Algebraic Geometry Seminar

As the title suggests, the topic of this talk will bridge between Combinatorics and Geometry. Despite some unavoidable technical terminology, I will aim at making the talk enjoyable by both communities. In this seminar I am going to show that the class of the classifying stack of a finite group, BG, is trivial if G is a finite subgroup of GL_3(k) or if G is a linear (or projective) reflection group. I will relate these results to the study of the motivic class of the quotient variety U/G - U is the open set of a representation V of G where the group acts trivially. Such classes and the class of BG exhibit the same combinatorial structure.