Fukaya–dimer quasi-equivalence conjecture for convex lattice polygons

Let $\Delta$ be a convex lattice polygon containing the origin in its interior. A Laurent polynomial $W$ has Newton polygon $\Delta$, and a pair $(G,D)$ consists of a consistent dimer model $G$ and a perfect matching $D$ whose characteristic polygon is $\Delta$. The pair determines a directed $A_\infty$-category $\dirscA$, while $W$ determines its Fukaya category $\Fuk W$. Fukaya–dimer quasi-equivalence conjecture. There exist such $W$ and $(G,D)$ for which one has a quasi-equivalence

$$\dirscA \cong \Fuk W$$

of $A_\infty$-categories. This proposes a categorical correspondence between dimer models and Fukaya categories of Laurent polynomials, providing a route toward homological mirror symmetry for toric orbifolds of toric del Pezzo surfaces. The source does not state a resolution of the conjecture.