The geometry and cohomology of moduli spaces of curves

本项目旨在发展代数几何中模空间的新见解。代数几何是使用几何方法分析代数方程的数学领域，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相关方程集合的几何分析提供了强有力的方法。使用创新的新技术，该项目旨在产生关于基本模空间的新知识。预期的结果包括在澳大利亚建立一个活跃的代数几何学者社区。这些结果将为纯数学和相关科学领域提供显著的好处。

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.