New Foundations for Algebraic Geometry

代数几何的新基础

• 批准号: DE230100303
• 负责人: Dr Jean-Simon Lemay
• 金额: $ 24.82万
• 依托单位: Macquarie University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2023
• 资助国家: 澳大利亚
• 起止时间: 2023-01-01 至 2025-12-31
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE230100303
• 关键词: New; Foundations; Algebraic; Geometry

Differential calculus is one of the most important and widely applied areas of mathematics. Differential categories are a modern foundational theory of differential calculus with applications throughout mathematics and computing. This project aims to use differential categories to create new foundations for algebraic geometry, and to generate new knowledge on the connection between algebraic and differential geometry. The generality of these foundations will allow for novel applications of algebraic geometry with significant benefits to computer science, such as in machine learning and differentiable programming. We expect this to build Australia's profile in these important fields and help train the next generation of mathematicians.

微分学是数学中最重要和应用最广泛的领域之一。微分范畴是微分学的现代基础理论，在数学和计算领域都有应用。这个项目的目的是使用微分范畴来创建代数几何的新基础，并产生代数几何和微分几何之间的联系的新知识。这些基础的普遍性将允许代数几何的新应用，对计算机科学有显著的好处，例如机器学习和可微编程。我们希望这将建立澳大利亚在这些重要领域的形象，并帮助培养下一代数学家。