12 problems

Let $(Q,W)$ be a self-dual quiver with potential, and let $\tau$ and $\widetilde{\tau}$ be self-dual weak stability conditions on the associated self-dual abelian category. Let…

Let $\underline{w}_0$ be a reduced expression of the longest element and let $[a,b]$ be a finite integer interval. Let $\mathbf{\Gamma}^{[a,b]}(\underline{w}_0)$ and…

Let $\underline{w}_0$ be a reduced expression of the longest element and let $[a,b]$ be a finite integer interval. Let $\widehat{\mathbf{\Gamma}}^{[a,b]}(\underline{w}_0)$ be the c…

Let $\delta$ and $\check{\epsilon}$ be weights for a quiver with potential, and write $\check{f}_{\delta}$ and $f_{\check{\epsilon}}$ for the dual and ordinary tropical $F$-polynom…

Let $X$ be a compact, acyclic, orientable circle bundle of dimension $n$, and let $k[pi_1(X)]$ denote its fundamental group algebra over a field $k$. A superpotential algebra is an…

Let $Q$ be a quiver, and let $(\widetilde{Q},\widetilde{W})$ be the associated tripled quiver with potential. Let $\mathfrak{g}_Q$ be the Lie algebra associated to $Q$ in the Okoun…

Let $(Q,W)$ be a quiver with a generic potential, and suppose that its Jacobian algebra $J_{(Q,W)}$ is finite dimensional. Genteelness conjecture. The Jacobian algebra $J_{(Q,W)}$…

Let $(Q,W)$ be a quiver with superpotential of degree $N$, and let $\Gamma$ be its associated Ginzburg differential graded algebra. Write $\operatorname{CT}(Q,W)$ for the cluster b…

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…

Let $\mathcal{A}$ be a category satisfying conditions (7) and (8), let $W$ be its potential, and let $\phi^{mot}$ denote the motivic vanishing-cycle realization. For each dimension…

Let $(Q,W)$ be a symmetric quiver with potential, and suppose that $(Q,W)$ admits two cuts $I$ and $I'$ such that $I\cap I'=\emptyset$. Let $\Om_\al$ denote the Donaldson–Thomas in…

Let $Q$ be a finite quiver, let $W$ be a polynomial potential on $Q$, and let $\operatorname{\mathsf{nil}}(\mathcal P(Q,W))$ be the category of finite-dimensional right modules ove…