Broadly speaking how do ideas of leading singularities and Grassmanian help in curing infrared divergences when calculating N=4 scattering amplitudes? My understanding is that one gets infra red divergences because the external gluon momenta becomes collinear with the loop momenta. I am confused as to what Nima's and Freddie's collaboration are doing to avoid this? If people can clarify my confusion and direct me to the appropriate literature I would be grateful. Also, is there a clear way to understand this for theories like planar QCD?