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.

量子物理学和 数学导致了一些最令人兴奋的数学进步 过去30年。然而，这两个领域仍然存在许多难题。在这个 提案我们研究通过借贷在几何形状中产生的数学问题 来自Alain Conne所谓的量子力学的想法 “非共同”几何形状：代数和几何思想的综合。 我们提出这些想法的新颖应用 到构建交换性和不变性的问题 非共同的几何结构。示例包括更高的维度 表面或拓扑空间，以及非共同代数 起源于量子现象的物理模型。我们会攻击一些 突出的未解决的数学问题。