Representation Theory Group Seminar - Cologne

Summer Semester 2025

04.02 Maximilian Kaipel (Köln)

Title: Mutating ordered τ-rigid modules

Abstract: A mutation operation for τ-exceptional sequences of modules over any finite-dimensional algebra was recently introduced, generalising the mutation for exceptional sequences of modules over hereditary algebras. In this talk I will interpret this mutation in terms of TF-ordered τ-rigid modules, which are in bijection with τ-exceptional sequences. As an application I will show that the mutation is transitive for Nakayama algebras. This is joint work with Aslak Buan and Håvard Terland.

11.03 Odysseas Giatagantzidis (Thessaloniki)

Title: Arrow reductions, quasi-uniform Loewy length algebras and the Finitistic Dimension Conjecture

Abstract: This is a report on two new reduction techniques in the context of the Finitistic Dimension Conjecture (FDC), i.e. the claim that the finitistic dimension(s) of every Artin algebra is finite. In the first one, building on work of Kirkman-Kuzmanovich-Small, we show that given a homological homomorphism of Artin algebras with superfluous kernel, its surjectivity can be replaced by the more general condition of radical preservation, satisfied automatically whenever the target algebra is basic. The second reduction technique generalizes substantially the arrow removal operation of Green-Psaroudakis-Solberg by allowing the arrows to be removed to participate in generating relations.

As a consequence of the first technique, we introduce the notion of quasi-uniform Loewy length and show that every bound quiver algebra with this property satisfies the FDC. Secondly, we characterize split epimorphisms of basic finite-dimensional algebras (over an algebraically closed field) with superfluous kernel in terms of pre-removable sets of arrows. Lastly, we provide an explicit algebra shown to satisfy the FDC, a highly non-trivial fact, through consecutive one-arrow reductions.

18.03 Calvin Pfeifer (Köln)

Title: A strategy to classify stable modules over E-tame algebras

25.03 Kyoungmo Kim (Köln)

Title: From gentle to semi-gentle algebras

01.04 Severin Barmeier (Köln)

Title: Module varieties via one-sided Gröbner bases