Ubiquity of K-theory and T-duality

最近，一种名为K理论的抽象数学工具在两个并不明显相关的物理学领域找到了应用：弦理论中的D-膜的分类，以及凝聚态理论中的拓扑相。本项目旨在利用物理学的思想推动K理论的发展。特别是，该项目旨在将先前的构造，如T-对偶性，推广到循环空间，并发展与强相互作用系统中的拓扑相的分类相关的K-理论。该项目将研究生培训作为实现其目标的重要工具，并加强了澳大利亚在国际研究领域的前沿地位。

An abstract mathematical tool, called K-theory, has recently found application in two, not obviously related, areas of physics: the classification of D-branes in String Theory, and topological phases in Condensed Matter Theory. This project aims to advance the development of K-theory using ideas from physics. In particular, the project aims to generalise previous constructions, such as T-duality, to loop spaces, and to develop the K-theory relevant to the classification of topological phases in strongly interacting systems. This project involves postgraduate training as a crucial tool in achieving its aims and enhances Australia's position at the forefront of international research.