Integrable Deformations for N = 4 Super Yang-Mills and ABJM Amplitudes

Integrands for scattering amplitudes admit deformations that preserve the integrable symmetries. I will explain these deformations in terms of Grasmannian integrals and on-shell diagrams, and discuss possible applications. This is a slightly extended version of a talk that I gave at the Simons Center in Stony Brook on November 11, 2014.