Nilpotent counting problems in arithmetic statistics

Original Announcement

The aim of this workshop is to bring these methods together, and investigate the potential for combining techniques to prove stronger results. The workshop also aims to study minimal, nontrivial working examples of these methods in new settings both as a means to further develop these tools and to increase access to the methods.

The main topics for the workshop are counting number fields with nilpotent Galois group and the distribution of the $p$-torsion of the class group for extensions of degree divisible by $p$, with methods including

• Smith's methods for proving the distribution of $2^\infty$-torsion in class groups of quadratic extensions. For example, the first moment of 8-torsion of class groups of quadratic fields relates to $D_8$-extensions of $\mathbb{Q}$, for which Malle's conjecture has yet to be verified.
• Solutions to central embedding problems, as employed by Koyman and Pagano to parametrize nilpotent extensions. Explicit presentations of Galois groups, including those proven by Liu.
• Multiple Dirichlet series methods for producing an analytic continuation of a generating series, as utilized by Altug, Shankar, Varma, and Wilson.
• Galois cohomology and the study of twisted counting problems studied by Alberts and O'Dorney.
• Geometric techniques for function field analogs and the insight they can give into the number field case, as in work by Liu, Wood, and Zureick-Brown.

Material from the workshop

The workshop schedule.

Workshop videos