Symmetric functions and Hodge polynomials

对称函数和霍奇多项式

• 批准号: DP170102648
• 负责人: Prof S. Ole Warnaar
• 金额: $ 22.99万
• 依托单位: The University of Queensland
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2017
• 资助国家: 澳大利亚
• 起止时间: 2017-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP170102648
• 关键词: Symmetric; functions; Hodge; polynomials

This project aims to explain a connection between two seemingly disparate mathematical notions: mixed Hodge polynomials of certain varieties, naturally arising in algebraic geometry, and Macdonald polynomials from the theory of symmetric functions. This project will resolve this connection using symmetric function theory, algebraic combinatorics and representation theory. This project could enhance Australia's international reputation in algebraic combinatorics, combinatorial representation theory and algebraic geometry.

该项目旨在解释两个看似不同的数学概念之间的联系：代数几何中自然出现的某些种类的混合霍奇多项式，以及来自对称函数理论的麦克唐纳多项式。该项目将利用对称函数理论、代数组合学和表示论来解决这种联系。该项目可以提高澳大利亚在代数组合学、组合表示论和代数几何方面的国际声誉。