Whittaker coefficients in quantum geometric Langlands program

David Ben-Zvi and David Nadler introduced the 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. I’ll give an overview of this conjecture, introduce geometric Whittaker coefficients, and briefly discuss their role in constructing the quantum Betti Langlands functor and in understanding some of its properties.

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