I will discuss recent and ongoing work with Emil Have, Stefan Prohazka and Jakob Salzer on possible kinematics for flat space holography. I will discuss how a seemingly novel projective compactification of Minkowski spacetime reveals a rich asymptotic geometry homogeneous under the Poincare group and including the blow-ups at spatial and timelike infinities as well as a novel four-dimensional space intimately associated to null infinity. This allows for novel geometric descriptions of the Minkowski asymptotic geometries and gives us a glimpse of the asymptotic geometry of asymptotically flat spaces.

I will report on joint work with Andrea Santi outlining an algebraic reformulation of the classification problem of eleven-dimensional supergravity backgrounds. The basic object of study is the Killing superalgebra of the background, whose algebraic structure has recently been elucidated. If time permits I will also comment on work also involving Paul de Medeiros applying these techniques to the construction of rigidly supersymmetric theories in curved spaces.

We've known since childhood that symmetry can be a very powerful tool in solving partial differential equations. With a little symmetry, one can reduce the number of independent variables, whereas with some more symmetry one can usually separate variables and reduce the problem to solving ordinary differential equations. Given enough symmetry, though, partial differential equations become algebraic. A large body of current research in our field requires finding solutions to the (super)gravity field equations and in this talk I will motivate the search for homogeneous supergravity backgrounds and mention some recent results in this area.

I will discuss several constructions of superalgebras associated to the Killing spinors of a supergravity background, with special emphasis on the ten- and eleven-dimensional supergravities.