perturbations of the Kerr black hole directly from mode sums, for the first time.

Visit Sam's website

Projects in Cosmology

Constraints on models beyond the standard LCDM by using current and future cosmological data (Eleonora Di Valentino)

The Cosmic Microwave Background (CMB) temperature and polarization anisotropy measurements from the Planck mission have provided robust support for the ΛCDM model, which relies on the cosmological constant (Λ) and cold dark matter—two components that remain largely mysterious. However, intriguing discrepancies, known as "cosmological tensions," have emerged, hinting that the standard ΛCDM model may not fully describe our universe. The most prominent of these is the Hubble tension, which reflects a mismatch between the Hubble constant inferred from Planck data and direct measurements by the SH0ES collaboration. Other tensions, like the clustering parameter discrepancy observed between Planck and the weak lensing surveys (e.g., DES and KiDS-1000), further challenge the standard model.

This project aims to explore beyond the standard ΛCDM framework, investigating alternative cosmological models that could reconcile these tensions. We will examine a range of possibilities, including Dark Energy and Modified Gravity models, extended Dark Matter scenarios, alternative inflationary theories, and modifications to the neutrino sector. The analysis will combine current available data from multiple sources, and we will assess how future CMB experiments—such as CMB-S4, DESI, PIXIE, PRISM, and PICO—could refine these constraints. Additionally, we will consider how these experiments can be complemented by future low-redshift observations.

The project requires a foundational understanding of cosmology and we will be using and modifying widely adopted cosmological codes, such as CAMB/CLASS, and performing statistical analyses with Monte Carlo Markov Chain (MCMC) packages like Cobaya and SimpleMC.

Contact Eleonora about this project

Projects in Quantum Field Theory in Curved Spacetime

Quantum fields on black-hole spacetimes (Elizabeth Winstanley)

Classically a black hole can only absorb and not emit particles. Black holes do however emit quantum Hawking radiation. This project is concerned with the behaviour of quantum fields on black hole spacetimes.

The construction and properties of quantum states on black hole backgrounds will be studied, including the computation of renormalized expectation values of observables such as the vacuum polarisation or stress-energy tensor. A particular focus will be on black holes with either rotation or charge, where superradiance effects play an important role. Expectation values can then be used to study the backreaction of the quantum field on the space-time geometry.

Visit Elizabeth's website

Projects in Quantum Gravity and Quantum Cosmology

Time and relational dynamics in models of quantum gravity (Steffen Gielen)

One of the main obstacles in unifying general relativity and quantum mechanics is known as the 'problem of time': in general relativity, unlike in usual quantum mechanics, statements about evolution in a particular time coordinate have no invariant physical meaning. Physically meaningful statements need to be made in relational terms, as the change in a 'system' relative to the change in the 'clock'. In cosmology, the clock can for instance be a scalar field, or the volume of the universe.

In this project you will study relational formulations of dynamics in classical relativity and their realisations in quantum models of cosmology or quantum black holes. Depending on interest, some specific questions can include the role of unitarity in quantum gravity (related to evolution and hence the definition of time), approaches using a standard of time based on dark energy (known as unimodular gravity), or the clocks used by observers encountering singularities in black holes and cosmology. You could also work on the explicit construction of new models for material clocks in approaches to quantum gravity such as group field theory. Such constructions can be used to compare quantisations based on different clocks, and potentially link these ambiguities to observational effects.

Visit Steffen's website

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