Special Year on p-adic arithmetic geometry
During the 2023-24 academic year the School will have a special program on the $p$-adic arithmetic geometry, organized by Jacob Lurie and Bhargav Bhatt, who will be the Distinguished Visiting Professor.
The last decade has 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 intends to bring together a mix of people interested in various facets of the subject, with an eye towards sharing ideas and questions across fields.