11 problems

Resolution conjecture. The generalized Kauffman bracket is given by

Let $(L_+,L_-,L_0)$ be an oriented skein triple, and let $\mathbf{p}$ be a set of basepoints away from the resolutions. Denote by $\widetilde{\operatorname{HMR}}_*(L,\mathbf{p})$ t…

Bordered-surface cluster-algebra conjecture. Such arcs are elements of the cluster algebra for bordered surfaces.

Let $L_+$, $L_-$ and $L_0$ be oriented links, with $L_0$ the resolution of a distinguished crossing, and suppose the skein exact triangle involves the module … If $L_0$ has $\ell$…

Let $C$ be the relevant ultraviolet curve, let $Y$ be a puncture, and let $[1^N]$ denote the full puncture. Write $d_C^{[1^N]}$ and $d_C^Y$ for the corresponding quantities associa…

Skein-invariant level conjecture. The various invariants that use skein relations will not detect the level of a link.

Congruent skein relation. If the crossing is a self-crossing of a knot, then

Congruent skein relation for reformulated composite invariants. When the crossing is the linking between two different components of $\mathcal{L}$,

Congruent skein relations. For any such link,

Let $\mathcal{L}$ be a link and let $p$ be a prime number. Write $\check{\mathcal{Z}}_p(\mathcal{L};q,t)$ for the reformulated colored HOMFLY-PT invariant associated with the $p$-r…

In the setting of higher-rank theories, geometric webs are constructed from tropical $a$ coordinates, while their algebraic descriptions are given by the associated line operators…