Conference: CBMS Conference Representations of p-adic Groups and Noncommutative Geometry

This award provides support for the NSF-CBMS (Conference Board of the Mathematical Sciences) regional research conference "Representations of p-adic groups and noncommutative geometry" to be held June 9-13, 2025 at the Queens campus of St. John’s University in New York City. The research topic of the conference is at the interface between the representation theory of the p-adic groups, the Langlands program, and noncommutative geometry.

The principal lecturer is Anne-Marie Aubert, who will give ten lectures on the interplay between the representation theory of p-adic groups, noncommutative geometry, and operator algebras. The talks will be self-contained and accessible to students and non-experts. The conference will expose early career researchers to cutting-edge research and provide a platform for researchers in the tri-state area around New York City, and more broadly, to build collaborations.

In more detail, the Langlands program is a series of conjectures that connects representations of algebraic groups over the adeles with number theory. The conference will focus on the local Langlands program, where one works with a p-adic field instead of a number field. The lectures will explore the representation theory of p-adic groups from a new perspective, namely that of noncommutative geometry and operator algebras.

The lectures will introduce the notion of stratified equivalence, formulate the strong form of the ABPS Conjecture (Aubert, Baum, Plymen, Solleveld), and explain the role that asymptotic Hecke algebras are expected to play in the proof of the conjecture. Finally a strategy to construct the explicit local Langlands correspondence applicable for the p-adic group G2 and for all pure inner twists of classical p-adic groups will be described. The conference website is https://sites.google.com/view/nsf-cbms-ncg-repag/home.

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.