New constructions and techniques for tensor categories

张量类别的新结构和技术

• 批准号: DP210100251
• 负责人: A/Prof Kevin Coulembier
• 金额: $ 29.71万
• 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://dataportal.arc.gov.au/RGS/Web/Grants/DP210100251
• 关键词: New; constructions; techniques; 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.

这个项目的目标是在张量范畴的结构理论中取得根本性的进展。这类范畴在数学、物理等众多领域发挥着至关重要的作用。新的方法，理论和例子将开发，启发代数，表示论和几何。然后，这些将被应用在张量范畴的基础研究（disproving）在该领域的几个最重要的开放式结构。这将为其他领域的应用开辟新的前景，特别是在表征理论中。其他好处包括加强国际合作和澳大利亚的科学能力。