12 problems

Kalck–Yang conjecture. The graded clock condition is invariant under derived equivalence.

Let $A$ be a graded gentle or skew-gentle algebra, and let $\mathbf S=(S,\Sigma,\eta)$ be the graded surface associated to $A$. For a formal dissection $\Delta$ of $\mathbf S$, let…

Let $A$ be a graded skew-gentle algebra, and let the three conditions in Theorem 1.3 be the conditions concerning $\tau$-tilting finiteness, silting-discreteness, and the correspon…

Let $A$ be a connected $\mathbb{R}$-algebra. An algebra is locally complexified-gentle of uniform type if it is Morita equivalent to an algebra satisfying condition (1) or (2) of T…

The support tau-tilting enumeration conjecture. The number of support-$\tau$-tilting objects for the gentle quiver-with-relations $G_t$ is equal to the number of elements of $P_t$.

Let $\mathbf S=(S,\Sigma,\eta)$ be a graded smooth surface with stops, and let $\mathcal W(\mathbf S)$ denote its partially wrapped Fukaya category. A formal generator is a generat…

Let $d4ac$ be an $A_n$-type quiver, and let $d524$ be a subcategory of $d53d\operatorname{rep}(d4ac)$. For strings, write $\mathsf{Supp}_0(\rho)$ for the relevant vertex support an…

Assume that the ground ring $k$ is a field. Let $\mathscr{J}_\mathcal{T}$ and $\mathscr{G}_\mathcal{T}$ be the algebras appearing in the construction, and let … be the inclusion of…

Let $R=k$ be a field. In the construction, a pure matching curve is a matching curve whose local value is $f^*(k)$, and the heart is the heart of the relevant derived category asso…

Let $cs$ be the homotopy category considered in the paper, and let $cSigma$-pure-injective objects be the objects classified by Theorem. Pure-injective classification conjecture. T…

Graded clock condition conjecture. A graded gentle one-cycle algebra satisfies the graded clock condition if and only if it is derived equivalent to $\Gamma(p,q,0)$ for some…

Let $\Lambda_0(p,r)$, for $p\in\mathbb{N}_+$ and $r\in[0,p-1]$, and $\Lambda_0'(p,0)$, for $p\in\mathbb{N}_+$, be the algebras in the classification of degenerate gentle two-cycle…