Title: Cohomological support varieties and their applications
Abstract: Cohomological support varieties have been invaluable as a geometric approach to study the representation theory of algebras. They were imported to local 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 twenty years this theory has been further extended and applied by Avramov-Iyengar, Burke-Walker, Jorgensen, Stevenson, and myself, as well as many others. In this talk, classical and recent applications of cohomological support will be discussed. Notably, I will present a recent collaboration with Briggs and Grifo where we establish bounds for the Krull dimensions of these geometric objects, which have applications in commutative algebra.
