Workshop on Applied Geometry and Topology for Data Sciences

February 24-28, 2025, ICCM Satellite Conference, Shanghai

Organizers

• Fei Han (NUS, Singapore)
• Theodore Papamarkou (ZJNU, China)
• Zhi Lv (Fudan, China)
• Jie Wu (BIMSA, China)
• Kelin Xia (NTU, Singapore)

Overview

The emergence of data-driven sciences has transformed the landscape of research and has triggered an industrial revolution. Landmark accomplishments, such as AlphaFold’s groundbreaking success in predicting protein structures, highlight this shift. Similarly, the impact of models like ChatGPT and Sora is opening unprecedented avenues for AI-generated content, ushering in a transformative era. Yet, significant hurdles remain, particularly in creating efficient methods for data representation and feature extraction. In this endeavor, computational and discrete geometry/topology provide essential tools for effectively capturing, representing, and modeling data. Geometric/topological deep learning, in particular, have become instrumental in equipping models to navigate the complex geometric and topological aspects found in challenging datasets. The combination of geometric and topological insights with machine learning can redefine the future of data sciences.

This workshop seeks to merge cutting-edge geometric and topological methods with machine learning models rooted in data-driven techniques. We will delve into recent progress in discrete geometry/topology, computational approaches, geometric/topological data analysis, and deep learning that leverages geometry and topology. Topics will include, but are not restricted to,

• Discrete Ricci curvatures; Ollivier Ricci curvature; Forman Ricci curvature; Sectional curvature
• Conformal geometry
• Gromov-Hausdorff distance
• Information geometry
• Index theory
• Discrete exterior calculus and its applications; Discrete Laplace Operator; Discrete Optimal Transport; Discrete mapping; Discrete parametric surface
• Geometric flow and applications (Ricci curvature flow, Mean curvature flow, etc)
• Geometric modelling
• Combinatorial Hodge theory; Hodge Laplacian; Discrete Dirac operator
• Dimension reduction (Manifold learning, Isomap, Laplacian eigenmaps, Diffusion maps, UMAP, MAPPER, Hyperbolic geometry, Poincare embedding, etc)
• Geometric signal processing
• Geometric deep learning: Graph neural networks; Weisfeiler Leman graph isomorphism; Graph neural diffusion; PDE-based GNNs; Equivariant GNNs; Clifford GNN
• Topological deep learning: Simplex neural networks; Cellular neural networks; Sheaf neural networks; Quiver neural networks; combinatorial complex neural networks; hypergraph neural networks
• Geometric and topological methods for generalization in neural networks
• Probabilistic geometric and topological neural networks
• Higher-order network datasets
• Hyperbolic geometric graph; Hyperbolic Deep Neural Networks
• Geometric analysis of deep learning; Geometric GAN; Explainable deep learning; Geometric optimal transportation
• Geometric/topological learning models for molecular data from chemistry, biology, and materials

Activities

To be announced

Venue

To be announced