Higgs bundle moduli spaces and spectral data

希格斯丛模空间和光谱数据

• 批准号: DE160100024
• 负责人: Dr David Baraglia
• 金额: $ 21.65万
• 依托单位: The University of Adelaide
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2016
• 资助国家: 澳大利亚
• 起止时间: 2016-06-30 至 2021-06-29
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE160100024
• 关键词: Higgs; bundle; moduli; spaces; spectral

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.

这个项目的目的是利用一种被称为光谱数据的结构来推进对希格斯束的研究。希格斯束是连接几个数学分支的几何结构，包括微分几何、表示理论和数学物理。这将导致新的结果，并解决有关希格斯束模空间及其对称群几何的一些重要开放问题。项目中获得的结果将有利于与希格斯束相互作用的许多数学分支。这些理论基础是科学和工程领域的新创新和新技术发展的基础。