Gauge Theory and Holomorphic Bundles

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9703869 Bradlow This research project lies in the interface of geometry and mathematical physics. More specifically, the investigator is to undertake a systematic study of holomorphic vector bundles equipped with extra structures. Examples of such bundles include Higgs bundles, parabolic bundles, holomorphic pairs, and coherent systems. These bundles have applications in several other branches of mathematics and physics. For example, on a Kahler surface the Seiberg-Witten monopole equations are equivalent to the metric equations for holomorphic pairs on a line bundle. Holomorphic bundles are objects defined over a curved space or a manifold; they have simple local structures allowing algebraic calculations, and when these local calculations are pieced together, they often reveal important geometric properties about the underlying manifold. In recent years holomorphic bundles have played an important role in various parts of mathematics as well as theoretical physics.