Higgs bundle moduli spaces and spectral data

该项目的目的是利用一种被称为光谱数据的结构来推进希格斯束的研究。希格斯丛是连接包括微分几何、表示论和数学物理在内的几个数学分支的几何结构。这将导致新的结果，并解决与Higgs丛模空间及其对称群的几何有关的一些重要的公开问题。在该项目中获得的结果应该会对与希格斯束相互作用的许多数学分支有利。这些理论基础是科学和工程领域的新创新和新技术得以发展的基础。

The aim of this Project is to advance the study of Higgs bundles using a construction known as spectral data. Higgs bundles are geometric structures bridging several branches of mathematics including differential geometry, representation theory and mathematical physics. This should lead to new results and solve some important open problems concerning the geometry of Higgs bundle moduli spaces and their symmetry groups. The results obtained in the Project should benefit the many branches of mathematics interacting with Higgs bundles. Such theoretical underpinnings are the basis on which new innovations and technologies in science and engineering may be developed.