8 problems

Rozansky's rationality conjecture. Each term of the expansion of the Kontsevich integral should be given by a series of trivalent graphs with rational functions attached to their e…

Wheels conjecture.

Rozansky's integrality conjecture. The invariant satisfies

Perturbative Wilson-loop conjecture. The corresponding perturbative series expansion for vacuum expectation values of Wilson loops should be related to the Kontsevich integral for…

Let $K$ be a knot in the complement ${\mathbb R}^{3}\backslash\{K'\}$ of a knot $K'\subset{\mathbb R}^{3}$ with even linking number $lk(K,K')$. Put $K'$ in general position with re…

Let $K$ be a long knot, let $\operatorname{rot}(K)$ denote its Gramain cycle, and let $w_1,w_2$ be the weight systems obtained from the two principal parts of the Teiblum–Turchin c…

Let $\alpha$ be a Vassiliev $1$-cocycle of degree $m$, and let $\tilde{\alpha}$ be the $1$-cocycle obtained by composing the weight system associated to the principal part of…

Let $L$ be a link represented in the book notation, and suppose its crossings are partitioned into groups as in the book of $M$ pages. A group of crossings is positive or negative…