Mathematical Sciences: Topology and Potential Theory of Complete Kahler Manifolds

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9626169 Ramachandran This project deals with compact and complete Kahler manifolds and their topological properties, in particular, the fundamental group. The project is in the main motivated by the Shafarevich conjecture: Is the universal cover of every compact Kahler manifold holomorphically convex? This area of research interfaces several complex variables and algebraic geometry; uses techniques from analysis as well as geometry. Kahler manifolds are a complex analog of Euclidean space. They arise in a variety of settings in mathematics as well as theoretical physics. For example, solutions to systems of polynomial equations with complex number coefficients are Kahler manifolds. Also, the space of all solutions to Yang-Mills type equations in elementary particle theory can be thought of as Kahler manifolds.