Coarse Geometry: a novel approach to the Callias index & topological matter

粗几何：一种新的 Callias 索引方法

• 批准号: DP200100729
• 负责人: Prof Mathai Varghese
• 金额: $ 35.64万
• 依托单位: The University of Adelaide
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2020
• 资助国家: 澳大利亚
• 起止时间: 2020-07-01 至 2024-12-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP200100729
• 关键词: Coarse; Geometry; novel; approach; Callias

Coarse geometry is the study of the large-scale structure of metric spaces, in terms of operator algebras. This project aims to use coarse geometry to develop novel approaches to Callias index theory and its applications, and to topological phases of matter, where the Nobel Prize in physics in 2016 was awarded. This will yield new techniques in index theory and other areas, and solutions to several important problems. Outcomes include a noncompact generalisation of the famous Guillemin-Sternberg conjecture that quantisation commutes with reduction, and new models of topological phases of matter in terms of K-theory of operator algebras. This project will benefit Australia by reinforcing its position in these highly active areas in science.

粗几何是研究度量空间的大尺度结构，根据算子代数。该项目旨在使用粗糙几何来开发Callias指数理论及其应用的新方法，以及2016年诺贝尔物理学奖授予的物质拓扑相。这将产生指数理论和其他领域的新技术，并解决几个重要问题。结果包括著名的Guillemin-Sternberg猜想的非紧化推广，即量子化与约简交换，以及根据算子代数的k理论的物质拓扑相的新模型。该项目将加强澳大利亚在这些高度活跃的科学领域的地位，从而使澳大利亚受益。