Abstract:

Einstein's theory of General Relativity beautifully realises gravity as a theory of geometry: matter causes space-time to curve. "Supergravity" is an very particular and intricate extension of Einstein's theory that appears as a low-energy limit of string theory. In this talk, I will describe how, despite its apparently complexities, supergravity also has an elegant geometrical description that unifies the different symmetries of the theory in a direct analogue of Einstein's theory. The appropriate extension of conventional differential geometry is a version of "generalised geometry" first introduced by Hitchin. This formulation gives hints as to what notions of geometry might underlie string theory, and hence perhaps our own space-time. It also gives a number of unexpected extensions to conventional complex, symplectic and Kähler geometries.