Talks & Posters

Abstract: Classic Auslander-Reiten theory is a neat tool used to paint a portrait of the category of modules over an Artinian ring. Nakayama functors play an important role in this painting. In suitable settings, the theory generalises to abelian categories, triangulated categories and their subcategories. In this talk, we will construct Nakayama functors on proper abelian subcategories. These categories, defined by Jørgensen in 2022, are generalisations of hearts of t-structures.

Abstract: Chuang and Lazarev introduced the concept of rank functions on triangulated categories as a generalisation of classical work by Cohn and Schofield on Sylvester rank functions. In this talk, we propose a generalisation of this notion to the broader framework of higher homological algebra.

Abstract: Complexes are a fundamental object in homological algebra, and as such, grading is deeply ingrained in the subject. But what happens if we remove the grading from a complex? This leads us to the notion of a differential module. In this talk, we will explore how the finiteness of the injective dimension of a finitely generated module over a local commutative noetherian ring can be detected using this ungraded framework. As an immediate application, we will see that this perspective also detects when such a ring is Cohen–Macaulay. This approach offers a new perspective on a classical question posed by H. Bass.