In this talk I will start by revisiting the calculation of entanglement entropy in free Maxwell theory in 3+1 dimensional Minkowski spacetime. I will characterize the soft sector associated with a subregion and demonstrate that conformally soft mode configurations at the entangling surface, or equivalently correlated fluctuations in the large gauge charges of the subregion and its complement, give a non-trivial contribution to the entanglement entropy across a cut of future null infinity. I will conclude with some comments on the holographic description of bulk subregions in asymptotically flat spacetimes.

The search for pragmatic observables of quantum gravity remains at the forefront of fundamental physics research. A large set of ideas collectively known as the gauge-gravity duality have proven fruitful in tackling this problem. While such a duality is believed to universally govern gravitational theories, its nature in theories of gravity that describe our universe to a good degree of approximation is still little understood. In this talk I will discuss efforts in formulating a holographic correspondence for gravity in four-dimensional asymptotically flat spacetimes. The proposed dual theory lives on a two-dimensional celestial sphere at infinity and is constrained by a wide range of symmetries. I present recent evidence for this proposal by showing that it arises naturally in a flat space limit of AdS/CFT. I will illustrate this construction with two related examples: the propagation of a particle in a shockwave background and the high-energy scattering of 2 particles.