Abstract: |
Representation theory of algebras aims at understanding various categories attached to a given ring. The rings we are interested in are, for example, finite dimensional algebras over a field and commutative Cohen-Macaulay rings etc. In this talk, starting from some backgrounds, I would like to talk about representation theory of these rings, especially in triangulated categories such as derived categories, singularity categories, cluster categories, and their enhancements. I will present some of my (previous) results which can be seen as classifying ``most fundamental'' ones among these triangulated categories. |