Gravitational scattering amplitudes: matrices, trees and the Grassmannian

I will review some recent progresses in understanding scattering amplitudes in gravitational theories. We apply the matrix-tree theorem to establish a link between certain diagrammatic and determinant expressions, which appear ubiquitously in gravity amplitudes. Two notable examples include the diagrammatic expansion of Hodges' new formula for tree-level, maximally-helicity-violating (MHV) amplitude, and the matrix form of the one-loop rational part in N=4 supergravity. Furthermore, from a recent "twistor-string like" formula by Cachazo and Skinner, we use a similar approach to derive the Grassmannian formulation for N=8 supergravity, which contains all the tree-level amplitudes and possibly loop-level leading singularities of the theory.