Mathematical Sciences: The Geometry and Topology of Moduli Spaces

主要研究者将继续研究瞬子模空间的同伦。他们将使用瞬子和全纯丛之间的关系来继续与他们最近解决Atiyah-Jones猜想有关的工作。主要研究人员还将研究紧凑的、具有正标量曲率的非齐次爱因斯坦流形。该奖项将支持在微分几何和全球分析的一般领域的研究。微分几何是研究空间几何和定义在该空间上的解析概念之间的关系的学科。全局分析是通过拼凑局部信息来研究空间的整体几何和拓扑性质的学科。这些领域的数学在其他科学中的应用包括复杂分子结构、液体-气体边界和宇宙的大尺度结构。

The principal investigators will continue their study of the homotopy of instanton moduli spaces. They will use the relationship between instantons and holomorphic bundles to continue work related to their recent solution of the Atiyah- Jones conjecture. The principal investigators will also study families of compact, non-homogeneous Einstein manifolds of positive scalar curvature. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.