10 problems

Let $A$ be a finite-dimensional algebra over a field $K$. Write $K_0(\operatorname{\mathsf{proj}} A)$ for the Grothendieck group of finitely generated projective $A$-modules, and l…

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…

Silting mutation conjecture. Then $T$ is tilting and $\operatorname{End}_A(T)$ is a $d$-representation infinite algebra.

Let $d$ be a positive integer, and let $\Pi$ be an $H^0$-finite connective $(d+1)$-CalabiYau dg algebra over a field $k$. Let $\mathcal{C}(\Pi)$ be its $d$-CalabiYau cluster catego…

Equivariant stability-space homeomorphism conjecture. There should exist a homeomorphism

Let $\Lambda$ be an artin algebra, and let $\mathbf{D}_{\rm sg}(\Lambda)$ denote its singularity category. In a triangulated category $\mathcal{T}$, an object $M$ is presilting if…

Let $\mathcal{T}$ be a triangulated category, and let a presilting subcategory be a full additive subcategory $\mathcal{M}$ such that ${\rm Hom}_{\mathcal{T}}(M, \Sigma^n(M))=0$ fo…

Let $k$ be a field, let $A$ be a finite-dimensional $k$-algebra, and let $n$ be the number of pairwise non-isomorphic simple $A$-modules. Let $\mathsf{D}^{\rm b}(\mathsf{mod} A)$ b…

Let $k$ be a field, let $A$ be a finite-dimensional $k$-algebra, and let $\mathsf{D}^{\rm b}(\mathsf{mod} A)$ be its bounded derived category. An object is presilting if it has no…

Compact Wakamatsu-silting conjecture. Every compact Wakamatsu-silting complex over an artin algebra is silting. This asks whether compactness forces the broader notion of Wakamatsu…