Gaitsgory, DennisChen, Lin2021-07-1320212021-04-292021-05Chen, Lin. 2021. Nearby Cycles and Dualities in Geometric Langlands Program. Doctoral dissertation, Harvard University Graduate School of Arts and Sciences.28418884https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37368200In this thesis, we study nearby cycles on certain Vinberg-style degenerations in the geometric Langlands program. We relate them to various exotic dualities in this field, such as the (local and global) geometric second adjointness and the miraculous duality. We also prove the Deligne-Lusztig duality for automorphic sheaves, which was conjectured by Drinfeld-Wang and Gaitsgory.application/pdfenMathematicsThesis or Dissertation2021-07-130000-0002-8676-9907