Index Theory and Spectral Flow for Non-unital Spectral Triples and Twisted Spectral Triples

非单位谱三元组和扭曲谱三元组的指数理论和谱流

• 批准号: 41224-2012
• 负责人: Phillips, John
• 金额: $ 0.87万
• 依托单位: University of Victoria
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=568840
• 关键词: Index; Theory; Spectral; Flow; Non

The interaction between theoretical models in quantum physics and mathematics has led to some of the most exciting mathematical advances of the last 30 years. Yet many puzzles remain in both fields. In this proposal we study mathematical questions arising in geometry by borrowing ideas from quantum mechanics in the form of Alain Conne's so-called "noncommutative" geometry: a synthesis of algebraic and geometric ideas. We present novel applications of these ideas to the problem of constructing invariants of both commutative and noncommutative geometric structures. Examples include higher dimensional surfaces or topological spaces, and also noncommutative algebras with origins in physical models of quantum phenomena. We will attack some prominent unresolved mathematical questions.

量子物理理论模型与量子物理理论模型之间的相互作用 数学带来了一些最激动人心的数学进步 在过去的30年里。然而，这两个领域仍然存在许多谜题。在这 建议我们通过借用的方式研究几何中的数学问题 阿兰·康恩所谓的量子力学思想 “非对易”几何：代数和几何思想的综合。 我们展示了这些想法的新应用。 关于构造可换和可换的不变量的问题 非对易几何结构。例子包括更高维度 曲面或拓扑空间，以及具有 起源于量子现象的物理模型。我们会攻击一些人 突出的未解决的数学问题。