Equidistribution of Steinitz Classes

Number theory has many important equidistribution results, such as Dirichlet's theorem on arithmetic progressions or the more general Chebotarev density theorem. In this talk, we will (mostly) reprove a result of Kable and Wright on the equidistribution of an invariant called a Steinitz class for quadratic extensions of a number field using very simple machinery from algebraic number theory. We will also discuss Steinitz classes of larger degree extensions, Steinitz classes for elliptic curves, square factors of integers, and some cautionary tales about sorting and computation in Sage, Magma, and Pari. This talk is intended to be accessible to a general grad student audience with some knowledge of algebra.