HET-Discovery seminar: John Golden

In this talk I will review to the beautiful interconnection between scattering amplitudes, polylogarithms, and cluster algebras. Coordinates generated by the cluster algebra on Gr(4,n) provide a natural set of variables which appear as the arguments of polylogarithms in integrated amplitudes in planar N=4 SYM. Furthermore, these coordinates parameterize a convex polytope known as the associahedron, and there is a natural map between polylogarithm functions and the geometry of this polytope. This connection allows us to write down novel decompositions of two-loop amplitudes in terms of subgeometries of the associahedron.