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.
At present the group consists of the following members, with the following research interests and supervision availability.
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 am happy to supervise a suitably well-qualified student on any of the above aspects depending on their interests.
I have two main research interests: an active interest in supersymmetry in many of its manifestations, and a more latent one on homological methods in mathematical physics. Sometimes the two interests align and sometimes they don't. Right now they are partially aligned and much of the supersymmetric research I'm currently pursuing involves homological methods in Lie theory.
I am currently pursuing several research topics:
I am presently supervising three students: one student in his final year on the latter topic, and two students (one in his second year and another who has just started) in the third of the above topics. I may be able to supervise a student in either of the first two (related) topics, but it is not a priority. In any case, a good solid background in differential geometry and Lie (representation) theory is a must.
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.
A PG student in this area will work on one of the following topics:
I work on general relativity and gravitational aspects of string theory and holography. I have a particular interest in higher-dimensional black hole solutions in these contexts. I'm open to supervising suitably qualified students.
I work on the relation between quantum mechanics and gravity. 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, in particular the Algebra, Geometry and Topology group has a similar webpage listing potential supervisors.