32 problems

DWZ-mutation homeomorphism conjecture. The DWZ-mutation of modules is a homeomorphism between the Ziegler spectra of the Jacobian algebras

Asai–Iyama's conjecture. If $(Q,W)$ is a non-degenerate Jacobi-finite quiver with potential, then

Let $(Q,\mathcal{S})$ be a Jacobi-finite connected quiver with potential. A decorated representation is rigid when it has no nontrivial self-extension, a negative representation is…

Let $(Q,\mathcal{S})$ be a Jacobi-finite nondegenerate quiver with potential, let $\delta$ be a $\delta$-vector, and let $\check{\eta}$ be a coweight. Write $f_{\check{\eta}}$ for…

Let $(S,M,D)$ be a $d$-angulation of a marked surface, let $(Q,W)$ be its associated quiver with superpotential, and let $\Gamma$ be the associated $d$-dimensional Ginzburg algebra…

Let $C(W_n^I)$ be the potential associated with the cyclic quiver construction, for parameters $m,n\in\mathbb{Z}_n$. Non-degeneracy conjecture. For any $m,n\in\mathbb{Z}_n$, the po…

Let $G$ be a finite abelian subgroup of $\operatorname{SL}_3(\mathbb{C})$, and let $Q$ be the curve quiver for a crepant resolution of $\mathbb{C}^3/G$. A minimal potential on $Q$…

Let $(Q,\mathcal{S})$ be a nondegenerate Jacobi-finite quiver with potential. A pair $(\delta,\check\epsilon)$ has the saturation property when…

Let $(Q,\mathcal{S})$ be a nondegenerate Jacobi-finite QP. For a pair $(\delta,\epsilon)$ of $\delta$-vectors, call it $\operatorname{hom}$-vanishing when…

Let $(Q,\mathcal{S})$ be a Jacobi-finite quiver with potential, and let a decorated representation mean a representation together with its decorated part. A decorated representatio…

Let $(Q,\mathcal{S})$ be a nondegenerate Jacobi-finite QP. For a pair $(\delta,\epsilon)$ of $\delta$-vectors of $(Q,\mathcal{S})$, say that the pair has completely extremal rank w…

Let $(Q,W)$ be a quiver with potential and assume that $Q$ is symmetric. Let $\chi_R|_{\Gamma_l}$ be the associated symmetric quadratic form, let $\mathbb{T}$ denote the torus appe…

Let $(\mathbf{s,w})$ be a seed with non-degenerate potential. Let ${\mathfrak D}_{\mathbf{s,w}}$ and ${\mathfrak D}_{\mathbf{s}}$ be the stability and cluster scattering diagrams,…

Let $(\mathbf{s,w})$ be a seed with non-degenerate potential. The Donaldson–Thomas scattering diagram ${\mathfrak D}^\mathrm{DT}_{\mathbf{s,w}}$ and the initial-data scattering dia…

Let $(Q,W)$ be a non-degenerate quiver with potential, and let $(Q',W')$ be mutation equivalent to $(Q,W)$. Quiver-determines-potential conjecture. If $Q'\cong Q$, then $(Q',W')$ i…

Let $Y_\Phi$ be the open Calabi–Yau threefold associated to a generic point of the Hitchin base, let $Q_{\mathcal{T},m}$ be the associated quiver, and let $W$ be a potential on it.…

Let $S$ be a complex curve with marked-point divisor $D$, let $m\geq 1$, let $\Phi$ be an admissible generic point of the Hitchin base, and let $Y_\Phi$ be the associated open Cala…

Let $S$ be a complex curve with marked-point divisor $D$, let $m\geq 1$, and let $Y_\Phi$ be the open Calabi–Yau threefold associated to a generic point $\Phi$ of the Hitchin base.…

Ginzburg's conjecture. All 3-dimensional Calabi–Yau algebras should arise as Jacobi algebras. This conjecture concerns a proposed description of all such algebras by quivers with p…

Let $\mathcal{C}$ be a rigid monoidal abelian category with a system of renormalized $r$-matrices, and let $(\{\mathcal{F}_i\}_{i \in I}, \widetilde{B})$ be a monoidal seed, where…

Let $\mathbb{T}$ be a triangulation of a not necessarily orientable surface, and suppose that there is a rigid potential $W_l$ on the quiver-with-potential $\Diamond_l(\mathbb{T})$…

Let $(\underline{\Delta},W)$ be obtained from $(\Delta,W)$ by extending at a vertex $e$, and suppose the direction from the cluster-model property of $(\Delta,W)$ to that of…

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…

Mutation compatibility conjecture. For $2$-Calabi–Yau-tilted algebras which are Jacobian algebras, the mutations of $2$-Calabi–Yau-tilted algebras coincide with those of Jacobian a…

Kontsevich–Efimov conjecture. The stated purity and Lefschetz result holds for generic $W$. The source proves the result when $Q$ admits an edge grading making $W$ a graded potenti…