Mathematical Sciences: Minimal Surfaces, Complex and Symplectic Geometry

首席研究员会提出一个最小化的理论 Kahler流形的曲面 将特别强调 复切点与 这些曲面的黎曼几何和稳定性质。 他还将调查 向量丛的特征形式和 束映射 他将扩展他过去在调和映射上的工作 给无数格拉斯曼人 辛拓扑的新研究 将开始。 极小曲面是数学家的肥皂剧。 异国 最小的表面可以通过将普通的弯曲线 变成肥皂水溶液 朝着一个完整的 近年来，人们对这些表面有了了解。 现在，首席研究员和其他几何学家正在使用 这些新理论与新兴的 Kahler流形的几何物理学

The principal investigator will develop a theory of minimal surfaces for Kahler manifolds. Special emphasis will be paid to the relationship between the complex tangent points and the Riemannian geometry and stability properties of these surfaces. He will also investigate the relationship between the characteristic forms of vector bundles and the singularities of bundle maps. And he will extend his past work on harmonic maps to infinite Grassmannians. A new study of symplectic topology will begin. Minimal surfaces are the mathematicians' soap films. Exotic minimal surfaces can be formed by dipping ordinary curved wires into a soap and water solution. Great progress toward a complete understanding of these surfaces has been made in recent years. Now, the principal investigator and other geometers are using these new theories to build connections with the emerging geometrical physics of Kahler manifolds.