Applied and Computational Topology

Members

Group lead

Portrait
Prof. Dr. rer. nat. Ulrich Bauer
e-mail
Tel.: +49 (89) 289 - 18361

Team assistant

No image
Nadja Vadlau
e-mail
Tel.: +49 (89) 289 - 17984

Research group

Portrait
M.Sc. Fabian Roll
e-mail
Tel.: +49 (89) 289 - 18376
No image
Jacob Skarby
e-mail
Tel.: 18370
Portrait
M.Sc. Nico Stucki
e-mail
Tel.: +49 (89) 289 - 18362

2024

  • Bauer, Ulrich; Medina-Mardones, Anibal M.; Schmahl, Maximilian: Persistent homology for functionals. Communications in Contemporary Mathematics, 2024 mehr…
  • Bauer, Ulrich; Roll, Fabian: Wrapping Cycles in Delaunay Complexes: Bridging Persistent Homology and Discrete Morse Theory. 40th International Symposium on Computational Geometry (SoCG 2024) (Leibniz International Proceedings in Informatics (LIPIcs)), Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, 2024 mehr…
  • Mody, Tejasvinee Atul; Rolle, Alexander; Stucki, Nico; Roll, Fabian; Bauer, Ulrich; Schneitz, Kay: Topological analysis of 3D digital ovules identifies cellular patterns associated with ovule shape diversity. Development, 2024 mehr…

2023

  • Alpert, Hannah; Bauer, Ulrich; Kahle, Matthew; MacPherson, Robert; Spendlove, Kelly: Homology of configuration spaces of hard squares in a rectangle. Algebraic & Geometric Topology 23 (6), 2023, 2593-2626 mehr…
  • Bauer, Ulrich; Kerber, Michael; Roll, Fabian; Rolle, Alexander: A unified view on the functorial nerve theorem and its variations. Expositiones Mathematicae 41 (4), 2023, 125503 mehr…
  • Bauer, Ulrich; Lenzen, Fabian; Lesnick, Michael: Efficient Two-Parameter Persistence Computation via Cohomology. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023 mehr…
  • Bauer, Ulrich; Natarajan, Vijay; Wang, Bei: Topological Data Analysis and Applications (Dagstuhl Seminar 23192). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023 mehr…
  • Bauer, Ulrich; Rathod, Abhishek; Zehavi, Meirav: On Computing Homological Hitting Sets. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023 mehr…
  • Bauer, Ulrich; Schmahl, Maximilian: Efficient Computation of Image Persistence. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023 mehr…
  • Bauer, Ulrich; Schmahl, Maximilian: Lifespan functors and natural dualities in persistent homology. Homology, Homotopy and Applications 25 (2), 2023, 297-327 mehr…
  • Lenzen, Fabian: Clifford-symmetric polynomials. Communications in Algebra 51 (9), 2023, 3981-4011 mehr…

2022

  • Bauer, Ulrich; Bjerkevik, Håvard Bakke; Fluhr, Benedikt: Quasi-Universality of Reeb Graph Distances. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022 mehr…
  • Bauer, Ulrich; Roll, Fabian: Gromov Hyperbolicity, Geodesic Defect, and Apparent Pairs in Vietoris-Rips Filtrations. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022 mehr…
  • Rolle, Alexander: The Degree-Rips Complexes of an Annulus with Outliers. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022 mehr…

2021

  • Bauer, Ulrich: Ripser: efficient computation of Vietoris–Rips persistence barcodes. Journal of Applied and Computational Topology 5 (3), 2021, 391-423 mehr…
  • Lenzen, Fabian: Shuffling functors and spherical twists on Db(0o). Journal of Algebra 579, 2021, 26-63 mehr…
  • Shit, Suprosanna; Paetzold, Johannes C.; Sekuboyina, Anjany; Ezhov, Ivan; Unger, Alexander; Zhylka, Andrey; Pluim, Josien P. W.; Bauer, Ulrich; Menze, Bjoern H.: clDice - a Novel Topology-Preserving Loss Function for Tubular Structure Segmentation. 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), IEEE, 2021 mehr…

