Spencer Leslie (Boston College)

Abstract: I will discuss the motivation for a theory of endoscopy in the context of the relative Langlands program. I then outline the construction of endoscopic varieties, which are spherical varieties of an associated endoscopic group. The construction works for most hyperspherical varieties induced from symmetric varieties, and relies on new rationality results for such varieties. We highlight the role played by the dual Hamiltonian variety associated with a symmetric variety a la Ben-Zvi, Sakellaridis, and Venkatesh.