Homology theories in quantum topology

该项目旨在解决一个25年来主要的开放问题，该问题涉及结的量子拓扑，3维和4维空间与更高表示理论，代数结构的隐藏对称性研究。该项目期望使用结点的同调不变量和量子群的高级表示理论来构建备受期待的3维和4维流形的不变量，并通过简化基本构建块来计算这些不变量。预期的结果还包括与数学不同领域的新联系。预计这将通过促进数学和理论物理领域的合作，吸引学生和杰出的研究访问者，从而使澳大利亚科学受益。

This project aims to resolve a major 25-year-old open problem relating the quantum topology of knots, 3- and 4-dimensional spaces to higher representation theory, the study of hidden symmetries of algebraic structures. The project expects to use homological invariants of knots and the higher representation theory of quantum groups to construct highly anticipated invariants of 3- and 4-dimensional manifolds and tools to compute these invariants by reduction to basic building blocks. Expected outcomes also include new connections to diverse areas in mathematics. This is expected to benefit Australian science by invigorating collaboration in mathematics and theoretical physics and by attracting students and distinguished research visitors.