The Amplituhedron

In this talk we show that scattering amplitudes in N=4 SYM can beunderstood as volumes of “The Amplituhedron”, a natural generalization of convex polygons into the Grassmannian. This invariant definition of the amplitude makes no reference to the usual concepts of quantum field theory. All fundamental properties of the amplitude, such as Unitarity, Locality follow from positivity. Any representation of the amplitude can be then understood as a particular triangulation of this object.