Abstract:

In this talk I will describe scalar invariants, in the geometric invariant theory sense, that arise in the study of algebraic structures.

I will then explain why and how they can be realized as covering spaces.

As a result, positive self-adjoint Hopf (PSH)-algebras appear.

These algebras were originally studied by Zelevinsky in the framework of the representation theory of families of finite groups. I will explain what can we learn about invariant theory from this, and discuss some open problems and applications to subgroup growth questions.