Analytic and Geometric approaches to the Bhargava-Malle and Batyrev-Manin conjectures
Aug. 2, 2027 – Aug. 6, 2027
This workshop, sponsored by AIM and the NSF, will be devoted to arithmetic statistics. We want to formulate a unifying point of view for the Bhargava-Malle and Batyrev-Manin conjectures using (multiple) Dirichlet series. The workshop aims to bring together researchers to explore statistical questions about number fields, class groups, and point counting. It will concentrate on counting problems coming from recent connections between the Bhargava-Malle and Batyrev-Manin conjectures.
The main topics for the workshop include:
- Connections between Bhargava-Malle and Batyrev-Manin conjectures: work of Darda-Yasuda and Ellenberg-Satriano-Zureick-Brown introduce a framework for counting rational points on stacks which unifies and interpolates these conjectures.
- Multiple Dirichlet Series and connections to Batyrev-Manin: can one formulate the equivalent of Malle's conjecture for the count by arbitrary inertial height/invariant instead of just by discriminant ordering?
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.
For more information email workshops@aimath.org