Prof Xia’s group focuses on Mathematical AI for Molecular Sciences. We use computational tools from PDE, differential geometry, algebraic topology and statistical learning to study the material, chemical and biomolecular structure, flexibility, dynamics, and functions. In particular, we are interested in topological data analysis (TDA) and generalized persistent models (including weighted persistent homology, persistent Ricci curvature, persistent spectral, etc), TDA-based machine learning/deep learning models, and their applications in perovskite design, catalyst design, polymer design, drug design, biomolecular interaction analysis, chromosome structure analysis, and more generally molecular data analysis from materials, chemistry, and biology.