16 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 $(S,M,D)$ 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 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 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 $S$ 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 $\mathcal{C}$ 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 $(\Sigma,\mathbb{M})$ be a positive-genus surface with empty boundary and exactly two punctures, and let $\tau$ be a tagged triangulation of $(\Sigma,\mathbb{M})$. Write…

Component-cluster conjecture. For any basic algebra $\Lambda$:

Let $G$ be a consistent brane tiling, let $(Q,W)$ be the corresponding quiver with potential, and let $A=\mathbb{C}Q/(\partial W)$ be its quiver-potential algebra. Fix a vertex…