Homogeneous Space

Homogeneous spaces, mathematical structures representing spaces with symmetries, are increasingly central to various fields. Current research focuses on leveraging their properties in quantum information theory to characterize randomness and symmetry, in machine learning to develop efficient and equivariant neural networks (including those based on Gaussian processes and stochastic differential equations), and in geometric deep learning to design algorithms for data residing on non-Euclidean spaces. These advancements offer powerful tools for modeling complex systems with inherent symmetries, leading to improved performance in applications ranging from time series analysis to molecular modeling.