Motivated by the enhancement of Lorentz symmetry to Virasoro in four-dimensional (4D) gravity in asymptotically flat spacetimes, a path has emerged to approaching scattering problems in this context with two-dimensional (2D) conformal field theory (CFT) methods. In the first part of this talk I will discuss some of the related results and their implications, including their relevance for infrared divergences, the construction of gravitational observables that make the 2D conformal symmetry manifest and the additional symmetries they must obey. As an application of this framework, I will show in the second part how the rich symmetry structure of the 2D (celestial) CFT can be used to infer non-trivial information about four-dimensional gravitational dynamics. In particular, I will demonstrate that a recently discovered tower of conformally soft symmetries in 2D implies a set of dynamical evolution equations for an infinity of asymptotic charges in general relativity. I will finally provide evidence that these charges realize a representation of a higher-spin symmetry algebra on the gravitational phase space.

Seminar in hybrid mode: Itzykson room and BBB link sent by mail.