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These are lecture notes for five lectures given at MPI Leipzig in May 2024. We study the moduli space M₀, ₍ of n distinct points on P¹ 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.
Thomas Lam (Mon,) studied this question.
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