Conference: Arithmetic and p-adic Geometry in Chile

The award supports US-based graduate students and postdocs to attend and participate in the international conference and summer school “Arithmetic and p-adic geometry in Chile” in December 2024 (https://hdc-g.github.io/agchile2024/index.html). Arithmetic and number theory is the study of properties and patterns in the integers. These questions are deep, and geometric tools have emerged as a powerful structure that helps us understand them. Often, this geometry is not the usual Euclidean geometry, but a p-adic one in which distance is governed by divisibility properties of a prime number p such as 2, 3, 5. There have been fundamental recent advances in the theory of p-adic geometry, and the impact of those advances on questions in arithmetic is only just beginning to be understood. This conference will bring together experts in arithmetic and p-adic geometry to share their work and explore connections between these fields. The early career participants funded by this award will learn the newest developments from experts, enabling them to carry these ideas into their burgeoning research. Moreover, the location of the conference, in Santiago, Chile, will facilitate collaborations between mathematicians in the northern and southern hemispheres. Both the summer school and the conference will be organized around three themes: p-adic L-functions and Iwasawa theory, the p-adic Kudla program, and the p-adic Langlands programs. These are three active areas of number theory research where the recent advances in p-adic geometry are already making an important impact. These three areas also have important connections with each other. By bringing together experts in all of these fields, the conference will facilitate a sharing of knowledge and a flowering of new collaborations coming from different perspectives on the complicated objects studied in p-adic geometry. Participating in these conversations will be especially beneficial for the early career participants funded by this award. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.