Comprehensive Study of Kahler-Ricci Flows

卡勒-里奇流的综合研究

• 批准号: FT150100341
• 负责人: A/Prof Zhou Zhang
• 金额: $ 52.62万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: ARC Future Fellowships
• 财政年份: 2016
• 资助国家: 澳大利亚
• 起止时间: 2016-01-01 至 2022-06-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/FT150100341
• 关键词: Comprehensive; Study; Kahler; Ricci; Flows

The intended outcome of the project is to reveal the deep relation between geometry and topology of underlying spaces. Ricci flow has attracted major attention in pure mathematics over the past 30 years, including ground-breaking contributions by Perelman on Ricci flow regarding the famous Poincare and Thurston's Geometrisation Conjectures. The project focuses on the complex version of Ricci flow: Kahler-Ricci flow. The project plans to explore the Kahler-Ricci flow in the closed and complete non-compact settings and the corresponding versions of Geometric Minimal Model Program; and the Kahler-Ricci flow in the Fano manifold setting and stability conditions.

该项目的预期成果是揭示底层空间的几何和拓扑之间的深层关系。在过去的30年里，Ricci流在纯数学中引起了极大的关注，包括Perelman对Ricci流关于著名的Poincare和Thurston的几何化猜想的突破性贡献。该项目的重点是Ricci流的复杂版本：Kahler-Ricci流。该项目计划探索封闭和完全非紧设置中的Kahler-Ricci流以及相应版本的几何最小模型程序;以及Fano流形设置和稳定性条件中的Kahler-Ricci流。