42 problems

Let $\pi:W\to D$ be an exact symplectic Lefschetz fibration over the disk, and let $L_1,\dots,L_m$ be its vanishing cycles. Let the associated $A_\infty$-category be the category w…

Cazassus–Herald–Kirk–Kotelskiy conjecture. The deformed Floer homology

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…

Critical-value bound and semisimplicity conjecture. The following holds:

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 $Y$ be a knot complement regarded as a cobordism from $\emptyset$ to $T^2$, let $\underline{Y}$ and $\underline{f}$ be obtained by deleting neighborhoods of extrema and adding…

Let $K$ be a knot, let $\mathcal I$ be the finite intersection set generating the tangle Lagrangian Floer complex, and let $x\in\mathcal I$ be the distinguished generator independe…

Let $L$ be a link decomposed into tangles along a Conway sphere, and let R_\u03c0(T) denote the perturbed traceless $\mathrm{SU(2)}$ character variety of a tangle $T$, viewed as…

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…

Bottman–Wehrheim conjecture. The bounding cochains corresponding to figure-eight bubblings define a twisted Lagrangian Floer homology and produce the isomorphism

Invariance conjecture. Invariance can be shown in the presence of a pseudo-isotopy satisfying those additional regularity assumptions.

Let $(X,\omega)$ be a compact symplectic manifold with a compact Lie group $G$ acting symplectically, let $\mathcal D\subset X$ be a $G$-invariant divisor as in the introduction, a…

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…

Let $\Lambda^{{\mathbb Q}}_+$ be the positive Novikov subring, let $\frak L=\{L_i\mid i=1,\dots,N\}$ be a finite set of relatively spin compact Lagrangian submanifolds of…

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 $Y$ be a Fano manifold, and consider monotone Lagrangians in $Y$. Their Lagrangian Floer theoretic potential is the generating function obtained by weighted counts of Maslov-in…

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 $L_0$.…

Diagonal Lagrangian mirror functor conjecture. This decorated Floer complex is isomorphic to the matrix factorization

Let $(X,[?]$

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

Let $(Y,L)$ be decomposed along a separating sphere as … and let $I^\natural(Y,L)$ denote the $\mathbb{Z}/4$-graded instanton Floer homology defined using a sufficiently small holo…

Conjecture 4. For some class of nice decompositions, including $n$-bridge decompositions of links in $S^3$, the assignment

Let $(Y_2,L_2)$ be an $n$-tangle in a decomposition of a link along a sphere, with $(Y_1,L_1)$ chosen to be an unknotted, trivial tangle, and let…