Unlocking the secrets of modular representations

解开模块化表示的秘密

• 批准号: FL230100256
• 负责人: Prof Geordie Williamson
• 金额: $ 229.9万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Australian Laureate Fellowships
• 财政年份: 2024
• 资助国家: 澳大利亚
• 起止时间: 2024-09-02 至 2029-09-02
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/FL230100256
• 关键词: Unlocking; secrets; modular; representations

This Fellowship aims to greatly increase our understanding of the fundamental symmetries of discrete structures, like those present in computer science and cryptography. The research will generate transformative new knowledge in pure mathematics concerning the representations of finite groups, problems that have been unsolved for over a century. Expected outcomes of this fellowship include new algorithms to compute far beyond what is currently possible and a new understanding of the arithmetic difficulties present. Key benefits will be seen in the development of an emerging technology with significant implications for mathematics, and the training of Australian scientists in sophisticated theory and large-scale computation in concert.

该奖学金旨在极大地增进我们对离散结构基本对称性的理解，例如计算机科学和密码学中存在的对称性。这项研究将在纯数学领域产生关于有限群表示的革命性新知识，这些问题一个多世纪以来一直没有得到解决。 该奖学金的预期成果包括计算远远超出目前能力的新算法，以及对当前算术困难的新理解。主要好处将体现在对数学具有重大影响的新兴技术的开发，以及澳大利亚科学家在复杂理论和大规模计算方面的培训。