Asymptotic symmetries and Soft theorems

In this talk I will review some recent progress in understanding the symmetry group of Gravitational S matrix. More in detail I will describe a proposal for a generalization of the so-called BMS group in which the conformal isometries of the sphere (Lorentz group) are replaced by arbitrary sphere diffeomorphisms. We will then see how the associated Ward identities are equivalent to the various Soft theorems for Quantum Gravity. This talk is based on joint work with Miguel Campiglia.