12 problems

Let $\mathbf H(q,t,a)$ be the uncolored link series, and let $\kappa$ be the number of components of the algebraic link. Weak Riemann hypothesis. At $a=0$, $\mathbf H(q,t,0)$ has o…

Let $\mathcal H^{daha}(q,t,a)$ be the DAHA superpolynomial of an algebraic link, colored by rectangle Young diagrams, and let $\kappa$ be the number of link components. Positivity…

Let $\mathcal{R}=\mathbf{F}_q[[x,y]]\subset\Omega=\mathbf{F}_q[[\epsilon_j,\zeta_j]]$, and let $\widetilde{\mathcal R}=\mathbf{F}_q[[\widetilde x,\widetilde y]]$ be the sufficientl…

Let $\mathcal{L}$ and $'\!\mathcal{L}$ be algebraic links with coloring partitions $\lambda^j$ and $'\!\lambda^j$, and let their iterated-torus data be…

Let $\mathcal{R}$ be a plane-curve-singularity ring with branches indexed by $1\le i\le\kappa$, and let $\sigma=(c_1\ge\cdots\ge c_\kappa>0)$. Define the motivic superpolynomial ……

Let an uncolored algebraic link have $\kappa$ components, and let $\varpi_0$ be the threshold beyond which the stable zero pattern is considered. Weak Riemann-hypothesis conjecture…

Let $\widehat{H}^i$ be the $i$th $a$-coefficient of a hat-normalized DAHA superpolynomial after $q\mapsto qt$, and let $\omega=1/q>0$. Strong and weak Riemann-hypothesis conjecture…

DAHA superpolynomial $a$-degree conjecture.

ORS conjecture. The polynomial $\mathscr{P}_{\!\operatorname{alg}}$ coincides with the reduced stable Khovanov–Rozansky polynomial of the corresponding link, equivalently the Poinc…

Let $C$ be the algebraic curve whose link is under consideration, and let $\mathcal{L}^{-}$ be its lattice complex. Write $\operatorname{gr}\mathcal{L}^{-}$ for the associated grad…

Positive-tail thickness conjecture. The link is $\overline{Kh}'$-thick if $q>1$ and either

Mixed-tangle thickness conjecture. The link is $\overline{Kh}'$-thick if $m\ge3$, $q>1$, each $p_i$ of length at least $2$ satisfies $\overline p_i=1$, and