Geometry of Character Varieties

The proposed research addresses fundamental problems in representation theory and arithmetic geometry, with significant implications for mathematical sciences and broader applications. This project will develop novel methodologies to computing intricate algebraic and geometric objects, advancing our understanding and capabilities in crucial areas of pure mathematics. This project will therefore align with Australias STEM priorities and offer excellent training ground for young Australian researchers. The outcomes of this project are both diverse and impactful. They address deep questions in foundational areas of pure mathematics. Among expected applications are development of novel optimisation algorithms with potential applications across various industries. Furthermore, by leveraging the combined expertise in Canberra, Adelaide, Brisbane, and Auckland the project will strengthen Australias educational and research landscape, fostering a culture of innovation and exc