4 problems

Let $P$ be a Fano polygon. Two Fano polygons are mutation-equivalent if they lie in the same equivalence class under polygon mutations. A del Pezzo surface with cyclic quotient sin…

Let $f \in \mathbb{C}[x_{1}^{\pm 1},\ldots,x_{n}^{\pm 1}]$ be mirror dual to an $n$-dimensional Fano variety $X$, and let $P$ be the Newton polytope of $f$. Write $X_{P}$ for the t…

Quantum-period conjecture. If

Conjecture A. There is a one-to-one correspondence between $\mathfrak{P}$ and $\mathfrak{F}$. The correspondence sends $P$ to a generic qG-deformation of the toric surface $X_P$.