Geometric flows and distinguished geometric structures with symmetry

该项目旨在对复杂几何结构中的Ricci流和一些最近的流进行分析。几何演化方程是现代数学中的一个热门话题，它的成功应用如2002-03年间著名的Poincaré猜想在Ricci流中的证明。对具有对称性的解的行为的分析是任何关于这一主题的成熟理论的重要组成部分。该项目将使用这种分析产生的新工具和想法来解决阿列克谢夫斯基猜想，这是该领域40年来的一个基本开放问题，在数学和其他领域都有重大影响。该项目将进一步加强澳大利亚在几何分析领域的领先地位。

This project aims to carry out analysis for the Ricci flow and a number of recent flows in complex geometry. Geometric evolution equations are a trending topic in modern mathematics, with successful applications such as the celebrated proof of the century-old Poincaré Conjecture in 2002-03 by means of the Ricci flow. An analysis of the behaviour of solutions with symmetry is an essential component in any mature theory on the subject. The project will use the novel tools and ideas resulting from this analysis to address the Alekseevskii Conjecture, a 40-year old fundamental open question in the field with major ramifications in mathematics and beyond. This project will further reinforce Australia's leading role in geometric analysis.