Abstract:

The Langlands program is a web of far-reaching and influential conjectures about connections between number theory, representation theory and geometry proposed. Within this program, the relative Langlands program has emerged as one of its most important and productive branches. In this talk, I will give an overview of key problems in the relative Langlands program, with a focus on the elegant theory of relative Langlands duality, recently developed by Ben-Zvi, Sakellaridis, and Venkatesh. I will also present some of my works in this area.