16 problems

Let $\kappa$ be a link, let $n>0$, and let ${{\mathscr{H}}_{{(n)} {\scriptscriptstyle{\mathrm{symp}}}}^k}(\kappa)$ denote the link invariant constructed from Lagrangian Floer theor…

Calabi–Yau critical-value conjecture. If $c^1(X)=0$, then

Finiteness conjecture for Weinstein deformations. Suppose $QH_{\frak b}(X;\Lambda)$ is semi-simple. Then there exist only finitely many $u$ for which there exists…

Let $\mathbb{L}$ be a compact, relatively spin, graded, oriented immersed Lagrangian of dimension $n$ in a symplectic manifold $M$, and let $\mathcal{A}_{\mathbb{L}}$ be its Maurer…

Let $Q$ be a tropical abelian variety, and let $V\subset Q$ be a rigid tropical curve admitting a pair-of-pants decomposition. Higher-dimensional unobstructedness conjecture. Then…

Let $(\Theta,\Phi)$ be a tangential pair, meaning based spaces equipped with maps fitting into a commutative diagram over $BO \to BU$. Let $X$ admit a $\Phi$-structure, set…

Let $(X,\omega)$ be a compact symplectic manifold, let $\mathcal D=\bigcup_{i=1}^m\mathcal D_i$ be a normal crossing divisor, and let $L\subset X\setminus\mathcal D$ be a compact r…

Suppose $(X,\omega)$ and $\mathcal D$ are as in the beginning of the introduction, and let $L\subset X\setminus\mathcal D$ be a relatively spin compact Lagrangian submanifold. Let…

Let $X$ be a compact almost Calabi-Yau manifold. Let $L_0$ be a reference Lagrangian, and consider graded immersed unobstructed Lagrangians in the same $D^bFuk(X)$ class as $L_0$.…

Let $(X,[?]$

Let $\Sigma^{\#}$ be the punctured Heegaard surface and let $X_{\operatorname{tw}}(\Sigma^{\#})$ be its twisted character variety. Let…

Open quantum Kirwan map conjecture. Counting affine vortices over the upper half-plane $\mathbb H$ defines an $A_\infty$ morphism

Let $(X,K)$ be a knot in a homology $3$-sphere, and choose a $2$-tangle decomposition $(X,K)=(Y,T)\cup(D,U)$ as in the paper. Let $P$ denote the pillowcase, let $R_\pi(Y,T)$ be the…

Let $(Y,T)$ be a 2-tangle in the 3-ball or in a homology 3-ball. Write $R_\pi(Y,T)$ for the perturbed traceless character variety and let … be its restriction map. A pillowcase per…

Let $\mathcal{X}$ be a Gorenstein toric orbifold, and let $W^{LF}_{\mathcal{X}}$ be its Lagrangian Floer superpotential. Denote by $QH^*_{\mathrm{orb}}(\mathcal{X})$ its orbifold q…

Let $X$ be a toric variety with at worst Gorenstein quotient singularities. Let $\mathcal{X}$ be the canonical toric orbifold with coarse moduli space $X$, and let $Y$ be a toric c…