Symposium

**13:30 Rosie Laking (Università degli Studi di Verona)**

*Cosilting sets and the Ziegler spectrum*

Abstract: In this talk I will explain how torsion pairs in the category modA of finitely generated modules over an artinian ring A can be parametrised by cosilting sets, that is, maximal rigid subsets of two-term pure-injective complexes in the derived category D(A). Moreover each cosilting set determines a t-structure such that the finitely presented objects in the heart coincide with the tilt of modA at the corresponding torsion pair.

I will explain how each cosilting set is a closed subset of the Ziegler spectrum of D(A) and that the induced topology is controlled by the Serre subcategories of the associated tilt of modA. I will end by discussing the open question of whether the mutation theory of cosilting sets for a finite-dimensional algebra is determined by the isolated points?

This talk is based on joint work with Lidia Angeleri Hügel and Francesco Sentieri.

**14:45 Charley Cummings (Aarhus University)**

*Metric completions of discrete cluster categories*

Abstract: The completion of a metric space is a familiar method to generate new mathematical structures from old. Recently, Neeman emulated this idea to define the metric completion of a triangulated category. In general, these completions are difficult to compute; often one needs to use properties of ambient, already completed, triangulated categories, like the derived category. Cluster categories of Dynkin type A are triangulated categories that can be defined by a combinatorial model, and, as such, we will see that many of their completions can be computed without the use of such an ambient triangulated category. Moreover, we will see an infinite family of metric completions that can be realised combinatorially. This talk is based on joint work with Sira Gratz.

**16:00 Laertis Vaso (NTNU)**

*τ-d-tilting theory for Nakayama algebras*

Abstract: τ-tilting theory and torsion theory are established areas of interest in representation theory. Recently, there have been attempts to generalize these theories in the setting of higher homological algebra. d-torsion classes were introduced by Jørgensen, and several versions of “τ_d-tilting modules” have been introduced by different authors (Jacobsen–Jørgensen, Martínez–Mendoza, Zhou–Zu and others). The aim of this talk is to give an explicit classification of some of these higher analogues of τ-tilting modules and torsion classes for truncated linear Nakayama algebras when d>2. This classification will also be used to illustrate the different proposed notions of higher tau-tilting modules. This is joint work with Endre S. Rundsveen.

*Tea, coffee and cake will be provided.*

Organised by: AarHomAlg