These are lecture notes for five lectures given at MPI Leipzig in May 2024. We study the moduli space M0,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.
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Thomas Lam (2024) studied this question.
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