|Location:||MSRI: Simons Auditorium|
Let be a finite dimensional algebra over an algebraically closed field, and
Rep(, d) the standard affine variety parametrizing the isomorphism classes of -modules with dimension vector d. We will address the problem of determining the irreducible componentsof the Rep(, d) in terms of representation-theoretic invariants, and of exploring
the generic structure of the modules these components encode. After giving an overview of existing theory, stemming from work of Kac, Schofield, Schr¨oer, Crawley-Boevey, Riedtmann, among others, we will present new results. We will conclude with a conjecture addressing the next plausible step in trying to push beyond the status quo.