New Foundations for Algebraic Geometry

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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.