Nick Early | Minimal Kinematics on $\mathcal{M}_{0,n}$, and beyond 

Amplituhedra, Cluster Algebras, and Positive Geometry Conference
May 31, 2024
Speaker: Nick Early, Weizmann Institute of Science
Title: Minimal Kinematics on $\mathcal{M}_{0,n}$, and beyond
Abstract: Minimal Kinematics (MK) identifies kinematic degenerations of the CHY scattering potential where the critical points are given by rational formulas. These rest on the Horn uniformization of Kapranov-Huh; they are specified combinatorially by 2-trees. On the other hand, Planar Kinematics (PK) identifies the locus in $M_{0,n}$ which is fixed by cyclic permutation. Combining MK and PK realizes a maximally thin relative of the associahedron known as the PK polytope; it is a reflexive polytope, and its polar dual, the root polytope, has volume a Catalan number. In this talk, we start by exploring MK and PK on the moduli space $M_{0,n}$. We explain how this story generalizes to moduli spaces $X(k,n)$ of points in projective space $\mathbb{P}^{k-1}$, to CEGM amplitudes and beyond.