Gaitsgory, DennisYang, David2022-06-0720222022-05-102022-05Yang, David. 2022. Categorical Moy-Prasad theory and applications to geometric Langlands. Doctoral dissertation, Harvard University Graduate School of Arts and Sciences.29208875https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37372115For any $G((t))$-category, we define a filtration which provides a categorification of the notion of depth studied by Moy and Prasad in the context of representations of a p-adic group. We also prove a generation statement which is the analogue of their theory of unramified minimal K-types and use it to compute our filtration on a number of categories of interest to geometric Langlands. Finally, joint with Sam Raskin, we apply this theory to prove an affine Beilinson-Bernstein localization statement conjectured by Frenkel and Gaitsgory.application/pdfenalgebraic geometrygeometric Langlandsrepresentation theoryMathematicsThesis or Dissertation2022-06-070000-0002-4672-3189