The Ricci curvature of homogeneous spaces (2018-2022)

The geometry of homogeneous spaces is a vibrant area of research with applications in numerous fields, including topology, harmonic analysis, relativity and quantum theory. The 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. The proposed research is expected to facilitate interdisciplinary interaction leading to exciting developments across a range of fields.