Group, Lie and Number Theory Seminar

We discuss the Cohen-Lenstra heuristics from the point of view of counting unramified number field extensions of quadratic fields. This point of view admits a natural generalization of the setting of those heuristics, in which one can ask the same type of questions.

We will focus on the specific case 2-group extensions of quadratic fields which has proven to be more tractable in recent years. We will put forth a conjecture about asymptotics and distributions of such extensions (beyond those considered by Cohen and Lenstra) and discuss our recent progress on this in the case of extensions with Galois groups which are central extensions of F_2 ^n by F_2. Speaker(s): Jack Klys (University of Toronto)