Appears in collection : Balzan Lectures

The asymptotic structure of gravity in the asymptotically flat context will be described at spatial infinity by Hamiltonian methods. The first lecture will provide the main ideas, give the Poisson bracket algebra of the BMS charges and propose a supertranslation-invariant definition of the angular momentum. The second lecture will discuss the connection with null infinity and provide in particular a justification of Strominger's matching conditions of the fields between past null infinity and future null infinity.