12 problems

Let $T$ be an irreducible hypertree, and identify it with its graph $G$, whose edges are the pairs occurring in the triples of $T$. Irreducible hypertree copiousness conjecture. Ev…

Let $G$ be a graph. A graph is copious when it satisfies the copiousness condition defined in the paper, and topologically copious when the associated map from the moduli space…

Let $G$ be a copious graph with $n$ vertices. For $3\leq s\leq n$, let $\pi_G(s)$ be the number of partitions of the vertex set $[n]$ into $s$ independent subsets of $G$. ML-degree…

Let $[n]=\{1,2,\dots,n\}$, and call a graph on $[n]$ a minimal kinematics graph when its edge set is inclusion-maximal among the graphs realizing minimal kinematics. Minimal kinema…

Let $G$ be a graph, and let conditions 1, 2, 3, and 4 be the four conditions in Theorem 1. The graph $G$ is matroidally copious when it satisfies the relevant matroidal condition d…

Let $L_m$ be the relevant linear space arrangement, let $\mathbb{L}_s$ be the linear space determined by the kinematic data $s$, and let $I_r(W)$ be a type (ii) flat, with associat…

Component-count conjecture. The lifted scattering correspondence $\widetilde{\rm C}(3,n,1)$ decomposes into five irreducible components, with exactly one component whose map onto…

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…

Smallest-number-of-solutions conjecture. The number $(n-3)!$ is the smallest possible number of saddle points among all stringy canonical forms reproducing the ABHY associahedron.

Minimal saddle-point conjecture. Among all stringy canonical forms for the ABHY associahedron, ${\bf I}_n$ has the smallest number of saddle points, namely

Minimal saddle-point conjecture. The same pushforward phenomenon holds for generalized associahedra.

Let $k=3$ and let $n=2m+1$ or $n=2m+2$, where $m\geq 3$. Consider the soft limit $X(k,n)\to X(k,n-1)$, and suppose that singular solutions are those for which some minors involving…