Canonical forms of positive geometries are constructed from Hodge theory and are unique exactly for 'genus zero pairs', with new formulas for polytopes and hyperplane arrangements.
Moduli spaces in positive geometry
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abstract
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.
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Positive geometries and canonical forms via mixed Hodge theory
Canonical forms of positive geometries are constructed from Hodge theory and are unique exactly for 'genus zero pairs', with new formulas for polytopes and hyperplane arrangements.