## Mathematical Physics

The research pursued in the Mathematical Physics group deals with the mathematical structures of fundamental interactions including approaches to quantum gravity. It covers a range of topics in field theory, quantum geometry and string theory.

In physics, we have by now acquired a deep understanding of the interactions that apparently govern all processes that we observe in the universe. The fundamental interactions have been identified as the electromagnetic, weak and strong nuclear force, and gravity. Whereas gravity is described by Einstein's theory of general relativity in terms of a curved space-time geometry, the other forces are described by quantum field theories. Although highly developed, there are still many fundamental (physical and mathematical) questions within these theories which remain open. Even more unsatisfactory is the fact that quantum field theory and general relativity do not seem to be compatible; we are missing a theory of quantum gravity that could unify these descriptions. As gravity is concerned with the geometry of space-time, it is the geometry itself that is expected to show quantum behaviour. This means that at the fundamental level, we do not know what space and time really mean, and they are likely to be replaced by a more fuzzy ''quantum geometry''.

There are different approaches to quantum gravity; some of them concentrate on generalisations of geometry like noncommutative geometry or quantum topology, and others try to extend gravity (and the other interactions) into a larger framework like string theory, supergravity or matrix models, to address the issue of quantisation there.

In our group we approach these fundamental questions in different, but often intertwined research directions including

- string theory and Calabi-Yau spaces
- higher-spin gravity and holography
- non-relativistic supergravity
- matrix models and the quantum structure of space-time and gravity
- topological and conformal quantum field theory
- quantum algebra and quantum topology