7 problems

Uniqueness conjecture for FK. The quantum $A$-polynomial equation together with this non-singularity condition should determine $F_K$ uniquely up to an overall factor.

The (a,t)-deformed $F_K$ conjecture. There should exist a four-variable function satisfying

The a-deformed $F_K$ conjecture. The function should also satisfy

Let $K$ be a knot, let $a$ and $q$ be parameters, and let $\hat{A}_K(\hat{x},\hat{y},a,q)$ be the $a$-deformed quantum $A$-polynomial. HOMFLY-PT analogue conjecture. There exists a…

Let $K$ be a knot, let $N$ be a positive integer, and let $F_K^{{\rm SU}(N),{\rm sym}}(x,q)$ be the specialization of the reduced higher-rank series obtained by setting the remaini…

Let $G$ be a root system of rank $r$, with Weyl group $W$, positive roots $\Delta^+$, weight lattice $P$, root lattice $Q$, Weyl vector $\rho$, and dominant weights $P_+$. Let…

Let $K$ be a knot. Write $\Delta_K(x)=\nabla_K(x^{1/2}-x^{-1/2})$ for its Alexander polynomial, and let $\hat{A}_K(\hat{x},\hat{y},q)$ denote its quantum $A$-polynomial. Gukov–Mano…