Categorical geometry and perfect group schemes

分类几何和完美群方案

• 批准号: FT220100125
• 负责人: A/Prof Kevin Coulembier
• 金额: $ 62.34万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: ARC Future Fellowships
• 财政年份: 2023
• 资助国家: 澳大利亚
• 起止时间: 2023-06-30 至 2027-06-29
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/FT220100125
• 关键词: Categorical; geometry; perfect; group; schemes

The aims of this project are to construct novel geometric theories based on newly discovered tensor categories, to apply the theories to solve open problems in representation theory, algebra and category theory, and to establish profitable new connections between the influential theories of affine group schemes and classifying spaces. The geometric theories will be developed in a universal way, generalising both classical algebraic geometry and super geometry from physics, and specialising to infinitely many new theories. This universality ensures a significantly broader basis for long term applications of geometry in many areas of science. Other benefits include enhanced international collaboration and scientific capacity in Australia.

该项目的目的是基于新发现的张量范畴构建新的几何理论，应用这些理论来解决表示论、代数和范畴论中的开放问题，并在仿射群方案和有影响力的理论之间建立有益的新联系。对空间进行分类。几何理论将以通用的方式发展，推广经典代数几何和物理学的超几何，并专门研究无限多种新理论。这种普遍性确保了几何学在许多科学领域的长期应用拥有更广泛的基础。其他好处包括增强澳大利亚的国际合作和科学能力。