From Geometry to Scattering Amplitudes
In recent years it has become clear that particular geometric structures, called positive geometries, underlie various observables in quantum field theories. In this talk I will review this connection for scattering amplitudes. After a broad introduction and review of the main ingredients involved, I will focus on maximally supersymmetric Yang-Mills theory and discuss a positive geometry encoding scattering processes in this theory — the momentum amplituhedron. Finally, I will present some of the main goals and research directions for the future.