Geometric evolution of spaces with symmetries

对称性是许多自然定律和数学构造的基础。这个项目的目的是发展一个全面的理论，著名的里奇流方程在对称性的存在。以前对这个方程的研究已经导致了许多突破性的结果，例如佩雷尔曼对百年历史的庞加莱猜想的著名证明。其成果有望填补数学领域的主要知识空白，为量子场论、相对论和其他领域的应用打开大门。预期的好处包括加强澳大利亚在数学创新方面的领导地位，推进澳大利亚研究领域的国际化，以及增加妇女对STEM的参与。

Symmetries underpin numerous laws of nature and mathematical constructions. This project aims to develop a comprehensive theory of the famous Ricci flow equation in the presence of symmetries. Previous study of this equation has led to many ground-breaking results, such as Perelman's celebrated proof of the century-old Poincaré conjecture. Outcomes are expected to fill major knowledge gaps in mathematics, opening doors to applications in quantum field theory, relativity and other fields. Anticipated benefits include strengthening Australia’s leadership in mathematical innovation, advancing the internationalisation of the Australian research scene, and increasing the involvement of women in STEM.