Algebraic Combinatorics Seminar - Freddy Cachazo

Title: Arrangements of Pseudolines, Tropical Grassmannians, and Generalized Scattering Amplitudes

Abstract: For each arrangement of (pseudo)lines on the projective plane, it is possible to construct a differential form that captures its combinatorial structure. The forms have simple poles whenever triangles shrink to a point in the arrangement, and share the same residue when two arrangements are connected via a "triangle flip". In this talk I will explain the construction and give evidence for the conjecture that integrating such differential forms, with the appropriate measure, computes generalized scalar scattering amplitudes. These amplitudes are defined as sums over arrangements of metric trees or generalized Feynman diagrams. While generic arrangements of metric trees span the Dressian, it is also conjectured that the "physical" ones define cones in the tropical Grassmannian.