Title: De Rham-Hodge Methods for Data on Manifolds

 

 

Abstract: Topological data analysis (TDA) provides powerful tools for understanding the structure of complex, high-dimensional data, yet most existing methods focus on points, graphs, or simplicial complexes. In this talk, I will present our recently developed de Rham-Hodge-based frameworks for analyzing data on manifolds. These methods provide effective and efficient ways to capture both the topological and geometric information of data and are well-suited for integration with machine learning tasks. I will demonstrate their usefulness through applications in mathematical biology, including protein-ligand binding affinity prediction, single-cell RNA velocity analysis, medical image classification, and B-factor analysis.

 

 

 

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