The boundaries of index theory

指数理论的边界

• 批准号: DP140100906
• 负责人: Prof Fedor Sukochev
• 金额: $ 25.52万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP140100906
• 关键词: boundaries; index; theory

In recent years there has been an influx of new ideas from other disciplines into mathematics and this has led to major advances in many areas, notably geometry and topology. Classical problems have been solved and new perspectives exposed. In this spirit this project will use the methods of noncommutative analysis and noncommutative geometry to extend the mathematical area of spectral geometry. A primary objective is to determine how the geometric and differential structure of certain spaces interacts with the new spectral invariants that will be introduced. The project aims to obtain more subtle and refined information about these spaces. In this fashion it expects to resolve several long standing questions in mathematics.

近年来，来自其他学科的新思想涌入数学，这导致了许多领域的重大进展，特别是几何和拓扑学。经典的问题已经解决，新的视角已经出现。在这个精神下，这个计画将使用非交换分析和非交换几何的方法来扩展光谱几何的数学领域。一个主要的目标是确定某些空间的几何和微分结构如何与将要引入的新谱不变量相互作用。该项目旨在获得有关这些空间的更微妙和更精细的信息。以这种方式，它预计将解决几个长期存在的问题，在数学。