Mathematical Sciences: Geometric Yang-Mills Theory

首席研究员将继续研究 杨-米尔斯模空间的几何 这将包括 模空间上半经典测度的分析 费米子，和唐纳森不变量的微分 forms. 他还将研究一种通用方法， 建立了4-上非极小杨-米尔斯场的存在性， 对称流形 20世纪80年代初，S. K.唐纳森展示了 杨-米尔斯方程的解与 四维空间上的可微结构 这 这一发现意味着两个四维时空可以 拓扑结构相同（形状相同），但 不同的区别。 没有任何实验能够 发现这些可微结构中的哪一个描述了我们的 时空 首席研究员将继续他的 对唐纳森发现的后果的分析。

The principal investigator will continue his study of the geometry of the Yang-Mills moduli space. This will include an analysis of the semiclassical measure on moduli space with fermions added, and Donaldson invariants in terms of differential forms. He will also investigate a general approach to establishing the existence of non-minimal Yang-Mills fields on 4- manifolds with symmetry. In the early 1980s S.K.Donaldson showed the intimate connection between solutions of the Yang-Mills equations and differentiable structures on four-dimensional space. This discovery meant that two four-dimensional space-times could be topologically the same (have the same shape) but be differentiably distinct. No experiments have been devised to discover which of these differentiable structures describes our space-time. The principal investigator will continue his analysis of the ramifications of Donaldson's discoveries.