12 problems

Let $V(3,n)_{\geq 0}$ be the totally nonnegative part of the ABCT variety, and let the momentum amplituhedron be the positive geometry arising in the corresponding scattering-ampli…

Let $\operatorname{Gr}(2,n)_{>0}$ be the positive Grassmannian, and let the scattering map of the twistor construction map it to the momentum amplituhedron. Denote the interior of…

Let $\mathcal{M}_{n,k}$ be the momentum amplituhedron. For a Grassmannian graph $G$, let $\Phi^\circ_G$ be the associated stratum, and let $\dim_{\mathcal{M}}(F)$ denote the dimens…

Let $\mathcal{M}_{n,k}$ be the momentum amplituhedron, and let $\mathcal{S}_{n,k}$ consist of the decorated permutations whose strata are boundary strata, together with the decorat…

Let $k,n$ satisfy $2\le k\le n-2$, let $(\tilde{\Lambda},\Lambda)$ be kinematic data as defined for the momentum amplituhedron, and let $\mathcal{M}_{n,k}(\tilde{\Lambda},\Lambda)$…

Let $n=2k$, let $\mathcal{M}_{0,n}^+$ be the positive moduli space, and define the Veronese-based $D=3$ twistor-string map … where $C_{\alpha i}(\sigma)$ is the orthogonal Veronese…

Let ${\cal M}_{0,n}^+$ be the positive moduli space of $n$ ordered points, and let the $D=3$ twistor-string map send it to the proposed positive geometry for ABJM. $D=3$ twistor-st…

Twistor-string map diffeomorphism conjecture. The twistor-string map provides a diffeomorphism from $G_+(2,n)$ to the interior of the momentum amplituhedron. If true, this would es…

Let $G_+(2,n)$ denote the positive Grassmannian of $2$-planes in an $n$-dimensional vector space, and let the $D=4$ twistor-string map send a point of $G_+(2,n)$ to the correspondi…

Let ${\cal M}_{0,n}^+$ be the positive moduli space of $n$ ordered points on a line, and let the $D=3$ twistor-string map send a point of this space to the corresponding kinematic…

Forbidden-diagram characterization. For all $n$, a cell in $G_+(3,n)$ is not in $[?]$ if and only if its associated $[?]$-diagram contains one of the three forbidden $[?]$-diagrams…

Momentum amplituhedron boundary–singularity conjecture. The physical singularities of tree amplitudes correspond to the boundaries of the momentum amplituhedron.