14 problems

Let $X$ be a Calabi–Yau manifold and $L\subset X$ a Lagrangian. For relative cohomology classes in $H_2(X,L)$, write the topological disk partition function as … where…

Open Gromov–Witten comparison conjecture. There is a homomorphism

The van Geemen lines are a distinguished family of lines on the mirror quintic, and the predictions of Jockers–Morrison–Walcher involve a constant associated with them. A hyperboli…

Let $(Y,D)$ be the del Pezzo surface with anticanonical divisor considered in the paper, and let $\tilde{\Omega}(\gamma;l)$ denote the limiting open Gromov–Witten invariant associa…

Let $\tilde{d4aa}(d4b3;u)$ be the open Gromov–Witten invariants defined by … Here $c=\pm 1$ is a quadratic refinement, and set $\Omega(\frac{d}{k}\gamma;u)=0$ when $\gamma$ is not…

Let $X$ satisfy the generic condition assumed in the construction. For a primitive relative class $\gamma$, let $l_{\gamma}$ be an affine line labeled by $\gamma$, let…

Let $S$ be the boundary surface of the Lagrangian 3-manifold $L=L(\mathcal{T})$ associated to a tangle obtained by smoothing the $1$-skeleton of a foam, and let $\mathcal{M}$ be th…

Let $\gamma$ be a primitive charge. Suppose that $u$ crosses a wall consisting of relative classes $\gamma_i$, for $i=1,\ldots,n$. For each $i$, let…

Seidel-element and Jacobian-generator conjecture. The isomorphism

Let $X$ be a semi-Fano toric manifold, and let $m$ denote the number of its toric divisors. For $i=1,\ldots,m$, let $\delta_i(q)$ be the generating-function correction determined b…

Let $X$ be a toric manifold with $-K_X$ numerically effective. Let $W^{\textrm{PF}}$ and $W^{\textrm{LF}}$ be the Picard–Fuchs and Lagrangian Floer superpotentials in the mirror, r…

Let $X$ be a toric Calabi–Yau manifold with mirror family $\check{X}_y$, and let … be the SYZ map, defined by … where $1+\delta_i(q)$ are generating functions of the genus $0$ open…

Let $X$ be an almost Calabi–Yau 3-fold and let $L\cong \mathbb{R}P^3\subset X$ be an embedded Lagrangian. For odd classes $\beta\in\Pi_2(X,L)$, the open Gromov–Witten invariants…

Let $M$ be the ambient symplectic manifold, $L$ a Lagrangian submanifold, $J$ an almost complex structure, and let $\beta$ range over the relevant relative homology classes. Let…