# Special Year on p-adic Arithmetic Geometry

During the 2023-24 academic year the School held a special program on the $p$-adic arithmetic geometry, organized by Professors Bhargav Bhatt and Jacob Lurie.

Confirmed participants included: Pierre Colmez, Johan DeJong, Ofer Gabber, Lars Hesselholt, Kiran Kedlaya, Matthew Morrow, Wieslawa Niziol, Peter Scholze, Annette Werner and Xinwen Zhu.

The last decade witnessed some remarkable foundational advances in $p$-adic arithmetic geometry (e.g., the creation of perfectoid geometry and the ensuing reorganization of $p$-adic Hodge theory). These advances have already led to breakthroughs in multiple different areas of mathematics (e.g., significant progress in the Langlands program and the resolution of multiple long-standing conjectures in commutative algebra), have uncovered new phenomena that merit further investigation (e.g., the discovery of new structures on algebraic $K$-theory, new period spaces in $p$-adic analytic geometry, and new bounds on torsion in singular cohomology), and have made hitherto inaccessible terrains more habitable (e.g., birational geometry in mixed characteristic). This special year brought together a mix of people interested in various facets of the subject, with an eye towards sharing ideas and questions across fields.

Fall workshop: November 13-17, 2023. See website for more information.

Spring workshop: March 11-15, 2024. See website for more information.