Elliptic representation theory: the study of symmetries across geometry, algebra and physics

椭圆表示理论：跨几何、代数和物理学的对称性研究

• 批准号: DE190101222
• 负责人: Dr Gufang Zhao
• 金额: $ 24.73万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2019
• 资助国家: 澳大利亚
• 起止时间: 2019-01-01 至 2024-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE190101222
• 关键词: Elliptic; representation; theory; study; symmetries

This project aims to study symmetries which control geometry and physics of four-dimensional manifolds. Representation theory is the area in pure mathematics which studies symmetries coming from geometry, algebra, and physics. The expected outcome is new families of quantum algebra, their character formulas, and a solution to an infinite-dimensional moduli problem. This project will further deepen the mathematical knowledge of symmetries, and show unexpected new connections between different areas of pure mathematics and mathematical physics.

这个项目旨在研究控制四维流形的几何和物理的对称性。表示论是纯数学的一个领域，它研究来自几何、代数和物理的对称性。预期的结果是量子代数的新家庭，他们的特征公式，并解决一个无限维模问题。该项目将进一步深化对称性的数学知识，并展示纯数学和数学物理不同领域之间意想不到的新联系。