| Abstract: In the planar limit of a large number of colors, N=4 super-Yang-Mills theory is integrable, and remarkable advances have been made in determining operator anomalous dimensions and more to all loop orders. In this talk Ill describe progress in constructing gluon scattering amplitudes in this theory to high loop order. Planar N=4 amplitudes are dual to light-like polygonal Wilson-loops, and are only nontrivial for six or more gluons. The spaces of functions to which the amplitudes belong are so restrictive that only a few constraints are needed to "write down the answer", through seven loops in the six-gluon case and four loops in the seven-gluon case. Recently a particular operator form factor, analogous to Higgs boson decay to three gluons, has been bootstrapped to five loops eight loops is imminent. The results in all cases are multivariate functions of the kinematics, which can be analyzed in various factorization limits, in some cases to all orders in the coupling. At strong coupling the results merge into the dual AdS/CFT description. Link to the Event Video |