Sheaves on Stratified Spaces

Algebraic Geometry and Number Theory Seminar

In this talk, we study constructible sheaves on spaces stratified via a Gm-action. We show how to understand the gluing data of these categories geometrically using hyperbolic localisation and the Drinfeld-Gaitsgory interpolation space. In particular, we apply this framework to flag varieties. Here, we explain how the gluing data can be understood explicitly in terms of a new multiplicative structure on open Richardson varieties, which were introduced in the work of Kazhdan-Lusztig. Lastly, we discuss applications in symplectic geometry and geometric representation theory.

This is joint work with Catharina Stroppel.