This workshop is directed at the participants in the Dual Trimester Program "Geometric Statistics: theory, application, and computation". It is not possible to apply only for this workshop.
Researchers from the HCM, in particular, early-career researchers, are welcome upon request.
Organizers:
- Shreya Arya (University of Pennsylvania)
- Stephan Huckemann (University of Göttingen)
- Wilderich Tuschmann (Karlsruhe Institute of Technology)
- Emil Saucan (Technion)
- Kelin Xia (Nanyang Technological University)
Description:
Our workshop focuses on the integration of geometric and topological methodologies into modern statistical learning, with particular emphasis on data defined over both smooth and singular spaces. By combining tools from geometric data analysis--such as Ricci curvature, Riemannian and sub-Riemannian structures, Laplacians, optimal transport, and information geometry--with techniques from topological data analysis, including persistent homology and Hodge theory, the program aims to develop richer data representations that capture both local geometric features and global structural properties. A central theme is the extension of statistical and learning frameworks from smooth manifolds to singular and stratified spaces, such as graphs, simplicial complexes, and other higher-order networks, which naturally arise in modern data analysis. This unified perspective enables geometric and topological methods to effectively model complex, non-Euclidean data across multiple scales and irregular domains. Moving beyond traditional linear assumptions, the workshop highlights advances in non-Euclidean statistics and probability ranging from manifolds to singular settings. Emphasis is placed on both theoretical foundations and computational frameworks, fostering scalable, robust, and interpretable models. Overall, the workshop aims to promote a synergistic paradigm in which geometry, topology, and learning on smooth and singular spaces jointly drive innovation in statistics and data science.