Nima Arkani-Hamed

Title: Frontiers in Positive Geometry.

Abstract: In this talk I will describe work in progress connecting scattering amplitudes to amplituhedra and positive geometries in kinematic space. For N=4 SYM in the planar limit, I will show how the geometry of the amplituhedron naturally provides a new approach to non-perturbative physics. I will also describe conjectural all-loop order, non-planar, non-supersymmetric amplituhedra for the tr(phi^3) theory–which are new (generally infinite) polytopes attached to any Riemann surface–and show how the connection to positive geometry forces the existence of “gravity” in this setting.