Braid groups via representation theory and machine learning

本课题旨在研究低维拓扑中具有重要意义的辫子群的表示理论问题。该项目期望在围绕纽结不变量的中心开放问题上取得重大进展，并创建在表示理论中具有广泛适用性的新工具。它将率先使用研究人员最近开发的范畴理论和机器学习中的高度创新方法。该项目的潜在好处包括：解决关于辫子群的重要长期猜测，开发对表示理论具有重大影响的新兴技术，以及在关键研究领域培训澳大利亚科学家。

This project aims to address questions about the representation theory of braid groups with important consequences in low-dimensional topology. This project expects to make significant progress on central open problems surrounding knot invariants, and create new tools that will have wide applicability in representation theory. It will pioneer the use of highly innovative methods from category theory and machine learning recently developed by the investigators. Potential benefits of this project include: the resolution of important long-standing conjectures about braid groups, the development of emerging technology with significant implications for representation theory, and the training of Australian scientists in a vital area of research.