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

粗几何是根据算子代数研究度量空间的大规模结构的学科。该项目旨在使用粗几何来开发新的方法来研究Callias指数理论及其应用，以及物质的拓扑相，2016年诺贝尔物理学奖就是在这里颁发的。这将在指数理论和其他领域产生新的技术，并解决几个重要问题。结果包括著名的吉列明-斯特恩伯格猜想的非紧致推广，即量子化与约化交换，以及根据算子代数的K理论建立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。

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.