Gaitsgory, DennisLin, Kevin2023-06-0220232023-05-152023-05Lin, Kevin. 2023. Poincare Series and Miraculous Duality. Doctoral dissertation, Harvard University Graduate School of Arts and Sciences.30490215https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37375643In the setting of global geometric Langlands, we show that miraculous duality on the stack of principal bundles on a curve intertwines the functor of Poincare series with the dual functor to Whittaker coefficients. We construct, for arbitrary parabolic subgroups, Jacquet functors controlling constant terms of Poincare series and Whittaker coefficients of Eisenstein series in local terms.application/pdfenMathematicsThesis or Dissertation2023-06-020009-0006-9293-2498