19 problems

Uniqueness conjecture. Every nonsingular homogeneous polynomial is nice. For degree greater than $2$, there is precisely one choice of coordinates in which a nice polynomial reache…

Let $L$ be an oriented link, let $n$ be a positive integer, let $GLZ^n_L(\tau,t)$ denote the invariant associated with the quantum superalgebra $U_q[\operatorname{osp}(2|2n)]$, and…

Let $L$ be an oriented link, let $m,n$ be positive integers, let $LG^{m,n}_L(\tau,t)$ denote the Links–Gould invariant, and let $\Delta_L$ denote the Alexander polynomial. Generali…

The conjecture that ${\cal C}_3$ and ${\cal C}_4$ differ.

The conjecture that ${\cal C}_2$ and ${\cal C}_3$ differ.

Cubic Tutte relation conjecture. The second derivative of Speyer's polynomial satisfies

4-edge-twist conjecture. Then

3-edge-cut conjecture. The Speyer polynomials satisfy

Let $c(P)$ be the alternative measure of a polynomial, and let $k\geq 2$. Consider the integer-exponent family $1+x+x^{n_2}+x^{n_3}+\cdots+x^{n_k}$ and take the iterated limit with…

Alternative-measure conjecture.

For each positive integer $d$, let ${\sf RSK}_{1^d,1^d}$ be the RSK operator indexed by the compositions $1^d$, and let ${\sf RSK}_{m,n,d}$ be the corresponding operator in dimensi…

Normalized flat Jones–Krushkal polynomial conjecture. For any almost classical flat knot $\alpha$, the normalized flat Jones–Krushkal polynomial satisfies

Let $K$ be a knotoid diagram. Let $K_1$ and $K_2$ be the starred knotoid diagrams obtained from $K$ by placing a star in the region incident to the tail and the region incident to…

Oura's conjecture. The following analogous properties hold for $Th(\widetilde{\varphi_\ell^{G_{\rm{II}}}})$: (1) all zeros lie on a segment of the circle…

Let $G$ be the connected bipartite graph from the construction above, with bipartition denoted by $V$ and $E$, and let $L_G$ be its associated link. Write $P_{L_G}(v,z)$ for the HO…

For the $m$-cycle, let $\Gamma_m$ denote the homogeneous cycle polynomial defining the relevant algebraic boundary component. Homogeneous cycle-polynomial degree conjecture. … The…

Symmetric-factorization conjecture. The determinant has the following factorization properties: (1) $\det G_n=u^2-v^2$ for some $u\in R_1$ and $v\in R_2$; (2) it factors as

New-factor divisibility conjecture. For the resulting sequence of factors,

Let $G_n$ be the Gram matrix in the paper, and let divisibility be taken in its polynomial ring. The first-determinant divisibility conjecture. For every integer $n\geq 1$, … The c…