The Ricci curvature of homogeneous spaces

齐性空间的几何是一个研究领域，在许多领域都有应用，包括拓扑学、调和分析、相对论和量子理论。该项目旨在解决这一领域的一个基本问题，即齐次度量的规定Ricci曲率问题，并解决与Ricci迭代存在性和收敛性密切相关的重要问题。此外，该项目旨在利用几何和代数之间的相互作用，为酉李代数表示分类的物理重要问题提供新的见解。该项目预计将促进跨学科的互动，从而在一系列领域取得令人兴奋的发展。

The geometry of homogeneous spaces is an area of research with applications in numerous fields, including topology, harmonic analysis, relativity and quantum theory. This project aims to resolve a fundamental problem in this area, known as the prescribed Ricci curvature problem for homogeneous metrics, and to settle the important and closely related question of Ricci iteration existence and convergence. Moreover, the project aims to exploit the interplay between geometry and algebra to provide new insight into the physically significant problem of classifying unitary Lie algebra representations. This project is expected to facilitate interdisciplinary interaction leading to exciting developments across a range of fields.