AIM Workshop: Arithmetic intersection theory on Shimura varieties

This workshop, sponsored by AIM and the NSF, will be devoted to recent advances in arithmetic intersection theory on Shimura varieties. 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.

Topics: The main topics for the workshop are: Kudla's program: modularity of arithmetic generating series, Kudla-Rapoport conjectures, and connections with L-functions Arithmetic Gan-Gross-Prasad program: arithmetic fundamental lemma, arithmetic transfer conjectures, and connection with L-functions Applications of arithmetic intersections: exceptional isogenies between reductions of abelian varieties, arithmetic of K3 surfaces, Gross-Stark units and singular moduli for real quadratic fields