Yau, Shing-TungXu, Kai2023-06-0220232023-05-112023-05Xu, Kai. 2023. Moduli of vector bundles on curve and semiorthogonal decomposition. Doctoral dissertation, Harvard University Graduate School of Arts and Sciences.30492379https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37375841The present dissertation studies the derived categories of coherent sheaves on various versions of moduli of bundles on an algebraic curve over a field of characteristic $0$, including the full moduli stack, the semistable locus and the coarse moduli space on proper curves and affine curves. We construct semiorthogonal decompositions of moduli of vector bundles on a curve into its symmetric powers. As essential ingredients in the proof, we develop Borel-Weil-Bott theory for loop groups on twisted moduli spaces and derived Schur-Weyl duality for current groups. We also carry out a detailed study the Harder-Narasimhan stratification in the general framework of $\Theta$-stratification.application/pdfenAlgebraic GeometryDerived CategoryModuli of vector bundlesSemiorthogonal decompositionSupersymmetric gauge theoryMathematicsPhysicsThesis or Dissertation2023-06-020009-0001-6241-9566