Minimal Kinematics on M₀,n and Beyond

Explore a 51-minute conference talk from the Amplituhedra, Cluster Algebras, and Positive Geometry Conference where Nick Early from Weizmann Institute of Science delves into the fascinating world of Minimal Kinematics (MK) and Planar Kinematics (PK) on moduli spaces. Discover how critical points in kinematic degenerations of the CHY scattering potential are expressed through rational formulas based on Horn uniformization of Kapranov-Huh and 2-trees. Learn about the intersection of MK and PK that creates the PK polytope - a reflexive polytope related to the associahedron, whose polar dual root polytope has a volume equal to a Catalan number. Examine how these concepts extend beyond the moduli space $M_{0,n}$ to moduli spaces $X(k,n)$ of points in projective space $\mathbb{P}^{k-1}$, encompassing CEGM amplitudes and further applications.