9 problems

SYZ and integrable-system conjecture. Near the large-complex-structure/large-volume limit: the SYZ picture holds on $\mathcal M_{\mathbb R}$; for a B-field $B'$ on $X'$, $X_{B'}$ a…

Metric SYZ conjecture. There should exist special Lagrangian torus fibrations on generic regions of the Calabi--Yau manifolds near the limit $t\to 0$.

SYZ conjecture. A Calabi--Yau manifold should admit a special Lagrangian torus fibration, and its mirror Calabi--Yau manifold should be obtained by taking the dual fibration.

Let $\pi:X\to B$ be a symplectic manifold equipped with a Lagrangian torus fibration, with smooth locus $X_0\to B_0$, and let $X^{\vee}$ be a compactified SYZ mirror of $X$. For a…

Let $\pi:X\to B$ be a Lagrangian torus fibration with smooth locus $X_0\to B_0$, and let $X_0^{\vee}=TB_0/\Gamma^{\vee}$ be its semi-flat mirror. SYZ quantum-correction conjecture.…

In the Calabi-Yau case, let $Y$ and $Z_t$ be mirror manifolds of complex dimension $n$. Let $B$ be a real $n$-dimensional manifold homeomorphic to a sphere, and let … be fibrations…

Let $\mathcal{R}$ be a simple eigenray diagram and let $\mathcal{Y}_{\mathcal{R}}\to B_{\mathcal{R}}$ be the Stein continuous map asserted in the Stein mirror fibration conjecture.…

Let $\check{Y}(\Phi)$ be the Weinstein manifold associated with the fanifold $\Phi$ extracted from the integral affine base $(B,\mathscr{P})$, and let $B$ be the base of the corres…

Strong Strominger–Yau–Zaslow conjecture. For $|t|\ll 1$, the 3-fold $X_t$ admits a special Lagrangian $T^3$-fibration over a base $B$ homeomorphic to a 3-sphere. The base $B$ is eq…