String theory is the most developed theory of quantum gravity, as well as providing deep insights into non-perturbative aspects of quantum field theory via the AdS/CFT correspondence. It also has deep connections with many interesting areas of pure mathematics, such as differential and algebraic geometry, topology, algebra and even number theory, and research in string theory has gone hand-in-hand with many exciting developments in those areas.
Strings 'see' the spacetime geometry very differently to point particles in more conventional theories, which give rise to exotic features such as string dualities - equivalences between seemingly very different string theory scenarios. Indeed, a full formulation of the theory is currently beyond our reach, and most researchers believe that we will have to develop many new mathematical concepts to provide one, including a much better understanding of this 'stringy geometry'.
One strand of our research is focused on the development of a new notion of geometry, known as generalised geometry, which gives an elegant geometrical reformulation of the low energy field theory limit of string theory, and includes some of the features of string dualities, hinting that it may be the first step towards a better understanding of the geometry of the full theory. The mathematical technology is also very useful for studying supersymmetric solutions and consistent truncations of supergravity, both of which are also important for the AdS/CFT correspondence.