8 problems

Let $X$ admit a Lagrangian torus fibration … and let the semi-flat SYZ mirror carry Maurer–Cartan solutions whose Fourier modes are taken along its Lagrangian torus fibers. Near a…

Let $C\subset M$ be a special Lagrangian cycle in a Calabi–Yau threefold $M$, and let $W$ be its mirror Calabi–Yau threefold. The ordinary Chern–Simons theory is defined on $C$, wh…

Positive holomorphic disk-count conjecture. All disks specified by Proposition $$ have positive holomorphic disk count in the monotone case.

Let $X$ be the mirror of a Calabi–Yau manifold, let $X_{\mathrm{sf}}$ denote its semi-flat part, and let the Kodaira–Spencer differential graded Lie algebra govern deformations of…

Regular disk gluing conjecture. There are regular holomorphic disks with boundaries on $L_V$ whose moment-map projections are:

Let $X$ be a symplectic manifold with a Lagrangian torus fibration $p:X\to B$, and let $B^{sing}\subset B$ denote the singular points of the fibration. Fukaya's conjecture. Holomor…

Let $X$ be the symplectic manifold under consideration, let $L$ be the singular deformed Lagrangian used to define the matrix-valued function $\Psi_{L,\nabla}$, and let $L$ be smoo…

Joyce's holomorphic-disk boundary conjecture. The region $\mathcal H$ provides the region whose complement retracts to $\Delta$ and across whose boundary the fibration fails to be…