New dualities in modular representation theory

模表示理论中的新对偶性

• 批准号: DP180102563
• 负责人: A/Prof Oded Yacobi
• 金额: $ 19.04万
• 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: 2018
• 资助国家: 澳大利亚
• 起止时间: 2018-04-02 至 2021-06-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP180102563
• 关键词: New; dualities; modular; representation; theory

This project aims to introduce new geometric techniques in the modular representation theory of the general linear group, and resolve fundamental questions about modular representations of orthogonal and symplectic groups. Representation theory, the mathematical study of symmetry, has applications in many areas ranging from physics to computer science. The modular setting, where the characteristic of the field is positive, is a source of the deepest conjectures in this subject. Recent breakthroughs have provided approaches to some problems in modular representation theory that were previously inaccessible. This project will promote research at the forefront of the field, and help maintain Australia's international standing. It will train Australian postgraduates, who will be able to apply their research skills in industry, and strengthen the country's ties to a vibrant international community.

这个项目的目的是在一般线性群的模表示理论中引入新的几何技术，并解决正交和辛群的模表示的基本问题。表示论是对对称性的数学研究，在从物理学到计算机科学的许多领域都有应用。模块化设置，其中领域的特点是积极的，是在这个问题上最深层次的知识来源。最近的突破提供了一些方法，在模块化表示理论，以前无法访问的问题。该项目将促进该领域前沿的研究，并有助于保持澳大利亚的国际地位。它将培养澳大利亚的研究生，使他们能够在工业中应用他们的研究技能，并加强该国与充满活力的国际社会的联系。