26 problems

Let $L$ be a Lagrangian with boundary $S_\Gamma$, let $A$ be a choice of phase and framing, and let $W_\Gamma^{(A)}$ be a primitive function whose graph of the differential gives t…

Let $(M,\omega,\Phi)$ be a Calabi–Yau $n$-fold, and let $\eta$ be an $n$-dimensional homology class in $M$. For an oriented exact Lagrangian $L$ in $M$, write … where…

Let $0<a_1\le a_2\le\cdots\le a_n<\infty$, and let $E^{2n}(a_1,\dots,a_n)$ be the corresponding ellipsoid with standard symplectic form $\omega_{\mathrm{std}}$. A Lagrangian torus…

Let $\omega_{\mathrm{FS}}$ denote the Fubini–Study form on $\mathbb{CP}^n$. For a closed Lagrangian torus $L\subset(X,\omega)$, call $L$ extremal when…

Let $0<a_1\le a_2\le\cdots\le a_n<\infty$, and let $E^{2n}(a_1,\dots,a_n)\subset\mathbb{C}^n$ be the ellipsoid defined by … For a closed Lagrangian torus $L\subset(X,\omega)$, set…

Let $(X,\omega,\Omega)$ be a compact Calabi–Yau manifold, and let $L_1,\dots,L_r$ be special Lagrangian submanifolds in $X$ with the same phase that intersect transversely. Let…

Let $K$ be an orientable polyhedral Lagrangian in $(\mathbb{R}^4,\omega)$, let $v$ be a valence-$4$ vertex, and let $\Gamma_{v,\delta}\subset (S^3,\xi_{\mathrm{std}})$ be the Legen…

Let $0<a_1\leq a_2\leq\dots\leq a_n<\infty$, and let $E^{2n}(a_1,a_2,\dots,a_n)$ be the corresponding ellipsoid with standard symplectic form. Ellipsoid extremal-torus conjecture.…

Let $X^{2n}_{\Omega}\subset \mathbb{C}^n$ be a convex toric domain, with standard symplectic form $\omega_{\mathrm{std}}$. Let $\operatorname{diagonal}(X^{2n}_{\Omega})$ denote the…

Let an extremal Lagrangian torus in $(\bar{B}^{2n}(1),\omega_{\mathrm{std}})$ mean a Lagrangian torus whose symplectic energy attains the relevant Lagrangian capacity. Cieliebak–Mo…

Let $X$ be a symplectic manifold, let $\bm L$ be a Lagrangian brane, and let $c_{\bm L}>0$ be as in the classification theorem. A sheaf quantization of $\bm L$ in $(X,u<c_{\bm L})$…

Let $X$ be a Calabi-Yau manifold with Kähler metric. Let $L$ be an almost calibrated exact Lagrangian brane in $D^bFuk(X)$ with a Harder-Narasimhan decomposition … whose distinguis…

In Tonkonog's setup, let $\mathcal{BS}\in SH^0(X;\Bbbk)$ be the class obtained by counting holomorphic caps, and write $\beta=\beta_1+\beta_2+\cdots$ for the filtration components…

Let $a\in QH^0(M;\Lambda)$ be the idempotent generating the ideal $QH^*(M;\Lambda)_{\mathrm{crit}}$, and let $\mathbb{L}$ be the skeleton. A subset is $a$-$SH$-full when its $a$-re…

Let $L$ be an unobstructed Lagrangian with a bounding cochain of valuation $c$, and let $L'$ be exactly homotopic to $L$ through an exact homotopy whose Hofer norm is less than $c$…

Let $\Sigma$ be an embedded annulus-type minimal Lagrangian surface in $\mathbb{B}^4$ with Legendrian capillary boundary on $\mathbb{S}^3$. Such a boundary has constant contact ang…

Let $(X,\omega,\Omega)$ be a Calabi--Yau manifold and let $L$ be a compact zero Maslov Lagrangian in it. A Lagrangian is stable when it satisfies the stability condition under disc…

Let an annulus-type surface be an embedded surface whose underlying domain is an annulus. Assume it is minimal and Lagrangian in the unit ball, with Legendrian capillary boundary o…

Let $D$ be a disk immersed in $4\mathbb{R}^4$. Assume that the immersion is Lagrangian, has conformal Maslov form, and has Legendrian capillary boundary on $4\mathbb{S}^3$. Classif…

Clifford torus energy minimization conjecture. The minimum of the energy functional is attained on the Clifford torus.

Lagrangian–Poisson correspondence conjecture. The map $f\mapsto\pi_f$ provides an equivalence between the space of $n$-shifted Lagrangian morphisms $f:X\to Y$ such that…

Filtered shifted-structure conjecture. There exists a relative $n$-shifted symplectic structure $\widetilde{\omega}$ on $\widetilde{Y}_f$ over $[\mathbb{A}^1/\mathbb{G}_m]$ such th…

For coprime positive integers $m,n$, let $W_{m,n}$ be the geometric model obtained by attaching a disk to the one-component link of the singularity $x^m=y^n$, let $Z_{m,n}$ be its…

Let $N$ be a simply connected closed Calabi–Yau manifold of any complex dimension, and let ${\mathcal S}$ denote the subgroup generated by special Lagrangian cycles. Lagrangian hom…

Let $K$ be a non-split link, let $K_n$ be its $n$th component, and let $K-K_n$ be the remaining link. Let $V_K(n)$ and $V_{K_n}(1)$ be the corresponding augmentation varieties, and…