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Method Development Unit
Project
MDU-4
Efficient Multi-Parameter Persistent Homology
Project Heads
Fabian Lenzen
Project Members
Fabian Lenzen
Project Duration
01.01.2026 – 31.12.2026
Located at
TU Berlin
Description
We investigate the optimization potential of computing resolutions of the multiparameter persistent homology of a finite metric space. We implement our methods in software, and apply them to biology related data analysis and for advancing topology informed machine learning.
External Website
Related Publications
Publications and Preprints
Lenzen, Fabian. 2026. “Computing Flat-Injective Presentations of Multigraded Persistence Modules.” To appear in: Homology, Homotopy and Applications. ArXiv: 2401.06008
Ulrich Bauer, Fabian Lenzen, Michael Lesnick. 2026. “Dualities in Multiparameter Persistence”. ArXiv: 2603.18224.
Fabian Lenzen, Leon Renkin. 2025. “Persistent Cycle Representatives and Generalized Landscapes for Codimension 1 Persistent Homology”. ArXiv: 2512.09668.
Software
Lenzen, Fabian. 2025. FlangePresentations.jl. A Julia package for computing Flat-Injective presentation matrices. https://gitlab.com/flenzen/flangepresentations.jl.
Lenzen, Fabian. 2023. 2pac. A C++ software package for computing two-parameter persistent homology and cohomology. https://gitlab.com/flenzen/2pac.
Related Pictures