Distinguished Geometric Structures with Symmetry in Four Dimensions

Ricci流是一种几何演化方程，在几何学、拓扑学、物理学、生物学和图像处理等领域有着重要的应用。这个项目的目的是提供一个完整的描述和分类的高度对称，自相似的解决方案，里奇流在四维。这样的分类对于理解流动的行为是必不可少的，但迄今为止还没有发现。本计画拟将纯数学的联合收割机技术与计算技术结合，以完成此分类。这样的结果将大大提高对四维流形几何的理解，可能导致在几个科学领域以及图像处理中的应用。

The Ricci flow is a geometric evolution equation having significant applications in geometry, topology, as well as in physics, biology and image processing. This project aims to provide a complete description and classification of highly symmetric, self-similar solutions to the Ricci Flow in four dimensions. Such a classification is essential to understanding the behaviour of the flow, but has so far evaded discovery. This project intends to combine techniques from pure mathematics with computational techniques to complete this classification. Such an outcome would greatly improve the understanding of the geometry of four-dimensional manifolds, potentially leading to applications in several areas of science as well as image processing.