Osamu Iyama: Tilting theory and Cohen-Macaulay representations

Tilting theory provides us with a powerful method to control triangulated categories and their equivalences. In particular they often enable us to realize abstract triangulated categories as concrete derived categories of associative rings. An important class of triangulated categories in representation theory is the stable categories of Cohen-Macaulay modules over Gorenstein rings, which are also known as the singular derived categories of Buchweitz and Orlov. In this talk, I will explain recent applications of tilting theory to Cohen-Macaulay representations, in particular, Geigle-Lenzing complete intersections which give a higher dimensional generalizations of weighted projective lines of Geigle-Lenzing and canonical algebras of Ringel.