Towards derived Satake equivalence for symmetric varieties

In an ongoing project of D. Ben-Zvi, Y. Sakellaridis and A. Venkatesh, the authors propose a conjectural generalization of the derived Satake equivalence for complex reductive groups to spherical varieties. I will describe a program aimed at establishing their conjecture in the case of symmetric varieties (an important class of spherical varieties). A key ingredient is the relation between the derived Satake equivalence for symmetric varieties and the geometric Langlands for real reductive groups.

This is joint work with David Nadler.