9 problems

Sign-valued twist conjecture. The only possible values of the twist parameters are

Gross–Siebert open mirror conjecture. The SYZ map should be inverse to the toric mirror map of $\mathcal{X}$.

Let $\mathcal{X}$ be a toric Gorenstein orbifold, and let $X \leftarrow Y$ be a crepant resolution of its coarse moduli space. A global quantum $D$-module is a tuple…

Let $\mathcal{X}$ be a Gorenstein toric orbifold, and let $W^{LF}_{\mathcal{X}}$ be its Lagrangian Floer superpotential. Denote by $QH^*_{\mathrm{orb}}(\mathcal{X})$ its orbifold q…

Let $X$ be a toric variety with at worst Gorenstein quotient singularities. Let $\mathcal{X}$ be the canonical toric orbifold with coarse moduli space $X$, and let $Y$ be a toric c…

Fredholm regularity conjecture. All the holomorphic orbidiscs obtained in the classification theorem are Fredholm regular.

The toric orbifold mirror theorem. The $I$-function and the $J$-function coincide under the coordinate change $\tau=\tau(q)$:

Let $\mathcal{X}$ be a toric orbifold and let $Y$ be a crepant resolution. Suppose their quantum $D$-modules are identified after analytic continuation, and equip both sides with t…

Let the toric data satisfy $\hat{\rho}\in \operatorname{cl}(\tilde{C}_\mathcal{X})$. Let $\mathcal{F}_{\rm B}$ be the B-model $\frac{\infty}{2}$ variation of Hodge structure associ…