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提高我们对离散结构的基本对称性的理解，例如计算机科学和密码学中的基本对称性。这项研究将在纯数学方面产生有关有限群体表示的纯粹数学知识，这些问题已经无法解决一个多世纪。 该奖学金的预期结果包括新算法，可以计算出远远超出目前可能的算法以及对算术困难的新理解。在开发新兴技术方面，将看到对数学具有重要意义的关键好处，以及在复杂理论和大规模计算中对澳大利亚科学家的培训。