The investigation of stable topological features of geometric complexes and the development of computational methods to leverage this topological information for applications in dynamical systems and data analysis.

# C04

Persistence and Stability of Geometric Complexes

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The following more detailed questions are studied within this project: The definition and construction of geometric complexes from data. Topological persistence. The homology of dynamical systems. The convergence of variants of Crofton's formula obtained with persistent homology to compute intrinsic volumes. The approximation of persistent homology through simplification of the representative complexes.
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**Group:**C. Computation-
**Principal Investigators:**Prof. Dr. Ulrich Bauer, Prof. Dr. Herbert Edelsbrunner -
**Investigators:**Benedikt Fluhr, Fabian Lenzen, Abhishek Rathod **Universities:**Institute of Science and Technology Austria, TU München**Term:**since 2016