Mattia Talpo: The class of BG in the Grothendieck ring of stacks

The Grothendieck ring of varieties over a field k is a ring that is additively generated by isomorphism classes of varieties over k, modulo a "cut and paste" relation with respect to closed subvarieties, and where the product is cartesian product. Its main application is currently Kontsevich's theory of motivic integration, but it is also important for several other reasons. There is a variant of this construction, due to T. Ekedahl, that replaces varieties with algebraic stacks.

I will start with an overview of these constructions, and then I will focus on the problem of computing the motivic class of the classifying stack BG of a connected algebraic group G, describing in particular some recent joint work with A. Vistoli and R. Pirisi.