Persistence and stability of geometric complexes (C04)

• Subject Area: Mathematics
• Term: from 2016 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 195170736

We study geometric complexes, that is, simplicial complexes constructed from geometric data, and their multiscale topological properties, using homological and Morse-theoretic methods. These complexes are defined for metric spaces, finite or infinite, Euclidean and general, and their persistent homology enjoys a stability property, which ensures that they serve, in a precise sense, as a structure-preserving discretization of the shape at a given scale with guaranteed topological properties. This allows for the treatment of the discrete case (finite point clouds) and the continuous case in a unified way. We investigate extensions and applications of this theory.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 109: Discretisation in Geometry and Dynamics
• International Connection: Austria
• Applicant Institution: Technische Universität Berlin
• Project Heads: Professor Dr. Ulrich Alexander Bauer; Professor Dr. Herbert Edelsbrunner