If you have reached this page, you are probably interested in pursuing a doctorate in Mathematical Physics at the School of Mathematics of the University of Edinburgh.
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. Instructions on how to apply can be found here. We actively encourage applications from women and under-represented minority candidates.
At present the group consists of the following members, with the following research interests and supervision availability.
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 not actively looking for new PhD students to start in 2021, but could be open to supervising an applicant with a strong background in quantum field theory, string theory or general relativity.
My research interests range across algebra, geometry, algebraic geometry and mathematical physics, with integrability a unifying theme. Integrable systems are those that can be solved exactly and they appear in significant physical and mathematical settings. Their modern study involves many branches of mathematics, particularly those just noted, with computational aspects of these also important. Examples of such systems range from classical mechanics to (quantum) field theory and indeed supersymmetric gauge theories relate both of these. Riemann surfaces, their geometry and function theory are an important ingredient here. I will not be taking on any new students this year.
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. I am happy to discuss this and related work. However, I am currently supervising five Ph.D. students at various stages, and am unfortunately unable to take on any new students this year.
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:
I am supervising one PhD student in each of the above two programmes. As one of them will be graduating next year, I am in principle open to the possibility of taking on a new student in 2021. Suitable candidates should have a strong background in mathematics, especially differential geometry and/or Lie theory.
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, 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. This year I will not take on any new PhD students.
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 not actively looking for a new student to start in 2022, but I could be open to taking a new student with suitable background and interests.
I work on the interface between quantum mechanics and general relativity together with possible observational consequences of near extremal Kerr black holes on gravitational waves. I could supervise a new PhD student if suitable requirements are fulfilled and there is enough overlap in 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.