Seminare und Vorträge im WS 2025/2026
| Date | Lecturer | Seminar | Theme | Time | Location |
|---|---|---|---|---|---|
| 07 Oct 2025 | Maximilian Kaipel (University of Cologne) | g-vector fans and picture categories for 0-Auslander extriangulated categories Abstract: Cluster algebras and cluster categories have had a revolutionary impact on tilting theory. In particular, they have inspired various theories of mutation, which have become central research topics since then. Important examples include cluster-tilting mutation,𝜏-tilting mutation and relative rigid mutation. Recently, Gorsky—Nakaoka—Palu showed that these, and other, mutations may be unified via the mutation of maximal rigid objects in 0-Auslander extriangulated categories (with certain finiteness assumptions). For a finite-dimensional algebra, 𝜏-tilting mutation is encoded by a geometric object, called its g-vector fan. In my talk, I expand this notion and define a polyhedral fan which encodes the mutation theories of the 0-Auslander extriangulated categories above. I will illustrate its properties through many examples. Building on my previous work, I will explain how thick subcategories induce an admissible partition of the fan and introduce the notion of a morphism of partitioned fans. This provides a unifying perspective on various results on $\tau$-cluster morphism categories and picture categories of myself and Erlend Børve. This is joint work-in-progress with Erlend Børve. | 2pm in person | ||
| 21 Oct 2025 | Markus Kleinau (Universität Bonn) | 2pm in person | |||
| 29 Oct 2025 | Sira Gratz (Aarhus University, Denmark) | ||||
| 04 Nov 2025 | Cyril Matoušek (Aarhus Universitet) | Hereditary rings and metric completions of their derived categories Abstract: A metric on a triangulated category, as developed by Neeman, provides a recipe for constructing a metric completion of the category. These completions are guaranteed to be triangulated categories as well and have recently been used to study, among other things, derived Morita theory, cluster categories, and t‑structures. The aim of this talk is to examine metric completions of bounded derived categories of hereditary rings and their connection to the concept of universal localisation. Notably, we explicitly describe the completions of bounded derived categories of hereditary finite dimensional tame algebras and hereditary commutative noetherian rings with respect to additive good metrics. | 2pm in person | ||
| 26 Nov 2025 | Timothy Logvinenko (Cardiff University, UK) |