The Ricci curvature of homogeneous spaces. 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 interpla ....The Ricci curvature of homogeneous spaces. 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.Read moreRead less
Deep Learning for Graph Isomorphism: Theories and Applications. This project aims to investigate graph isomorphism, a fundamental problem in graph theory, using deep learning techniques. Solutions to graph isomorphism are in demand by researchers in many fields of science, such as biology, chemistry, computer science, and quantum computing. The project expects to advance knowledge about graph isomorphism and state-of-the-art methodologies for its applications. The expected outcomes include new t ....Deep Learning for Graph Isomorphism: Theories and Applications. This project aims to investigate graph isomorphism, a fundamental problem in graph theory, using deep learning techniques. Solutions to graph isomorphism are in demand by researchers in many fields of science, such as biology, chemistry, computer science, and quantum computing. The project expects to advance knowledge about graph isomorphism and state-of-the-art methodologies for its applications. The expected outcomes include new theoretical insights on combinatorial structures of graphs, efficient heuristic techniques for (maximum) subgraph isomorphism, and structured representation learning. The project should provide significant benefits to research in a wide range of science fields, as well as many real-world applications.Read moreRead less