TL;DR
This paper explores the structure of moduli spaces in positive geometry, focusing on M_{0,n}, and develops formalism for scattering equations, amplitudes, and their connections to tropical geometry.
Contribution
It introduces a new formalism for studying moduli spaces as positive geometries and links scattering amplitudes to tropical geometry frameworks.
Findings
Moduli space M_{0,n} characterized as a positive and binary geometry.
Developed formalism for Cachazo-He-Yuan scattering equations.
Connected superstring amplitudes to tropical geometric structures.
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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Taxonomy
TopicsMathematics and Applications · Advanced Numerical Analysis Techniques · Digital Image Processing Techniques