11 problems

Sign conjecture. For any tree on $n$ vertices,

Steiner distance hyperdeterminant value conjecture. The value of $\det(M)$ depends only on $n$ and $k$, not on the choice of the tree $T$.

Let $\Delta_k$ denote the $k$-simplex, and let … where $k_0\geq\cdots\geq k_r$. The configuration $A$ is GKZ-rational when its associated GKZ hypergeometric system has the rational…

Let $P_n$ be the prime ideal of the algebraic variety that is the image of the principal-minor map for complex symmetric $n\times n$-matrices. Let the hyperdeterminantal module be…

Let $[?]$

Let $T$ be a tree on $n$ vertices, and let $k$ be a positive integer. The $k$-Steiner distance hyperdeterminant is the hyperdeterminant of the $k$-th order Steiner distance hyperma…

Real three-qutrit hyperdeterminant maximum conjecture. The maximum value of the hyperdeterminant for real three-qutrit states is also the maximum value on complex states.

Let $f$ be a ternary quartic of real rank $6$ and signature $(3,3)$, $(4,2)$, or $(5,1)$. Let $\operatorname{VSP}(f)_\mathbb{R}$ be the real points of the variety of sums of powers…

Let $\mathscr A$ be the algebra of quantum hypermatrices, with quantum hyperdeterminant $\mathrm{Det}_q$. An intermediate quotient algebra is a quotient…

Let $X=\mathbb{P}^{k_1}\times\dots\times\mathbb{P}^{k_r}$ be a Segre embedding, and let $X^*$ be its dual variety. When $X^*$ is a hypersurface, its defining equation up to scale i…

Let $\lambda=(\lambda_1,\dots,\lambda_M)$ be a partition, and let $\mathcal{L}_\lambda$ denote the large-$N$ limit associated with the statistic indexed by $\lambda$. Factorization…