67 problems

Let $(X,\lambda)$ be a Weinstein Liouville domain with skeleton $\skel(X,\lambda)$. Denote by $\mW(X,\lambda)$ its wrapped Fukaya category. Kontsevich's cosheaf description conject…

Let $W$ be a Weinstein manifold and let $L$ be its Lagrangian skeleton. Denote by $\mathcal{W}(W)$ the wrapped Fukaya category of $W$ and by $\operatorname{MSh}(L)$ the microlocal…

Generation conjecture. The category $\mathcal{W}_\kappa(T^*Q)$ is split-generated by any $\kappa$-tuple of disjoint cotangent fibers.

Let $M$ be a Liouville manifold, let $\Lambda\subset M$ be a subset, and let $\mathcal B$ be a choice of brane data. Write $\lag^{\mathcal B}_\Lambda(M)$ for the associated Lagrang…

Let $X_{\mathrm{res}}$ be the resolution of the $A_n$ surface singularity, let $D_r$ be the indicated divisor, and let $\sigma$ be a stop. Let $s$ be a formal parameter, with coeff…

Let $X_{\mathrm{res}}$ be the resolution of the $A_n$ surface singularity, let $D_r$ be the indicated divisor, and let $s$ be a formal parameter with coefficient field…

Let $X_{\mathrm{Mil}}\smallsetminus D_m$ be the complement of a divisor in the $A_n$ Milnor fibre, and let the corresponding wrapped Fukaya and coherent-sheaf categories be the cat…

Let $\mathcal{S}$ be an abstract wrapped Floer setup, let $\mathcal{F}^{\text{pre}}_{\mathcal{S}}$ be its pre-wrapped Fukaya $A_\infty$-category, let $\widetilde{C}$ be the set of…

Let $R_k$ be the dga defined from $k$ parallel copies of the arc in the local model $S=D^2$, with no singular points and with two boundary stops. Its cohomology algebra is…

Partially wrapped Fukaya categories are related to spectral networks as described above, and Stokes local systems provide the corresponding generalization of local systems for this…

Core--cocore Koszul duality conjecture.

Let $T$ be a 2-tangle, let $R_\pi(T)$ be its holonomy-perturbed traceless character variety, and let $P^*$ be the pillowcase with its singular points removed. A bounding cochain is…

Assume the setting of the Lie monoid action conjecture in Floer theory, with the actions Hamiltonian. Let $\mathcal{W}(T^*G)$ and $\mathcal{W}(T^*H)$ denote the wrapped Fukaya cate…

Let $D_\alpha=f_\alpha^{-1}(0)$ be the toric boundary divisor under consideration. Let $\operatorname{L}$ be the Lazarev map, and let $\operatorname{L}_{\mathbb C}$ denote its comp…

Let $\alpha\notin V(A)$ and let $D_\alpha=f_\alpha^{-1}(0)$ be the corresponding Liouville manifold, with wrapped Fukaya category ${\cal W}{\cal F}(D_\alpha)$ and derived category…

The partially wrapped Fukaya category is a category associated to a stopped Weinstein manifold and is expected to carry additional higher-algebraic structure. Folklore pre-Calabi–Y…

The conjectural monodromy-twisted wrapped Fukaya category. There exists a $\mathbb{Z}$-graded $A_\infty$-category $\mathcal{C}_\rho(M)$ whose objects are the same as those of the w…

Let $M$ be a smooth compact manifold, let $R$ be a commutative ring, and equip $\mathcal W(T^*M;R)$ with its canonical grading and orientation data. Let $H^*(M;R)$ be the cohomolog…

Let $M$ be a smooth manifold, and let $\operatorname{Cuplength}(M)$ denote the cuplength of $H^*(M;k)$ for any field $k$. Let $\mathcal C(M)$ denote the wrapped Fukaya category ass…

Let $X\to Y$ be a rank-one algebraic torus fibration with discriminant divisor $D\subset Y$, and let $s$ denote the invertible variable associated with the $S^1$ action on $X$. Let…

Borman–Sheridan class compatibility conjecture. Under this equivalence, the action of $t$ on $\mathcal{W}_{S^1}(X)_{-1}$ coincides with the action of $\tau$ on…

Suppose $X$ is a Liouville manifold with a Hamiltonian $S^1$ action, and suppose $X$ has a mirror Landau–Ginzburg model $(\breve{X},\breve{W})$ such that the action is mirror to a…

Consider a rank-$r$ algebraic torus fibration $X\to Y$ with simple normal-crossing discriminant divisor $D=\bigcup_{i=1}^rD_i$, and let $\lambda\in(\mathbb{C}^*)^r$ be a spectral p…

Let $X$ be a Liouville manifold equipped with a Hamiltonian $S^1$ action such that the fixed locus $X^{S^1}$ has codimension four and there are no finite non-trivial stabiliser gro…

Let $X\to Y$ be an algebraic torus fibration, with discriminant divisor $D\subset Y$, and let $\mathcal{W}_{T}(X)_{-\mathbf{1}}$ denote the spectral component of its equivariant wr…