The geometry and cohomology of moduli spaces of curves

曲线模空间的几何和上同调

• 批准号: DE180101360
• 负责人: Dr Anand Deopurkar
• 金额: $ 23.5万
• 依托单位: The Australian National University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2018
• 资助国家: 澳大利亚
• 起止时间: 2018-01-02 至 2024-12-07
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE180101360
• 关键词: geometry; cohomology; moduli; spaces; curves

This project aims to develop new insights on moduli spaces in algebraic geometry. Algebraic geometry is the field of mathematics that uses geometric methods to analyse algebraic equations, with wide applications ranging from cryptography to genetics. Moduli spaces in algebraic geometry provide powerful methods to geometrically analyse collections of related equations. Using innovative new techniques, the project aims to generate new knowledge about fundamental moduli spaces. Expected outcomes include the establishment of an active community of algebraic geometers in Australia. These outcomes should provide significant benefits to pure mathematics and related scientific fields.

这个项目旨在发展代数几何中模空间的新见解。代数几何是一个数学领域，它使用几何方法来分析代数方程，从密码学到遗传学都有广泛的应用。代数几何中的模空间为几何分析相关方程的集合提供了强有力的方法。利用创新的新技术，该项目旨在产生有关基本模空间的新知识。预期成果包括在澳大利亚建立一个活跃的代数几何学家社区。这些成果将为纯数学和相关科学领域带来巨大的利益。