In this talk, we switch to Geometric Langlands over the complex numbers. The Galois representations are replaced by perverse sheaves or D-modules, the automorphic representations are replaced by Hecke eigensheaves, and the Hecke correspondences now live over the stack of bundles. We introduce these objects, then prove Geometric Langlands for G=GL_1.  Time permitting, we will discuss the categorified version of the Satake isomorphism, i.e. Geometric Satake.

Notes from Emmet Lennen.