8 problems

Let $M \to B$ and $\check{M} \to B$ be dual torus fibrations arising in the SYZ picture, and let a Lagrangian section of $M \to B$ be a Lagrangian submanifold mapping isomorphicall…

Let $({\cal X}_{mer},vol)=(X_q,vol_q)$ be a one-parameter family of maximally degenerate Calabi–Yau manifolds, let $X_q^{new}$ be the rescaled family, and let…

Let $X\to Y$ be a rank-one algebraic torus fibration with discriminant divisor $D\subset Y$, and let $s$ denote the invertible variable associated with the $S^1$ action on $X$. Let…

Let $X\to Y$ be an algebraic torus fibration, with discriminant divisor $D\subset Y$, and let $\mathcal{W}_{T}(X)_{-\mathbf{1}}$ denote the spectral component of its equivariant wr…

Let $F\hookrightarrow E\to B$ be a quasi-nilpotent fibration, with fibre $F$ equal to a torus $T^r$, and suppose that the rational cohomology of $B$ is finite dimensional. Generali…

Let $X$ be a variety with a smooth anticanonical divisor $D$, set $U=X\setminus D$, and let $\pi:U\to B$ be a special Lagrangian torus fibration, meaning that its smooth fibers are…

Equivariant torus-fibration mirror-symmetry conjecture. There should be equivalences

Let $B$ be a closed $\mathbb{Z}$-affine manifold, let $M=T^*B/T^*_{\mathbb{Z}}B$ be the associated symplectic torus fibration, and let $\mathcal{O}_B$ be its natural sheaf of…