New Foundations for Algebraic Geometry

微积分是数学中最重要、应用最广泛的领域之一。微分范畴是现代微积分的基本理论，其应用贯穿于数学和计算的各个领域。这个项目的目的是使用微分范畴为代数几何创造新的基础，并产生关于代数几何和微分几何之间联系的新知识。这些基础的普遍性将允许代数几何的新应用，对计算机科学具有显著的好处，例如在机器学习和可微编程中。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。

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.