Relative Langlands Program

Overview

The Langlands program, proposed by Robert Langlands in the late 1960s, is a network of far-reaching and influential conjectures connecting number theory, representation theory, and geometry. The relative Langlands program is a significant generalization of the classical Langlands program to hyperspherical varieties and has become one of its most important and productive branches. It links period integrals of automorphic forms (resp. multiplicities of irreducible admissible representations) to Langlands functoriality and special values of L-functions (resp. local root numbers). Over the past 30 years, remarkable progress has been made on both local and global problems, particularly in spherical pairs like the Gan–Gross–Prasad Conjectures. Recent work by Ben-Zvi, Sakellaridis, and Venkatesh has further established a general framework and introduced the notation of relative Langlands duality.

This minicourse and workshop will focus on recent developments in the Relative Langlands program, particularly those related to BZSV duality. The event aims to provide a platform for participants to exchange ideas, discuss the latest developments, and foster or strengthen collaborations.