Title: Representation type and support varieties

Abstract: Finite dimensional algebras come in three flavors, or representation types: finite, tame, and wild. Useful invariants of their modules are support varieties, defined when the algebra has associated to it a cohomology ring that is finitely generated commutative. Recent work of Farnsteiner shows that the theory of support varieties for modules of finite group schemes may be used to give a criterion for wildness.

In this introductory talk, we will give an overview of the theories of representation type and of support varieties for modules. Then we will explain how Farnsteiner's techniques may be adapted to give a wildness criterion for small quantum groups and more generally for finite dimensional Hopf algebras whose cohomology is finitely generated.

This is joint work with Joerg Feldvoss.