8 problems

Acyclic Ext-quiver conjectures. 1. If $A$ is twisted fractionally Calabi–Yau, then $A$ has an acyclic Ext-quiver. 2. If $A$ is $d$-representation-finite, then $A$ has an acyclic Ex…

Let $Q$ be a good 3d $\mathcal{N}=4$ quiver theory, let $\mathcal{M}_C(Q)$ denote its Coulomb branch, and let $\mathcal{L}$ be the set of decay and fission products of $Q$, ordered…

Temperedness conjecture. Quiver A-polynomials are tempered for every choice of the adjacency matrix.

Strong free product property conjecture. The map $\sigma'$ is a linear isomorphism, equivalently $(L_Q,r,\sigma,kQ_0[t,(t+q)^{-1}])$ satisfies the strong free product property.

Formality conjecture. If $Q$ is connected and not Dynkin, then

Let $Q$ be a connected non-Dynkin quiver and let $q\in (\mathbb{C}^\times)^{Q_0}$. Write $\Lambda^q(Q)$ for the multiplicative preprojective algebra of $Q$ with parameter $q$. 2-Ca…

Let $\mathcal{Q}$ be an acyclic quiver, let $P_{\mathcal{Q}}$ be the relevant set of seeds, and for each $\sigma\in P_{\mathcal{Q}}$ let $\Gamma_{\sigma}$ be the set of isotopy cla…

Cospectral cluster quiver mutation conjecture. The quivers $Q',Q”\in\operatorname{Mut}(Q)$ are cospectral if and only if there exists a cluster quiver $R\in\operatorname{Mut}(Q)$ s…