Local duality for Gorenstein algebras

From work of Auslander and Reiten we know that the stable category of maximal Cohen-Macaulay modules over a finite dimensional Gorenstein algebra admits a Serre functor. The talk is devoted to an analogue of Grothendieck's local duality in that context, which is induced by Auslander-Reiten duality and employs the action of Hochschild cohomolgy on the category of maximal Cohen-Macaulay modules. This is based on joint work with Benson, Iyengar, and Pevtsova.