Orbifolds of two-dimensional quantum field theories have a natural formulation in terms of
defects or domain walls. This perspective allows for a rich generalisation of the orbifolding …

We study the category of matrix factorizations associated to the germ of an isolated
hypersurface singularity. This category is shown to admit a compact generator which is …

This is an introduction to some aspects of Fomin-Zelevinsky's cluster algebras and their links
with the representation theory of quivers and with Calabi-Yau triangulated categories. It is …

The concept of cluster tilting gives a higher analogue of classical Auslander correspondence
between representation-finite algebras and Auslander algebras. The n-Auslander–Reiten …

We say that an algebra $\Lambda $ over a commutative noetherian ring $ R $ is Calabi-Yau
of dimension $ d $($ d $-CY) if the shift functor $[d] $ gives a Serre functor on the bounded …

We describe a ring whose category of Cohen–Macaulay modules provides an additive
categorification of the cluster algebra structure on the homogeneous coordinate ring of the …

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

By Auslander's algebraic McKay correspondence, the stable category of Cohen-Macaulay
modules over a simple singularity is triangle equivalent to the $1 $-cluster category of the …

The K3 category of a cubic fourfold Page 1 The K3 category of a cubic fourfold Daniel Huybrechts
Compositio Math. 153 (2017), 586–620. doi:10.1112/S0010437X16008137 …

Various classification theorems of thick subcategories of a triangulated category have been
obtained in many areas of mathematics. In this paper, as a higher-dimensional version of the …