"Recent years have seen a revolution in our understanding of the S-matrix of Yang-Mills theory. An even richer structure is expected to await us in gravity, but at present the gravitational S-matrix is much less well understood than its Yang-Mills counterpart.This project will investigate the beautiful and highly geometric properties of the gravitational S-matrix. It will develop the twistor string description of maximal supergravity discovered by the Researcher. This will involve i) extending the twistor string to higher genus worldsheets, so as to compute loop corrections to n-particle gravitational amplitudes with arbitrary external helicities, ii) generalising it to less supersymmetric gravities that may be coupled to matter, by orbifolding the fermionic directions of the target space and iii) broadening the class of space-times to which it applies by considering non-degenerate Poisson structures on twistor space, allowing for the computation of multi-point boundary correlation functions in AdS.In addition, the project will treat knowledge of gravitational amplitudes as `theoretical data' to guide the construction of an holographic theory of gravity on null infinity at the boundary of asymptotically flat space-time. This will involve i) an explicit construction of the S-matrix in terms of data at null infinity, ii) developing an understanding of how the (extended) Bondi-Metzner-Sachs group acts on this S-matrix and iii) building on the formulation of twistor strings with manifest parity invariance to create a theory of gravity that lives on holomorphic curves in (the complexification of) null infinity."