Speaker: Yiannis Sakellaridis (Johns Hopkins University)

Title: On the cotangent bundle of spherical varieties.

Abstract: I will present a very simple-minded theorem, describing the regular locus of the cotangent bundle of a strongly tempered spherical variety as a "toric embedding'' of the group scheme of regular centralizers. This deepens work of Knop (who described this cotangent bundle up to codimension one), confirms an observation of V. Lafforgue, and can be fed into the argument of Hameister–Luo–Morissey to prove a version of the semiclassical/Dolbeault relative Langlands conjecture. Moreover, this theorem gives a more satisfactory picture about a mysterious symplectic vector space appearing in the dual hyperspherical variety. Part of ongoing joint work with Ben-Zvi and Venkatesh.