Professor Michael Penkava from University of Wisconsin, Eau Claire speaking about "Moduli spaces of algebras are stratified by orbifolds."

Abstract: The algebra structures (Lie or associative) on a finite dimensional vector space determine a variety, and the action of the linear automorphism group of the vector space on this variety determines the moduli space of algebras on the space. As a topological space, the moduli space is not Hausdorff. In a series of papers, the speaker and Alice Fialowski have been studying these moduli spaces, using versal deformations of the algebras to determine the neighborhoods of points. We have found that the moduli spaces decompose uniquely into strata given by orbifolds, with all the non Hausdorff phenomena described by jump deformations between points on different strata. In the complex case, the orbifolds are given by actions of the symmetric group on projective spaces, while in the real case, they are given by actions of groups on spheres.