The natural structure of scattering amplitudes

In this thesis we present all the techniques needed for the functional reconstruction of univariate rational functions over Finite Fields and apply them to tree-level scattering amplitudes. In particular this procedure using the BCFW recursion as black-box algorithm is presented here for the first time. Furthermore, as a second novel result, we discuss some new aspects of the relation among BCFW tree-level recursion and the maximum-cut of multi-loop diagrams.