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This workshop, sponsored by AIM and the NSF, will be devoted to interactions between p -adic geometry and chromatic homotopy theory. In particular, we will focus on the use of period maps and perfectoid methods to study the moduli stack of formal groups. We hope to use these methods to further our understanding of chromatic and transchromatic phenomena in stable homotopy and to see how the chromatic picture motivates and hints at possible novel results in p -adic geometry.

The main topics of the workshop are:

The p-adic geometry of the moduli stack of formal groups and its role in chromatic homotopy theory. Perfectoid methods in p-adic geometry. Period maps and generalized Rapoport--Zink spaces. 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.

Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than August 15, 2024. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.

Before submitting an application, please read the description of the AIM style of workshop.