Venue

The widespread availability of data, coupled with advancements in computational power, has opened up new possibilities for leveraging the power of mathematics and artificial intelligence (AI) in the sciences. Nevertheless, the effective representation and featurization of data remain central challenges in AI-based data analysis today, particularly for data with complex structures, such as those arising from biological and material science. Computational and discrete geometry and topology have achieved noteworthy success in characterizing and modeling this data. Specifically, geometric deep learning has significantly enhanced the capacity to develop models for data exhibiting complex topological and geometric structures. The combination of geometric and topological methods with learning models holds great potential for a fundamental transformation in data sciences. Given that the field thrives on a combination of deep mathematical methodologies and challenging data, it is imperative to integrate both facets.

This workshop presents recent advancements in both the theories of algebraic topology and geometry, as well as their applications within AI and data science. The topics covered will include but are not limited to:

• Geometric deep learning, graph neural network (GNN)

• Topological deep learning, simplex neural network, sheaf neural network

• Applications such as protein structure prediction, protein folding, and molecular dynamics

• Path complex, neighborhood complex, and their persistent homology

• Discrete Ricci curvatures, Ollivier Ricci curvature, Forman Ricci curvature

• Combinatorial Hodge theory, Hodge Laplacian, discrete Dirac operator