We review recent progress on the information paradox. We explain why exponentially small
correlations in the radiation emitted by a black hole are sufficient to resolve the original …

We review the role that infinite-dimensional symmetries arising at the boundary of
asymptotically flat spacetimes play in the context of the celestial holography program. Once …

Scattering amplitudes in d+ 2 dimensions can be expressed in terms of a conformal basis,
for which the S-matrix behaves as a CFT correlation function on the celestial d-sphere. We …

It has been known since the earliest days of quantum field theory (QFT) that infrared
divergences arise in scattering theory with massless fields. These infrared divergences are …

A bstract We study general relativity at a null boundary using the covariant phase space
formalism. We define a covariant phase space and compute the algebra of symmetries at the …

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We discuss three different (conformally) Carrollian geometries and their relation to null
infinity from the unifying perspective of Cartan geometry. Null infinity per se comes with …

We develop a general framework for constructing charges associated with diffeomorphisms
in gravitational theories using covariant phase space techniques. This framework …

A bstract We develop the analysis of the asymptotic properties of gravity in higher spacetime
dimensions D, with a particular emphasis on the case D= 5. Our approach deals with spatial …

These notes are a transcript of lectures given by the author in the XVIII Modave summer
school in mathematical physics. The introduction is devoted to a detailed review of the …