Representation theory: studies of symmetry shadows

表示论：对称阴影的研究

• 批准号: DE190101099
• 负责人: Prof Dr Ulrich Thiel
• 金额: $ 2.32万
• 依托单位: The University of Sydney
• 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: 2019-04-01 至 2019-07-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE190101099
• 关键词: Representation; theory; studies; symmetry; shadows

This project aims to solve fundamental problems in representation theory by combining cutting-edge techniques and developing novel higher level structures. Representation theory is the mathematical study of symmetry, an essential concept in science. Since the 1990s, mathematicians have been observing shadows of a more general notion of symmetry but so far have failed to explain it. Expected outcomes include a structural explanation of these shadows, new mathematical software to understand them and solutions to important conjectures. This project will make a significant contribution to the field of representation theory, with ramifications in mathematical physics and computer science.

该项目旨在通过结合尖端技术和开发新的更高层次的结构来解决表征理论中的基本问题。表示论是对对称性的数学研究，对称性是科学中的一个基本概念。自20世纪90年代以来，数学家们一直在观察一个更普遍的对称性概念的阴影，但到目前为止还未能解释它。预期的成果包括对这些阴影的结构解释，理解它们的新数学软件以及重要问题的解决方案。该项目将对表示论领域做出重大贡献，并在数学物理和计算机科学中产生影响。