2020

  • Bauer, U.; Edelsbrunner, H.; Jabłoński, G.; Mrozek, M.: Čech–Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology 4 (4), 2020, 455-480 mehr…
  • Bauer, Ulrich; Botnan, Magnus B.; Oppermann, Steffen; Steen, Johan: Cotorsion torsion triples and the representation theory of filtered hierarchical clustering. Advances in Mathematics 369, 2020, 107171 mehr…
  • Bauer, Ulrich; Landi, Claudia; Mémoli, Facundo: The Reeb Graph Edit Distance is Universal. Foundations of Computational Mathematics 21 (5), 2020, 1441-1464 mehr…
  • Bauer, Ulrich; Lesnick, Michael: Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem. In: Topological Data Analysis. Springer International Publishing, 2020 mehr…

2019

  • Bauer, Ulrich; Rathod, Abhishek: Hardness of Approximation for Morse Matching. In: Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics, 2019 mehr…
  • Bauer, Ulrich; Rathod, Abhishek; Spreer, Jonathan: Parametrized Complexity of Expansion Height. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany, 2019 mehr…
  • Carrière, Mathieu; Bauer, Ulrich: On the Metric Distortion of Embedding Persistence Diagrams into Separable Hilbert Spaces. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany, 2019 mehr…

2017

  • Bauer, Ulrich; Kerber, Michael; Reininghaus, Jan; Wagner, Hubert: Phat – Persistent Homology Algorithms Toolbox. Journal of Symbolic Computation 78, 2017, 76-90 mehr…

2016

  • Bauer, Ulrich; Edelsbrunner, Herbert: The Morse theory of Čech and Delaunay complexes. Transactions of the American Mathematical Society 369 (5), 2016, 3741-3762 mehr…
  • Bauer, Ulrich; Fabio, Barbara Di; Landi, Claudia: An Edit Distance for Reeb Graphs. Eurographics Workshop on 3D Object Retrieval, 2016 mehr…

2015

  • Attali, Dominique; Bauer, Ulrich; Devillers, Olivier; Glisse, Marc; Lieutier, André: Homological reconstruction and simplification in R³. Computational Geometry 48 (8), 2015, 606-621 mehr…
  • Bauer, Ulrich; Lesnick, Michael: Induced matchings and the algebraic stability of persistence barcodes. Journal of Computational Geometry, 2015, Vol. 6 No. 2 (2015): Special issue of Selected Papers from SoCG 2014 mehr…
  • Bauer, Ulrich; Munch, Elizabeth; Wang, Yusu: Strong Equivalence of the Interleaving and Functional Distortion Metrics for Reeb Graphs. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany, 2015 mehr…
  • Bauer, Ulrich; Munk, Axel; Sieling, Hannes; Wardetzky, Max: Persistence Barcodes Versus Kolmogorov Signatures: Detecting Modes of One-Dimensional Signals. Foundations of Computational Mathematics 17 (1), 2015, 1-33 mehr…
  • Kwitt, Roland; Huber, Stefan; Niethammer, Marc; Lin, Weili; Bauer, Ulrich: Statistical Topological Data Analysis - a Kernel Perspective. Proceedings of the 28th International Conference on Neural Information Processing Systems - Volume 2 (NIPS'15), MIT Press, 2015 mehr…
  • Reininghaus, Jan; Huber, Stefan; Bauer, Ulrich; Kwitt, Roland: A stable multi-scale kernel for topological machine learning. 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), IEEE, 2015 mehr…

