9 problems

Dunfield–Gukov–Rasmussen conjecture. There is a spectral sequence from HOMFLY-PT homology to knot Floer homology.

Let $k>1$ and let $L$ be an oriented $k$-component link. Let $\widetilde{\mathrm{H}}(L)$ denote the proposed redefined triply graded link homology theory. Finite-dimensional extens…

Corrected HZ factorisability conjecture. If the HOMFLY–PT/Kauffman relation holds, then the HZ transform is factorisable:

Petrou's HZ factorisability conjecture. The HOMFLY–PT/Kauffman relation holds if and only if the HZ transform is factorisable:

HOMFLY–PT–Kauffman criterion. HZ factorisation for knots occurs if and only if

Cube-compatible identification conjecture.

Let $\{P_{K;n}(a,q)\}$ be the colored HOMFLY-PT polynomials of $K$, colored by the $n$-th symmetric power of the fundamental representation. Define operators by … Suppose these pol…

Let $K$ be a knot in $S^3$, and let $f(U)$ be the polynomial determined by the branch of the zero locus of $\operatorname{Aug}_K$ near $(\lambda,\mu,U)=(0,U,U)$ through … Here…

Let $B^{(m)}$ be the $m$-colored version of a braid diagram $B$, and let $H_N(B^{(m)})$ denote its colored $athfrak{sl}(N)$ link homology. Denote by $H$ the colored HOMFLY-PT link…