Discovery Projects - Grant ID: DP210100251

发现项目 - 拨款 ID：DP210100251

• 批准号: ARC : DP210100251
• 负责人: Dr Kevin Coulembier
• 金额: $ 42.29万
• 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: 2022
• 资助国家: 澳大利亚
• 起止时间: 2022-01-01 至 2024-12-31
• 项目状态: 已结题
• 来源: https://researchdata.edu.au/discovery-projects-grant-id-dp210100251/1782657
• 关键词: Discovery; Projects; Grant; ID; DP210100251

New constructions and techniques for tensor categories. The goal of this project is to make fundamental advances in the structure theory of tensor categories. Such categories play crucial roles in numerous fields of mathematics, physics and beyond. New methods, theory and examples will be developed, inspired by algebra, representation theory and geometry. These will then be applied in the foundational study of tensor categories for (dis)proving several of the most important open conjectures in the field. This will open new perspectives for applications in other areas, most notably in representation theory. Other benefits include enhanced international collaboration and scientific capacity in Australia.

张量范畴的新构造和新技巧。这个项目的目标是在张量范畴的结构理论方面取得根本性的进展。这些类别在数学、物理和其他许多领域发挥着至关重要的作用。在代数、表示理论和几何的启发下，将发展新的方法、理论和例子。然后，这些将被应用于张量范畴的基础研究中，以证明该领域中几个最重要的开放猜想。这将为其他领域的应用开辟新的视角，尤其是在表征理论方面。其他好处包括加强国际合作和澳大利亚的科学能力。