**Abhay Asktekar**, Pennsylvania State University

*Null Infinity, BMS Group and Infrared Sectors *

I will provide a broad overview of the relation between the structure of null infinity and infrared sectors for the Maxwell theory and full, non-linear general relativity. I hope this talk will serve as an introduction for the talks that will follow.

**Miguel Campiglia**, Universidad de Montevideo

*$U(1)$ asymptotic charges and soft photons*

In the first part of the talk I will describe how the subleading soft photon theorem can be understood as a Ward identity of singular $O(r)$ large gauge symmetry at null infinity. In the second part I will present a space-infinity description of the $O(1)$ large gauge symmetry that arise in the context of the leading soft photon theorem.

**Maximilian Duell**, Technical University of Munich

*Scattering of atoms and non-locality of the vacuum in QED*

In the setting of algebraic QFT we give a mathematically rigorous construction of the scattering matrix for massive Wigner particles in the presence of massless excitations. Our analysis may be applied, in particular, to the scattering of electrically neutral particles in QED. In contrast to previous approaches we do not impose any technical assumptions on the spectrum of the mass operator near the particle masses. Instead, our approach relies on non-local features of the relativistic vacuum state which are similar to the well established Reeh-Schlieder property.

**Wojciech Dybalski**, Technical University of Mun

*Non-relativistic QED in different gauges*

Charges localized at spacelike infinity are a traditional ingredient of discussions of the infrared problems in QED in mathematical physics. It is an old conjecture that these charges depend on the gauge fixing in the quantization procedure. In this talk I will discuss this problem in a non-relativistic model of QED. I will show how to pass from the usual Coulomb gauge to the axial gauge, compute the charges in both cases and give arguments in favour of the above conjecture. Rigorous mathematical conclusions are hindered (so far) by severe infrared problems in the axial gauge.

**Barak Gabai**, Perimeter Institute

*Large Gauge Symmetries and Asymptotic States in QED*

Large Gauge Transformations (LGT) are gauge transformations that do not vanish at infinity. Instead, they asymptotically approach arbitrary functions on the conformal sphere at infinity. Recently, it was argued that the LGT should be treated as an infinite set of global symmetries which are spontaneously broken by the vacuum. It was established that in QED, the Ward identities of their induced symmetries are equivalent to the Soft Photon Theorem. In this paper we study the implications of LGT on the S-matrix between physical asymptotic states in massive QED. In appose to the naively free scattering states, physical asymptotic states incorporate the long range electric field between asymptotic charged particles and were already constructed in 1970 by Kulish and Faddeev. We find that the LGT charge is independent of the particles' momenta and may be associated to the vacuum. The soft theorem's manifestation as a Ward identity turns out to be an outcome of not working with the physical asymptotic states.

**Andrzej Herdegen**, Cracow Jagiellonian University

*Asymptotic structure of electrodynamics revisited*

The lecture presents a personal view on the asymptotic structure of electrodynamics. Asymptotic variables form an algebra, in which infrared–long-range degrees of freedom count among full-fledged observables, not merely superselection labels.

**Sebastian Mizere**, Perimeter Institute

*Soft Theorems from Riemann Spheres*

I will review the reformulation of the S-matrix in terms of Riemann spheres due to Cachazo, He, and Yuan. I will show how it sheds new light on the derivation of Weinberg soft theorems for General Relativity and Yang-Mills theory, as well as allows to study soft behaviour of other quantum field theories.

**Burkhard Schwab**, Harvard University

*Large gauge symmetries and black hole absorption rates*

I will introduce Noether's second theorem as a way to derive the conserved currents associated with asymptotic symmetries. The large gauge symmetries of electromagnetism (along with conservation of energy) fully constrain the absorption rate of low-energy electromagnetic radiation by black holes. I will show this explicitly for non-evaporating, spherically symmetric black holes in arbitrary space-time dimensions larger than 3.