Mathematical Sciences: Applications of Differential Geometryand Global Analysis to Low Dimensional Topology

首席研究员将继续使用几何和分析技术研究光滑四维流形的结构。本研究的核心将是闭合光滑4-流形的同伦类型的分类。西蒙·唐纳森（Simon Donaldson）开创的规范理论方法是这项工作的最初推动力。它结合了理论物理、几何、分析和拓扑学，是近年来最引人注目的跨学科发展之一。

The principal investigator will continue his study of the structure of smooth 4-dimensional manifolds using techniques from geometry and analysis. At the heart of this investigation will be the classification of the homotopy types of closed smooth 4- manifolds. Gauge theoretic methods pioneered by Simon Donaldson were the original impetus for much of this work. In its marriage of theoretical physics, geometry, analysis, and topology, it is one of the most dramatic cross-disciplinary developments of recent years.