This workshop, sponsered by AIM and the NSF, will be devoted to arithmetic statistics, especially nonabelian aspects and connections to geometric methods. The workshop aims to bring together researchers to explore statistical questions about number fields, class groups, Galois representations, and point counting. It will concentrate on counting problems coming from nonabelian Cohen–Lenstra heuristics, recent connections between the Cohen–Lenstra–Martinet and Batyrev–Manin conjectures, and questions related to Galois representations.

The main topics for the workshop include:

• Nonabelian versions of Cohen–Lenstra heuristics: studying the distribution of Galois groups of maximal (usually nonabelian) extensions of number fields that are unramified away from a finite set of primes.
• Sato–Tate groups: understanding cases where we do not have access to complete classification results; applications to extreme value problems.
• Modular representations: even heuristics are not well-established. For example: what is the probability that a mod-$\ell$ modular representation of weight 2, when sorted by level, has a reducible or dihedral image.
• Connections between Bhargava–Malle and Batyrev–Manin conjectures: work of Darda–Yasuda and Ellenberg–Satriano–Zureick-Brown introduces a framework for counting rational points on stacks which unifies and interpolates these conjectures.

This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email workshops@aimath.org