I will give an overview of my recent research on the definition of asymptotic charges in asymptotically flat spacetimes, including the definition of subleading and dual BMS charges and the relation to the conserved Newman-Penrose charges at null infinity.
In this talk, we will discuss some recent progress on the study of six-dimensional S-matrices as well as their applications. Six-dimensional theories we are interested include the world-volume theories of single probe M5-brane and D5-brane, as well as 6D super Yang-Mills and supergravity. We will present twistor-string-like formulas for all these theories, analogue to that of Witten’s twistor string formulation for 4D N=4 SYM.
As the applications, from the 6D results we also deduce new formulas for scattering amplitudes of theories in lower dimensions, such as SYM and supergravity in five dimensions, and 4D N=4 SYM on the Columbo branch.
I will discuss ongoing work to provide a proof for the following
conjecture: if the development of a time symmetric, conformally flat
initial data set admits a smooth null infinity, then the initial data
is Schwarzschildean in a neighbourhood of infinity. The strategy
to construct a proof consists in a detailed analysis of a
certain type of expansions that can be obtained using H. Friedrich's
"cylinder at infinity" formalism. I will also discuss a toy model for
the analysis of the Maxwell field near the
spatial infinity of the Schwarzschild spacetime