5 problems

Uncolored specialization conjecture. For any knot $K$,

SO-type quantum super-A-polynomial conjecture. The minimal-order $q$-difference equation

Let $K$ be a knot and let $A^{\text{super}}(x,y;a,t)$ be its super-$A$-polynomial. A polynomial is quantizable when its face-polynomial data satisfy the required root-of-unity cond…

Let $K$ be a knot, and let ${\cal P}_n(K;a,q,t)$ denote its colored superpolynomial. The coefficients $a_0,\ldots,a_k$ are the coefficients of a recurrence operator, with the omitt…

Let $K$ be a knot, and let ${\cal P}_n(K;a,q,t)$ be its $S^{n-1}$-colored superpolynomial. Set $q=e^{\hbar}$, with $a$ and $t$ fixed, and hold $x=q^n$ fixed as $\hbar\to0$ and…