Braid groups via representation theory and machine learning

通过表示理论和机器学习编织辫子群

• 批准号: DP230100654
• 负责人: A/Prof Oded Yacobi
• 金额: $ 27.22万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2023
• 资助国家: 澳大利亚
• 起止时间: 2023-03-03 至 2026-03-02
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP230100654
• 关键词: Braid; groups; via; representation; theory

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.

这个项目的目的是解决问题的表示理论的辫子群的重要后果，在低维拓扑。该项目预计将在围绕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类别理论和机器学习的高度创新方法。该项目的潜在好处包括：解决关于辫群的重要的长期问题，发展对表征理论有重大影响的新兴技术，以及在一个重要的研究领域培训澳大利亚科学家。