Tree-level scattering forms of Yang-Mills theory
Inspired by the idea of viewing amplitudes as differential forms we will introduce in this talk scattering forms of bi-adjoint scalar theory and Yang-Mills theory on the worldsheet. These forms are defined such that their pushforward under the scattering equations provides the Cachazo-He-Yuan representation of color-ordered amplitudes in bi-adjoint scalar theory and Yang-Mills theory respectively. Scattering forms have some remarkable properties. In particular, the residue of scattering forms factorizes on the boundary components of the worldsheet into two forms of lower point. Moreover, the scattering form of the bi-adjoint scalar theory is associated to a real geometry called the associahedron.