Imprimitive arithmetic statistics

Based on their Galois group, number fields can be categorized as either primitive or imprimitive. A primitive field has no nontrivial subfields, while imprimitive fields contain a nontrivial subfield. Thus, when studying arithmetic statistics questions for families of imprimitive fields, it's natural to ask how to leverage that subfield in the solution. This perspective influenced the speaker's recent work with Wang and Wood proving certain cases of the Cohen--Lenstra--Martinet conjectures. In this talk, we'll place these problems into a broader context by describing ongoing joint work of the speaker, including some follow up work with Wang, Wood, and the welcome addition of Brandon Alberts. With enough time, we'll also describe why the title of this talk is perhaps a little misleading.