# The Ngô action via geometric Satake

 Locally Symmetric Spaces Seminar Topic: The Ngô action via geometric Satake Speaker: David Ben Zvi Affiliation: University of Texas at Austin; Member, School of Mathematics Date: Tuesday, February 13 Time/Room: 1:45pm - 4:15pm/Simonyi Hall 101 Video Link: https://video.ias.edu/locallysemetric/2018/0213-DavidBenZvi

I will explain an application of the geometric Satake correspondence (in its derived form due to Bezrukavnikov-Finkelberg) to the study of differential operators on $G$-spaces (for $G$ complex reductive) and its classical version, the study of cotangent bundles. The main result can be thought of as a "group" analog to Kostant's description of the center of $Ug$ by its action on Whittaker vectors, or a quantized version of Ngô's action of regular centralizers on all centralizers (both of which I will recall). This will aim to be a slower, gentler, expanded version of my talk from the member seminar (which will not be assumed).