4 problems

The gentle arbor F-triangle conjecture. In $SC_t$, there exists a facet $C$ such that the $F$-triangle for $(SC_t,C)$ coincides with the $F$-triangle associated with the transmuted…

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 $\Lambda$ be a finite-dimensional algebra. Let $\mathcal W\subseteq\mathsf{mod}\Lambda$ be a $\tau$-perpendicular subcategory of $\mathsf{mod}\Lambda$, and let…

Let $B$ be a 2-Calabi–Yau tilted algebra whose quiver satisfies the dimer-tree condition, and let $\tau_B$ denote the Auslander–Reiten translation in $\operatorname{mod}B$. Tau-rig…