Algebra/Topology Seminar

Abstract: Cohomological support varieties have been invaluable as a geometric approach to study the representation theory of algebras. They were imported to commutative algebra by Avramov in ‘89, and further developed by Avramov and Buchweitz in 2000 during their investigations of cohomology modules over complete intersection rings. In the past 20+ years this theory has been further extended and applied by a number of researchers. In this talk, I’ll highlight some recent applications of the theory; notably, I will present a collaboration with Briggs and Grifo where we establish bounds for the Krull dimensions of these geometric objects that have a number of consequences in local algebra.