Mathematical Sciences: Differential Geometry

这项研究将涵盖当代几何学的许多方面。伯克利的几何学家构成了世界上主要的卓越中心之一。所有四名研究人员都一直在几何学方面做出了杰出的贡献，目前的研究计划取得实质性进展的前景非常令人兴奋。向将继续他在子流形的整体微分几何、常曲率空间和对称空间中的单纯形的几何以及Lie变换群的几何和拓扑方面的工作。温斯坦将开展辛几何及其与几何分析和数学物理其他领域的关系的研究。特别是，他将研究辛几何和算子代数之间的联系。这是现代几何学中最令人兴奋的领域之一，而温斯坦被公认为是这项研究的前沿。陈冠希是现代微分几何界的老前辈，他在七十多岁时的持续活动令人振奋。他将主要致力于两个项目。第一个关乎紧浸入和李球几何。第二部分继续与Wolfson所做的关于曲面到经典空间的调和映射的工作。吴将研究调和映射、4-流形的几何以及黎曼几何中的有理同伦。这将继续他在将函数理论与曲率性质联系起来的Kaehler流形方面的出色工作。

This research will cover many aspects of contemporary geometry. The geometers at Berkeley form one of the world's major centers of excellence. All four investigators have consistently made outstanding contributions to geometry and the prospects for substantial progress in the present research program are very exciting. Hsiang will continue his work in global differential geometry of submanifolds, in geometry of simplexes in constant curvature spaces and symmetric spaces and in the geometry and the topology of Lie transformation groups. Weinstein will carry out research in symplectic geometry and its relations with other areas of geometric analysis and mathematical physics. In particular he will investigate the connections between symplectic geometry and operator algebra. This is one of the most exciting areas of modern geometry and Weinstein is universally acknowledged as being at the forefront of this research. Chern is the grand old man of modern differential geometry whose continued activity into his seventies is inspiring. He will work principally on two projects. The first concerns taut immersions and Lie sphere geometry. The second continues work done with Wolfson concerning harmonic maps of a surface into classical spaces. Wu will work on harmonic maps, the geometry of 4-manifolds and rational homotopy in Riemannian geometry. This will continue his excellent work on Kaehler manifolds relating function theory with curvature properties.