We give an overview of recent developments in silting theory. After an introduction on torsion
pairs in triangulated categories, we discuss and compare different notions of silting and …

Reading's" shard intersection order" on the symmetric group can be realized as the" lattice of
wide subcategories" of the corresponding preprojective algebra. In this paper, we first use …

Let $\Lambda $ be a finite-dimensional algebra. A wide subcategory of $\mathsf
{mod}\Lambda $ is called left finite if the smallest torsion class containing it is functorially …

We introduce the notions of τ-exceptional and signed τ-exceptional sequences for any finite
dimensional algebra. We prove that for a fixed algebra of rank n, and for any positive integer …

Abstract Recently, Buan and Marsh showed that if two complete τ-exceptional sequences
agree in all but at most one term, then they must agree everywhere, provided the algebra is τ …

arXiv:2302.12217v2 [math.RT] 19 Apr 2023 Page 1 arXiv:2302.12217v2 [math.RT] 19 Apr
2023 A GEOMETRIC PERSPECTIVE ON THE τ-CLUSTER MORPHISM CATEGORY SIBYLLE …

In this paper we study the behaviour of modules over finite dimensional algebras whose
endomorphism algebra is a division ring. We show that there are finitely many such modules …

Let $\mathcal {C} $ be an extriangulated category and let $\mathcal {R}\subseteq\mathcal
{C} $ be a rigid subcategory. Generalizing Iyama--Yang silting reduction, we devise a …

We establish some properties of $\tau $-exceptional sequences for finite-dimensional
algebras. In an earlier paper, we established a bijection between the set of ordered support …

We generalise $\tau $-cluster morphism categories to non-positive proper dg algebras. The
compatibility of silting reduction with support $\tau $-tilting reduction will be an essential …