PhD Opportunities
PhD applications and supervisors
We typically require a strong undergraduate degree in Mathematics and/or Physics and a Masters degree (or equivalent) in Mathematics and/or Mathematical/Theoretical Physics. We actively encourage applications from women and under-represented groups.
You must apply online for the Mathematical Physics PhD programme through the School of Mathematics application system.
Information and Instructions for applying to a PhD degree in the School of Mathematics.
Supervisors
Below is a list of the possible PhD supervisors, their interests, potential projects and their availability. Typically this will be updated in the autumn of each year. In your online application please include a description of your research interests and an indication of who you would like to work with (there is no need for you to write a research proposal).
My research develops new formulations of classical and quantum field theories which simplify the calculation of physical observables (like scattering amplitudes or correlation functions). Tools from string theory and twistor theory play a major role in my work, shifting the focus from space-time (the stage for most traditional approaches to field theory) to settings where powerful geometric techniques can be applied to the study of physics. I am open to taking a new PhD student in 2023 to work on projects related to alternative representations of the S-matrix (in particular, those arising in the 'celestial holography' program) or scattering amplitudes in the presence of strong (non-perturbative) gauge and gravitational fields. Applicants should have a strong background in quantum field theory, string theory or general relativity.
My current work centers around supersymmetric quantum field theories, and in particular gauge theories. I use modern techniques from topology and algebraic geometry to characterize the interactions of local and extended operators/defects; and, conversely, apply physical dualities to produce new mathematical results in geometry and topology. Some of colleagues and I hold regular group meetings related to these ideas. I will be supervising two students in the fall of 2023, and there is potentially room for one more.
I work on the application of representation theory and differential geometry to problems inspired by Physics. I am particularly interested in different manifestations of supersymmetry and I am partial to homological methods. I am currently involved in two research programmes from which any PhD project I would be willing to supervise would derive:
- Spencer cohomology and supersymmetry This is a homological approach to the classification of supersymmetric supergravity backgrounds and to the construction of rigidly supersymmetric field theories in curved space.
- Spacetime G-structures I have become interested in the question of which are the possible geometrical structures for space and time. Going beyond General Relativity and its edifice built upon lorentzian geometry, I have become interested in "non-lorentzian geometries", which can be defined in terms of G-structures. Much of my recent work is concerned with the representation theory of the non-lorentzian symmetry groups.
The former topic is in a sort of hiatus and I am currently supervising two PhD students in the latter topic. It is not likely that I will be taking on any new students in 2024, due to the fact that I'll be on sabbatical.
Differential geometry plays a crucial role in theoretical physics in particular in areas such as gravity, string theory, holography and formal aspects of quantum field theory. From a physical point of view the geometries involved typically obey Einstein's equivalence principle: locally a manifold is flat in the sense of Minkowski space-time. There are however many situations in which one encounters a different type of geometry where Einstein's equivalence principle is replaced by another kinematical principle. We call such geometries non-Lorentzian geometries. They appear for example as boundary geometries of various solutions of general relativity, which is relevant for non-AdS (anti-de Sitter) holography, and in various approximations of GR such as the post-Newtonian expansion, but also in non-relativistic limits of string theory such as the AdS/CFT correspondence, as well as in effective field theories that appear in condensed matter physics and fluid dynamics. I will not be taking on a new PhD student in 2024.
I work on general relativity and gravitational theories inspired by string theory and holography. Much of my research focuses on black hole solutions and related geometries in these contexts, with an emphasis on their construction and classification. I have a particular interest in higher-dimensional black holes, supersymmetric black holes, extremal black holes and near-horizon geometries. I'm currently supervising two PhD students and while I am not actively looking for new students to start in 2024 I am open to the possibility for suitable candidates with a strong overlap in interests.
I work on the interface between quantum information & computation, and General Relativity, using holographic ideas to bridge them together. I may supervise a new PhD student in 2024 if suitable requirements are fulfilled and there is enough overlap of research interests.
We also have a lot of common interests with colleagues in neighbouring fields and, in particular, the Hodge Institute have a similar webpage listing potential supervisors.
You can also apply for a PhD in the School of Physics and Astronomy via the Higgs centre for Theoretical Physics webpage (this requires a separate application through the School of Physics and Astronomy).