Course summary

We are a multidisciplinary research group with close connections with the School’s Algebra and Geometry & Topology groups. You’ll benefit from being not only in one of the largest mathematics research groups in the UK but also part of the Edinburgh Mathematical Physics Group – a joint research collective formed in 1999 with Heriot- Watt University and now part of the Maxwell Institute. The School of Mathematics is a vibrant community of more than 60 academic and related staff supervising 60 students. Our group pursues wide-ranging interests spanning a number of disciplines. A central goal is to understand the principles behind quantum gravity, through the study of black holes, cosmologies and spacetime singularities, and via the use of holography and the interplay with quantum gauge field theory through the gauge/gravity correspondence. Particularly fruitful areas of research are the geometry of higher-dimensional black holes and their near-horizon geometries in the context of higher-dimensional generalisations of general relativity. We’re fascinated by the various manifestations of supersymmetry: in string theory, supergravity and gauge theory. This has led us to several classification results on supersymmetric supergravity backgrounds, including a recent proof of the homogeneity conjecture. In addition we study gauge theoretic moduli spaces using supersymmetry and via integrable systems techniques, displaying an interplay between the algebraic geometry of curves and their associated function theory. This research has led to computer implementations of various algebro-geometric constructions. Recently we have made progress in some purely mathematical problems suggested by the gauge/gravity correspondence: namely, the classification of certain exotic algebraic structures related to superconformal field theories, as well as that of certain types of homogeneous supergravity backgrounds.