URegina Topology and Geometry Seminar: Kaveh Mousavand

For a finite-dimensional algebra A over an algebraically closed field k, varieties of finite-dimensional A-modules offer a geometric perspective on the homological and categorical properties of A and its modules. These varieties parametrize vector spaces of fixed dimension equipped with an A-module structure. While the connected components of these varieties are known from classical results, a structural understanding of their irreducible components remains largely open.

This talk begins with a brief geometric introduction to classical representation theory, then turns to several modern problems and foundational conjectures in the representation theory of finite-dimensional algebras. I will conclude by presenting recent progress on some of these challenging questions. Some of the new results are based on a series of joint work with Charles Paquette.

No prior background in representation theory is required; familiarity with undergraduate linear algebra and basic category theory will suffice.