Approximations to Classifying Spaces from Algebras

Ben Williams (University of British Columbia)

If A is a finite-dimensional algebra with automorphism group G, then varieties of generating r-tuples of elements in A, considered up to G-action, produce a sequence of varieties B(r) approximating the classifying space BG. I will explain how this construction generalizes certain well-known examples such as Grassmannians and configuration spaces. Then I will discuss the spaces B(r), and how their topology can be used to produce examples of algebras of various kinds requiring many generators. This talk is based on joint work with Uriya First and Zinovy Reichstein.