Geometry Seminar

David Ben-Zvi and David Nadler introduced Betti version of the Geometric Langlands correspondence, which is topological in nature, but still remembers the "core" information about Hecke eigensheaves. This equivalence was established recently in the work of D. Arinkin, D. Beraldo, J. Campbell, L. Chen, J. Faergeman, D. Gaitsgory, K. Lin, S. Raskin and N. Rozenblyum. However, Ben-Zvi and Nadler also described a quantum version of Betti Geometric Langlands correspondence, which remains a conjecture. The goal of this talk is to sketch a construction of the functor in one direction in this equivalence. The construction will go through geometric Whittaker coefficients and is conditional on the Fundamental local equivalence, which I will introduce first.