2014

  • Bauer, Ulrich; Edelsbrunner, Herbert: The Morse Theory of Čech and Delaunay Filtrations. Proceedings of the thirtieth annual symposium on Computational geometry, ACM, 2014 mehr…
  • Bauer, Ulrich; Ge, Xiaoyin; Wang, Yusu: Measuring Distance between Reeb Graphs. Proceedings of the thirtieth annual symposium on Computational geometry, ACM, 2014 mehr…
  • Bauer, Ulrich; Kerber, Michael; Reininghaus, Jan: Clear and Compress: Computing Persistent Homology in Chunks. In: Mathematics and Visualization. Springer International Publishing, 2014 mehr…
  • Bauer, Ulrich; Kerber, Michael; Reininghaus, Jan; Wagner, Hubert: PHAT – Persistent Homology Algorithms Toolbox. In: Mathematical Software – ICMS 2014. Springer Berlin Heidelberg, 2014 mehr…
  • Bauer, Ulrich; Lesnick, Michael: Induced Matchings of Barcodes and the Algebraic Stability of Persistence. Proceedings of the thirtieth annual symposium on Computational geometry, ACM, 2014 mehr…

2013

  • Attali, Dominique; Bauer, Ulrich; Devillers, Olivier; Glisse, Marc; Lieutier, André: Homological reconstruction and simplification in R³. Proceedings of the twenty-ninth annual symposium on Computational geometry, ACM, 2013 mehr…

2012

  • Bauer, Ulrich; Kerber, Michael; Reininghaus, Jan: Distributed Computation of Persistent Homology. In: 2014 Proceedings of the Sixteenth Workshop on Algorithm Engineering and Experiments (ALENEX). Society for Industrial and Applied Mathematics, 2012 mehr…

2011

  • Bauer, Ulrich; Lange, Carsten; Wardetzky, Max: Optimal Topological Simplification of Discrete Functions on Surfaces. Discrete & Computational Geometry 47 (2), 2011, 347-377 mehr…

2010

  • Bauer, Ulrich; Polthier, Konrad; Wardetzky, Max: Uniform Convergence of Discrete Curvatures from Nets of Curvature Lines. Discrete & Computational Geometry 43 (4), 2010, 798-823 mehr…
  • Bauer, Ulrich; Schönlieb, Carola-Bibiane; Wardetzky, Max; Simos, Theodore E.; Psihoyios, George; Tsitouras, Ch.: Total Variation Meets Topological Persistence: A First Encounter. AIP Conference Proceedings, AIP, 2010 mehr…

2009

  • Bauer, Ulrich; Polthier, Konrad: Generating parametric models of tubes from laser scans. Computer-Aided Design 41 (10), 2009, 719-729 mehr…

2008

  • Bauer, Ulrich; Polthier, Konrad: Detection of Planar Regions in Volume Data for Topology Optimization. In: Advances in Geometric Modeling and Processing. Springer Berlin Heidelberg, 2008 mehr…

2007

  • Bauer, Ulrich; Polthier, Konrad: Parametric Reconstruction of Bent Tube Surfaces. 2007 International Conference on Cyberworlds (CW'07), IEEE, 2007 mehr…

  • Persistence and Stability of Geometric Complexes
  • Ripser: Efficient Computation of Vietoris-Rips Persistence Barcodes: Ripser is a lean C++ code for the computation of Vietoris–Rips persistence barcodes. It can do just this one thing, but does it extremely well. To see a live demo of Ripser's capabilities, go to live.ripser.org. The computation happens inside the browser (using Emscripten to compile Ripser to WebAssembly, supported on recent browsers).
  • Approximation Algorithms and Parametrized Complexity in Computational Topology
  • Coarse Cohomological Models for Dynamical Systems: The aim of this project is to develop methods for constructing coarse models of the global behavior of a system with complicated dynamics. These models will abstract from individual trajectories and rather provide dynamical information on a discretization of the underlying invariant set in form of a directed graph or a finite state Markov chain. In contrast to existing approaches, our models will incorporate information about cycling motion, generalizing the classic notion of periodic or quasiperiodic dynamics.
  • Topological and Geometric Data Analysis of Random Growth Models
  • Derived Persistence Theory for Functions