Abstract: In this talk we show that scattering amplitudes in N=4 SYM can be
understood 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
The tak is based on the paper, see also a related popular article.