Geometric flows and distinguished geometric structures with symmetry

几何流动和独特的对称几何结构

• 批准号: DE190101063
• 负责人: Dr Ramiro Lafuente
• 金额: $ 22.43万
• 依托单位: The University of Queensland
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2019
• 资助国家: 澳大利亚
• 起止时间: 2019-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE190101063
• 关键词: Geometric; flows; distinguished; geometric; structures

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.

本项目旨在对Ricci流和一些最近的复杂几何流进行分析。几何演化方程是现代数学中的一个热门话题，其成功的应用包括在2002-03年通过Ricci流证明了具有百年历史的Poincaré猜想。对具有对称性的解的行为的分析是任何关于这个问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耶夫斯基猜想，这是该领域一个40年的基本开放问题，在数学及其他领域具有重大影响。该项目将进一步加强澳大利亚在几何分析方面的主导作用。