19 problems

Let $d\ge2$ and let $V_d^c$ be the scaled toric variety associated with the second hypersimplex, where $c\in(\mathbb{C}^*)^{d(d-1)/2}$ ranges over all scalings. Minimum ML degree c…

An orientable ribbon graph is a graph embedded in an orientable surface, and its partial-dual polynomial records the genera of all partial duals, with coefficients counting partial…

Canonical form conjecture. For each binary $\Delta$-matroid $D$, there is a sequence of handle slides taking $D$ to some $D_{i,j,k,l}$ where $i$ is the size of the ground set minus…

Consider the poset of delta-matroid orbits ordered by inclusion, where each orbit arises from scaling matrices associated with a second hypersimplex. Monotonicity conjecture. The M…

Let $C\in\mathbb{C}^{d\times d}$ be a scaling matrix of rank four. A principal $4$-minor is non-vanishing when the corresponding principal submatrix has nonzero determinant. Rank-f…

Let $C_1,C_2\in\mathbb{C}^{d\times d}$ be scaling matrices, with associated delta-matroids, and let $c_1,c_2$ be the corresponding scalings. Delta-matroid invariance conjecture. If…

Odd-dimensional Hermitian isotropic Grassmannian conjecture. The function $S\mapsto p_S(L)$ is a valuated $\Delta$-matroid for every maximal isotropic subspace $L$. The even-dimens…

Assume $\operatorname{char} K=2$, let $F$ be the fixed field of the involution on $K$ with $F\ne K$, and write $K=F[\omega]$ where $\omega^2+\omega+\beta=0$ for some $\beta\in F$ a…

Let $K$ be a valued field with an automorphic involution preserving the valuation. Let $A=B+C$, where $B\in K^{n\times n}$ is skew-Hermitian and $C\in K^{n\times n}$ is Hermitian o…

Flawlessness conjecture. The coefficients of

Let $G$ be a graph, let $\mathrm{D}(G)$ be its adjacency delta-matroid, and let $\operatorname{Int}_{\mathrm{D}(G)}(v)$ be its interlace polynomial. Interlace-polynomial unimodalit…

Let $\mathrm{D}$ be a delta-matroid, and let $U_{\mathrm{D}}$ denote its $U$-polynomial. Say that $\mathrm{D}$ has an enveloping matroid when it satisfies the hypothesis used in th…

Let $\Gamma$ be a finite abelian group of order at least $2$, and let $\mathbb{F}$ be a finite field. A $\Gamma$-graphic delta-matroid is a delta-matroid associated with a $\Gamma$…

A matroid stack delta-matroid is a delta-matroid whose proper set systems in its stack are matroids. It is sparse paving when every matroid in its stack is sparse paving, meaning t…

For each $n\geq 2$, let $\Gamma_n$ be the proportion defined in the paper for compatible pairs of labelled delta-matroids. The sequence $(\Gamma_n)_{n\geq 2}$ is decreasing and bou…

Let $G$ be a ribbon graph with ribbon-graphic delta-matroid $D(G)$. A delta-matroid $D$ is a twist of a matroid if $D=M\ast A$ for some matroid $M$ and some $A\subseteq E$, where…

Let $M$ be a delta-matroid and $v$ an element of its ground set. Theorem (9.2) of Bouchet's work concerns binary matroids, while Theorem 9.2 in the source states that the equicardi…

Tropical pure-spinor conjecture. The tropical pure spinor space equals the $\Delta$-Dressian:

Wick-basis conjecture. For all $n\leq 6$, the Wick relations are a tropical basis.