  These are lecture notes for five lectures given at MPI Leipzig in May 2024.
We study the moduli space M_{0,n} of n distinct points on P^1 as a positive
geometry and a binary geometry. We develop mathematical formalism to study
Cachazo-He-Yuan's scattering equations and the associated scalar and Yang-Mills
amplitudes. We discuss open superstring amplitudes and relations to tropical
geometry.
