6 problems

Let $K$ be a knot with corresponding quiver $Q_K$. For each crossing of type $L_+$, let $K_{i,\tau}$, with $\tau\binom{}{}$ replaced by $tau eq$? be the knot or link obtained by ch…

Let $K$ be a knot and let $R$ be a coloring representation. Denote by $P_R(K;a,q)$ and $P_R(K;a,q,t)$ the colored HOMFLY-PT polynomial and its $t$-refinement. Colored HOMFLY-PT hom…

Quadruply graded HOMFLY-PT homology conjecture. A closely related quadruply graded homology theory and corresponding superpolynomials should exist.

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 the $1,2$-coloured $sl(N)$ link homology denote the corresponding coloured $sl(N)$ link homology for links whose components are labelled $1$ or $2$. Stable-limit conjecture. In…

The authors define a triply graded homology for links whose components are labelled $1$ or $2$, and prove that it is a link invariant. Categorification conjecture. This homology ca…