The purpose of these notes is to explain in detail some topics on the intersection of
commutative algebra, representation theory and singularity theory. They are based on …

This book is a comprehensive treatment of the representation theory of maximal Cohen-
Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative …

Simple or ADE-singularities have attracted much attention during the last two decades,
mostly because very different classification principles led finally to the same list of …

In this article we study Cohen–Macaulay modules over one-dimensional hypersurface
singularities and the relationship with the representation theory of associative algebras …

Apart from confirming conjectures in algebraic combinatorics and integrable systems, having
an interesting representation theory, and connecting with real algebraic geometry …

We recall several results in Auslander-Reiten theory for finite-dimensional algebras over
fields and orders over complete local rings. Then we introduce $ n $-cluster tilting …

This book is a lightly edited version of the unpublished manuscript Maximal Cohen–
Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz …

Let R be an isolated Gorenstein singularity with a non-commutative resolution A= End R
(R⊕ M). In this paper, we show that the relative singularity category Δ R (A) of A has a …

Let X be a Gorenstein normal 3-fold satisfying (ELF) with local rings which are at worst
isolated hypersurface (eg terminal) singularities. By using the singular derived category D sg …

Cluster algebras were introduced by Fomin-Zelevinsky in 2002 in order to give a
combinatorial framework for phenomena occurring in the context of algebraic groups …