Algebraic Number Theory and Arithmetic Geometry are among the most exciting and active domains of Mathematics. Inspired by important problems such as Fermat’s last theorem, the Birch and Swinnerton–Dyer conjecture or the Riemann hypothesis, these fields have seen some of the most impressive advances in Mathematics during the last century.

We are pleased to propose a semester program around some of the newest and most promising topics in the area. On the one hand we will focus on the emerging project of studying p-adic manifestations of the celebrated Kudla program (a vast program relating arithmetic cycles in Shimura varieties, special values of L-functions and Eisenstein series). On the other hand, we will be interested in the potential applications of the new methods in p-adic geometry to the classical Iwasawa theory, such as to the construction of p-adic L-functions or to the study of Selmer groups. We will give a precise description of these topics as well as of the purposes of the semester during the rest of this proposal.

The leitmotif of the semester will be to gather together people from different but complementary areas that play an important role in the development of these topics. We expect to welcome specialists from the theory of p-adic automorphic forms, p-adic geometry, Iwasawa theory, and arithmetic geometers to foster collaborations and push the development of this beautiful theory.