Affine flags, folded galleries and euclidean reflection groups

仿射旗、折叠画廊和欧几里得反射组

• 批准号: DP180102437
• 负责人: A/Prof Anne Thomas
• 金额: $ 22.15万
• 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: 2018
• 资助国家: 澳大利亚
• 起止时间: 2018-09-18 至 2024-06-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP180102437
• 关键词: Affine; flags; folded; galleries; euclidean

This project aims to answer important geometric questions about subvarieties of the affine flag variety which are fundamental to algebraic geometry and number theory. It will answer basic questions about these central objects of mathematics, affine flags and their subspaces, using powerful new methods which combine ideas from geometry and algebra. The project expects to include finding the patterns of non-emptiness of these subvarieties and formulae for their dimension. It will develop and apply new methods which combine folded galleries and the geometry of Euclidean reflection groups, and these methods will have applications in algebraic combinatorics and representation theory. The project will also inspire productive connections between geometric group theory, a new and fast-growing area, and the classical fields of algebraic geometry, algebraic combinatorics and representation theory.

本项目旨在回答关于仿射旗变异子变种的重要几何问题，这些问题是代数几何和数论的基础。它将使用结合几何和代数思想的强大新方法，回答关于这些数学中心对象，仿射标志及其子空间的基本问题。该项目预计将包括寻找这些子变种的非空模式和它们的维数公式。它将开发和应用将折叠长廊和欧几里得反射群几何相结合的新方法，这些方法将在代数组合学和表示理论中得到应用。该项目还将激发几何群论（一个新兴和快速发展的领域）与代数几何、代数组合学和表示理论等经典领域之间的有效联系。