Hodge Number

Hodge numbers are topological invariants characterizing the structure of complex geometric objects, particularly relevant in algebraic geometry and related fields. Current research focuses on leveraging Hodge numbers, often through Hodge decompositions and associated Laplacians, within machine learning frameworks, including neural networks and contrastive learning approaches, to analyze and predict properties of complex data structures like simplicial complexes and graphs. This work has implications for diverse applications, ranging from classifying edge flows in networks to predicting properties of materials with topological features, highlighting the increasing importance of Hodge theory in data analysis and scientific modeling.