Advances in index theory and applications

该项目旨在开发新的技术来研究无限维束的几何分析，以及以Cantor集为纤维的病理空间的几何分析，这些分析出现在分数量子霍尔效应和拓扑物质的模型中，这些领域获得了1998年和2016年诺贝尔奖。根据申请人在该领域的专业知识，该项目将涉及研究生和博士后培训，以提高澳大利亚在几何分析国际研究前沿的地位。最终，该项目将通过开发新技术来解决具有挑战性的问题，并指导HDR学生和ECR，从而提高澳大利亚在指数理论领域的领先地位。

The project aims to develop novel techniques to investigate Geometric analysis on infinite dimensional bundles, as well as Geometric analysis of pathological spaces with Cantor set as fibre, that arise in models for the fractional quantum Hall effect and topological matter, areas recognised with the 1998 and 2016 Nobel Prizes. Building on the applicant’s expertise in the area, the project will involve postgraduate and postdoctoral training in order to enhance Australia’s position at the forefront of international research in Geometric Analysis. Ultimately, the project will enhance Australia's leading position in the area of Index Theory by developing novel techniques to solve challenging conjectures, and mentoring HDR students and ECRs.