Abstracts and Available Videos
Lecture 1, Auslander-Reiten Duality Revisited.
Abstract: The cornerstones of Auslander-Reiten duality are two
formulas that relate for any module category the functors Ext and Hom.
In my talk I'll explain how these formulas generalise to any
Grothendieck abelian category having a sufficient supply of finitely
presented objects. This general point of view provides a new
interpretation of the dual of the transpose for a finitely presented
module. Also, the connection with Serre duality for algebraic varieties
is discussed.
Lecture 2, Local Serre Duality for Modular Representations of Finite Groups.
Abstract: Given a finite group scheme, its modular representations
enjoy a Gorenstein property which implies a "local Serre duality" for
the representations supported at a point of the projective variety of
the cohomology ring. To explain this new type of Serre duality is the
aim of my talk. All this is based on recent work with D. Benson, S.
Iyengar, and J. Pevtsova.