9 problems

Suppose that a planar diagram of an oriented link $L$ intersects the vertical line $x=0$ at $(0,-b)$, $(0,-a)$, $(0,a)$, and $(0,b)$, where $0<a<b$. Suppose that $L$ is directed to…

Let $G$ and $G'$ be connected simple plabic graphs whose quivers $Q_G$ and $Q_{G'}$ are mutation equivalent. Let $L^{\operatorname{plab}}_G$ and $L^{\operatorname{plab}}_{G'}$ be t…

Let $G$ be a plabic graph with $\operatorname{c}(G)$ connected components and $n$ interior faces. Let $L^{\operatorname{plab}}_G$ be its associated plabic graph link, and let…

The $Q^r$ shift conjecture. For all odd integers $a,b,c$ and symmetric representations $[r]$,

The normalized $Q^1$ periodicity conjecture. For the indicated values of $c$ and $r$,

The $9_{46}$ transformed-factor conjecture.

The $9_{46}$ odd-index divisibility conjecture. For odd positive integers $i>1$,

The $9_{35}$ divisibility conjecture. For positive integers $i>1$,

Let $C$ be a curve in $\mathbb{C}^2$ given by $f(x,y)=0$ and passing through the origin. Intersecting $C$ with the boundary of a sufficiently small ball around the origin gives an…