46 problems

Calabi–Yau Drinfeld-double conjecture. The assignment

Let $A$ be a homologically smooth, compact, finite-dimensional $A_{\infty}$-algebra. A non-degenerate cohomology class $[\varphi]$ of degree $\dim A$ is a class defining the corres…

For a Calabi–Yau $A_\infty$ category, let the Gromov–Witten potential define a left ideal in the sheaf of Weyl algebras associated to its periodic cyclic chain complex, and let thi…

Let a Calabi–Yau category be a category equipped with a trace map … inducing a functorial duality … for all objects $A,B$. Consider two stability conditions on this category with t…

Backreacted Calabi–Yau category conjecture. Given a holography package $\mathcal{P}_{\mathcal{C},\lambda,h,s}$ as above, there is a family of Calabi–Yau categories…

Categorical 't Hooft expansion conjecture. The outcome of the categorical 't Hooft expansion for the chiral algebra associated to $A$ will be a category of D-branes associated to…

Let $d$ be a positive integer, and let $\Pi$ be an $H^0$-finite connective $(d+1)$-CalabiYau dg algebra over a field $k$. Let $\mathcal{C}(\Pi)$ be its $d$-CalabiYau cluster catego…

Let $\Lambda$ be a Legendrian link with marked points, let a Morse function be chosen, and let $\mathcal{A}ug_+$ and $\mathcal{C}$ be the associated strictly unital proper…

Conjecture C. For a fixed $d\in\mathbf{D}$, any Calabi–Yau object in $\mathcal{D}^b(\mathcal{O}_0)$ of dimension $2\mathbf{a}(w_0d)$ admits a filtration with subquotients of the fo…

Indecomposability criterion. The category $\mathcal{B}$ is indecomposable if and only if

Kuznetsov's conjecture. There exists such a variety $\mathsf{X}'$ for which

Let $\mathcal C$ be the 2-Calabi--Yau category associated to a finite connected quiver. Assume the hom spaces in $\mathcal C$ are finite-dimensional, define…

Let $k$ be an algebraically closed field of characteristic zero. Let ${\mathcal C}$ be a $2$-Calabi--Yau algebraic triangulated category with a cluster-tilting object $T$. Amiot's…

Realizability conjecture. Each such category $\mathcal{C}$ can be realized as a generalized cluster category for a quiver with potential.

Let $(M,\sigma)$ be a Weinstein pair such that $M$ and $\sigma$ are individually Calabi–Yau. The relative smooth Calabi–Yau conjecture says that the Orlov functor $\imath_\sigma$ h…

Let $\Gamma^{\mathbb{X}}_{\mathbf{T}}$ be the Calabi-Yau-$\mathbb{X}$ Ginzburg algebra, let $\Gamma^{N}_{\mathbf{T}}$ be its Calabi-Yau-$N$ reduction, and let…

Assume that $k$ is of characteristic $0$. Let ${\mathcal C}$ be a 2-Calabi–Yau algebraic triangulated category with a cluster-tilting object $T$. For a quiver with potential…

Let $k$ be a field of characteristic zero. Let ${\mathcal C}$ be a 2-Calabi–Yau triangulated category with cluster-tilting objects, and let…

The vertex-algebra existence conjecture. One can associate to $\mathcal{C}$ a class of vertex algebras parametrized by rays and by a choice of framing object; for almost all rays,…

A Calabi–Yau category here means a category equipped with the Calabi–Yau structure required for the Cohomological Hall algebra construction; the approach in question constructs act…

Let $(Q,W)$ be a quiver with potential, and consider the conclusions of the bimodule $3$-Calabi–Yau result [?]. In particular, these include the corresponding conclusions for the q…

Wrapped Fukaya category conjecture. The ${\rm CY}_3$ $A_\infty$-categories associated to the quivers with potentials for the moduli space of framed $n$-dimensional local systems on…

Let ${\cal W}$ be an ideal ${\rm A}_{m-1}$-web on a decorated surface, and let ${\cal C}_{\cal W}$ be the associated 3d Calabi–Yau ${A}_\infty$-category defined by the quiver with…

Let ${\cal W}$ be an ideal bipartite web on a decorated surface, and let $({\cal C}_{\cal W},{\cal S}_{\cal W})$ be the associated 3d Calabi–Yau category with cluster collection. L…

Let $\mathsf{A}$ be an abelian category in a 3CY category, let $K_{0}(\mathsf{A})$ be its Grothendieck group, and let $\Omega^{\mathrm{DT}}(\gamma,Z)\in\mathbb{Q}$ denote the Donal…