The work pursued during the period of the project made several major advances on the objectives of the project.
First, an action principle for chiral higher spin gauge fields described by tensors of mixed Young symmetry with self-dual field strengths has been explicitly built. This question is relevant to chiral maximal supersymmetry in 6 spacetime dimensions and required the development of new algebraic and geometrical tools generalizing the Cotton tensor of ordinary Riemannian geometry.
Second, a major effort has been launched towards understanding the asymptotic structure of gravity at spatial infinity, putting the action and its invariance in the foreground. The identification of the infinite-dimensional symmetry group (BMS group) at spatial infinity has been successfully derived. This new approach not only crucially resolves long-standing tensions between null infinity and spatial infinity but it also inspires new lines of investigation and reveals unanticipated structures at infinity (nonlinear asymptotic symmetry algebras).
Third, a profound original insight on duality symmetry for higher spin gauge fields (a "hidden symmetry") that has been gained, where action principles explicitly invariant under duality have been constructed.
Fourth,higher spin charges associated with "large" ("improper") higher spin gauge transformations have been defined in three spacetime dimension by elucidating the asymptotic structure of the fields at infinity.
The work has resulted in 59 publications in leading peer-reviewed journals (plus 2 in press), as well as in a great number of seminars in foreign universities and of presentations at international conferences and at doctoral schools. A monograph "The cosmological singularity" co-authored with V. Belinski has been published by Cambridge University Press.
