Penrose conformal compactification allows for an elegant description of asymptotically flat spacetime where a boundary is added at null infinity. In particular the scattering data of massless fields naturally live on this boundary and this realises a representation of the BMS asymptotic symmetry group. I will review this and how this relates to recent developments in scattering amplitudes of massless fields.
A geometric description of spatial infinity is notoriously more elusive, I will however show that methods of projective geometry allows for a picture very similar to that of null infinity. A key idea here is the introduction of an extended, four dimensional, boundary. In particular scattering data of massive fields are naturally realised on this extended boundary and carry a representation of the BMS group. Finally strong evidence suggests that ``Strominger's matching conditions'' have a most natural realisation in this framework.
Jacopo Mazza
