6 problems

Let $L$ be a framed unoriented link with components $L_i$, and let $y_{\lambda_i}$ and $Q_{\lambda_i,\lambda_i}$ denote the corresponding Kauffman and Homfly annular decorations fo…

Let $L \subset \Sigma \times I$ be a link, where $\Sigma$ is a surface. An essential surface for $L$ is a surface of smallest genus in which $L$ can be embedded in the thickened su…

Specialization conjecture.

Oblomkov–Shende conjecture.

Let ${\cal L}$ be an unoriented link with $L$ components, colored by representations $R_1,\ldots,R_L$. Let $\hat f_{R_1,\ldots,R_L}(t,\nu)$ denote the reformulated colored HOMFLY i…

Let ${\cal K}$ be a knot, let $R$ be a representation, and let $\hat f_R(t,\nu)$ be the reformulated colored HOMFLY invariant obtained by applying the inverse matrix $M^{-1}$ to th…