updated: May 8, 2015, 16:40 EDT
Schedule of Distinguished Lectures
4:00 - 4:45
4:45 - 5:45
19:00 - 22:00
|The Coonamessett Inn
9:00 - 10:00
Abstracts and Available Videos
Lecture 1, Auslander algebras and preprojective algebras.
Abstract: Auslander correspondence gives a bijection between
representation-finite algebras and Auslander algebras. This was a
prototype of later Auslander-Reiten theory based on the language of
functor categories and stable module theory. A basic class of
representation-finite algebras is the path algebra of a Dynkin quiver,
and the corresponding preprojective algebra unifies all the possible
orientations of the quiver. The notion of cluster tilting modules gives
rise to a higher dimensional analog of both Auslander algebras and
preprojective algebras. I will discuss recent results on them based on
a joint work with Herschend and Oppermann.
Lecture 2, Tilting theory and Cohen-Macaulay representations.
Abstract: 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. I
will discuss recent applications of tilting theory to Cohen-Macaulay
representations, in particular, examples from higher preprojective
algebras and from Geigle-Lenzing complete intersections.
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