Study of Moduli of algebraic vector bundles

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I studied on the strange duality of generalized theta functions on moduli spaces of vector bundles. I described the behavior of the strange duality map for symplectic bundles as the base curve degenerates to a singular curve, and proved the strange duality conjecture for symplectic bundles. By considering quasi-bundles on a projective plane, I proved a special case of Le Potier's strange duality conjecture. I also computed the dimension of generalized theta functions on the moduli spaces of pure one-dimensional sheaves of degree four.