Liana Sega

In recent years, there has been growing interest in understanding the vanishing of Ext and Tor over Noetherian local rings. Some of the problems have been raised a long time ago by Auslander and Reiten, others have been motivated by recent work on complete intersections due to Avramov and Buchweitz. We will discuss several of these problems, by exploring relevant examples and particular cases. One of the goals of this talk is to show that patterns in vanishing/nonvanishing of (co)homology over Gorenstein rings can be surprisingly wild.