#### Osamu Iyama : Introduction to cluster tilting in 2-Calabi-Yau categories

Cluster tilting theory reveals combinatorial structure of 2-Calabi-Yau triangulated categories and is applied to categorify Fomin-Zelevinsky cluster algebras by many authors (Buan, Marsh, Reineke, Reiten Todorov, Caldero, Chapoton, Schiffler, Keller,...). In the first talk, we will introduce cluster tilting theory in 2-Calabi-Yau triangulated category. In particular, a combinatorial description of change of endomorphism algebras of cluster tilting objects via mutation process is given in terms of Fomin-Zelevinsky quiver mutation rule. In the second talk, a class of examples of 2-Calabi-Yau triangulated categories containing cluster tilting objects will be constructed from preprojective algebras and elements in the corresponding Coxeter groups.