Mathematical Sciences: Topology and Potential Theory of Complete Kahler Manifolds

9626169 Ramachandran这个项目研究紧致和完备的Kahler流形及其拓扑性质，特别是基本群。这个项目的主要动机是Shafarevich猜想：每个紧致Kahler流形的泛覆盖是全纯凸的吗？这一研究领域涉及多个复变量和代数几何；使用分析和几何中的技术。Kahler流形是欧几里得空间的复类比。它们出现在数学和理论物理的各种环境中。例如，复数系数多项式方程组的解是Kahler流形。此外，基本粒子理论中的杨-米尔斯型方程的所有解的空间也可以看作是Kahler流形。

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.