P-ADIC KUDLA PROGRAM AND P-ADIC AUTOMORPHIC FORMS LE PROGRAMME DE KUDLA P-ADIQUE ET FORMES AUTOMORPHES P-ADIQUES

Fabrizio Andreatta is professor at the Università degli Studi di Milano since 2006 Before he has obtained his PhD in Utrecht with Frans Oort and has held PostDoc positions in Montreal and in Rome and a tenure track position in Padova. His mathematical interests are in Arithmetic Geometry and include the study of models of Shimura varieties, p-adic automorphic forms and p-adic Hodge theory and, especially, the interplay among these three areas of research. In 2018 he, Adrian Iovita and Vincent Pilloni have been invited speakers at the ICM for their work on p-adic families of automorphic forms. In 2018 he has been awarded the Medal for Mathematics from the italian « Accademia Nazionale delle Scienze ». The paper Faltings heights of abelian varieties with complex multiplication, authored by Fabrizio Andreatta, Eyal Goren, Benjamin Howard and Keerthi Madapusi Pera has been selected by the International Congress of Basic Science, as a recipient of the 2024 Frontiers of Science Award in Mathematics. Prof. Andreatta has advised several PHD students and is the author of more than 40 publications.

Joaquín Rodrigues Jacinto is a maître de conférences (associate professor) at Aix-Marseille Université. His main research areas are Number Theory, Arithmetic Geometry and Representation Theory. He’s interested in the construction of p-adic L-functions, and in their connection to the p-adic Langlands correspondence. He is also interested in the study of special values of L-function framed in the setting of Deligne-Beilinson and Tate conjectures, and the theory of Euler systems. More recently, he has been working on the applications to p-adic representation theory of p-adic groups through the use of condensed mathematics.

SCIENTIFIC PROGRAM 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.

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.