The geometry and cohomology of moduli spaces of 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 high impact publications, international collaborations, and the establishment of an active community of algebraic geometers in Australia. These outcomes should provide significant benefits to pure mathematics and related scientific fields.