Despite recent progress, a complete formulation of a holographic correspondence for flat spacetimes remains elusive.
Any viable formulation of flat space holography should be based on a correspondence between bulk and boundary states built upon the equivalence of unitary irreducible representations (UIRs) of the asymptotic symmetry group of flat spacetimes, the BMS group. In this talk, I will present explicit wavefunctions for the UIRs of the BMS group (the so-called BMS particles). These are functions on supermomentum space that generalize the familiar notion of Poincaré particles by incorporating additional soft degrees of freedom. I will discuss their connections to infrared physics and outline prospects for defining an S-matrix for BMS states that is free from infrared divergences. This talk is based on joint work with X. Bekaert and Y. Herfray.