9 problems

Let $k$ be a field. A minor of a volume polynomial is obtained by applying deletions and contractions of variables, and limits are taken in the relevant coefficient space. The mino…

Let $k$ be a field, and let $\mathbb{V}^d_n(\mathbb{R},k)$ denote the set of volume polynomials over $k$. The field-independence conjecture. The set of volume polynomials over $k$…

The volume-realization conjecture. The following conditions are equivalent: there is a convex body $A\subseteq\mathbb{R}^5$ such that $p_{ij}$ is the volume of $\pi_{ij}(A)$ for ev…

Let $M$ be a realisable matroid, and let its independent set generating polynomial be the polynomial obtained by summing a monomial for each independent set of $M$. A polynomial is…

Let $x_1\leq\ldots\leq x_k$ be a chain, let $P_{\mathrm{KS}}$ be its Kahn–Saks polynomial, and let $N(P_{\mathrm{KS}})$ denote its normalization. For exponent vectors $\alpha$ and…

Let $P$ be a poset, let $F_P$ denote its Kahn–Saks polynomial, and let $\alpha$, $\beta$, and $\gamma$ be exponent vectors for which the displayed evaluations are defined. Generali…

Let $F(x,y)=\sum_{i=0}^d{d\choose i}a_ix^iy^{d-i}$ be a degree $d$ form, where $a_0,\dots,a_d$ are non-negative integers satisfying … for all $0\leq i\leq j\leq d$ and…

Let $M$ be a $3\times 3$ symmetric matrix with non-negative integer entries and let … be the corresponding ternary form. Assume that $\det(M)\geq 0$ and $\det(M_I)\leq 0$, where…

Gurvits's conjecture. The equality