Title: The τ-cluster morphism category of a 0-Auslander extriangulated category.
Abstract: Let C be a reduced 0-Auslander extriangulated category. Motivated by Pan–Zhu silting reduction for such categories and the theory of signed τ-exceptional sequences developed by Buan and Marsh, we introduce the notion of (signed) presilting sequences in C and establish an explicit bijection between (signed) presilting sequences in C and (signed) τ-exceptional sequences over Λ = End_C(P), where P is a projective generator of C. Motivated by this correspondence, we introduce a new category M(C), called the τ-cluster morphism category of C, whose objects are certain extension-closed subcategories of C and whose morphisms are described in terms of signed presilting sequences. As an application, we recover the τ-cluster morphism category of Λ—a category whose objects are τ-perpendicular subcategories of mod(Λ) and whose morphisms are described in terms of signed τ-exceptional sequences—from M(C).
Given at: CLAN VI, University of Edinburgh, UK - June 2026
Title: τ-exceptional sequences for representations of quivers over local algebras. Abstract: In the early 1990s, Crawley-Boevey and Ringel studied exceptional sequences and their mutation in the module categories of hereditary finite-dimensional algebras. More recently, Buan and Marsh introduced τ-exceptional sequences — a natural generalization of exceptional sequences that behaves well over arbitrary finite-dimensional algebras. Together with Hanson, the authors also developed a notion of mutation for τ-exceptional sequences, extending the classical concept of mutation in the hereditary setting. In this talk, we study τ-exceptional sequences and their mutation over algebras of the form Λ = RQ, where R is a finite-dimensional local commutative algebra over an algebraically closed field, and Q is an acyclic quiver. I will explain how τ-exceptional sequences and their mutation over Λ can be fully understood in terms of exceptional sequences and their mutation over kQ.
Given at:
York Algebra Seminar, University of York, UK - June 2025
Algebra and Representation Theory Oberseminar, University of Bonn, Germany - June 2025
Cologne Algebra Seminar, University of Cologne, Germany - June 2025
Maurice Auslander Distinguished Lectures and International Conference, Woods Hole Oceanographic Institution, Quissett Campus Woods Hole, Massachusetts, USA - April 2025
Verona Algebra Seminar, Università degli Studi di Verona , Italy - April 2025
Leeds Algebra Seminar, University of Leeds, UK - March 2025
Title: τ-exceptional sequences for representations of quivers over local algebras.
Presented at:
IDEAL (Inclusion, Diversity and Equity in Algebra), University of Leeds, UK - October 2025
Advances in Representation Theory of Algebra (ARTA) X - Cologne, Germany - September 2025.