The quantum-correction gluing conjecture for mirrors of anticanonical complements

Let $X$ be a Kähler surface with anticanonical divisor $D$, and let $M$ be the complexified moduli space of special Lagrangian tori in $X\setminus D$. A Maslov index 0 wall is a region boundary in $M$ associated with Maslov index 0 discs, and the wall-crossing changes of variables are the holomorphic coordinate transformations arising when crossing such walls. The quantum-correction gluing conjecture. The mirror to $(X,D)$ should differ from $M$ by quantum corrections which, away from the singular fibers, amount to gluing the various regions of $M$ delimited by Maslov index 0 discs according to those changes of variables. This conjecture adapts the Gross–Siebert and Kontsevich–Soibelman picture of quantum-corrected mirror gluing to the non-Calabi–Yau setting; a general construction and proof remain open.