Derived category, Mirror symmetry and McKay correspondence seminar

Speaker: Osamu Iyama (Nagoya U)
Title: Calabi-Yau triangulated categories and Cluster tilting
Date (JST): Tue, Nov 30, 2010, 10:30 - 17:00
Place: Seminar Room A
Abstract: Calabi-Yau (CY) triangulated categories are one of the major subjects in representation theory, and the notion of cluster tilting (CT) objects, which are certain analogue of tilting objects, plays an important role.

In the first part, I will discuss the combinatorics of CT objects in 2-CY categories. They give a "categorification" of cluster algebras of Fomin-Zelevinsky. For example, mutation of quivers (with potential) naturally appears in certain categorical operation called "CT mutation". This picture was recently used in proof of periodicity conjecture of T-systems.

In the second part, I will introduce "cluster categories" which are thought to be canonical one among Calabi-Yau categories containing CT objects. I will compare them with classical one, i.e. the stable categories of Cohen-Macaulay modules over Gorenstein isolated singularities, and show triangle equivalences for certain cases.
Remarks: The first part ends at 12:00.
The second part starts at 15:30.