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.

该项目的目的是构建新的几何理论的基础上新发现的张量范畴，应用理论来解决开放的问题表示论，代数和范畴论，并建立有利可图的新的联系之间的有影响力的理论仿射群计划和分类空间。几何理论将以一种普遍的方式发展，从物理学中概括经典代数几何和超几何，并专门研究无限多的新理论。这种普遍性确保了几何学在许多科学领域的长期应用有着广泛的基础。其他好处包括加强国际合作和澳大利亚的科学能力。