Institute of Geometry

Michael Kerber

Univ.-Prof. Dr.
Phone:+43-316-873-8446
Email: lastname AT tugraz.at
[dblp] [google scholar]

Mini-CV

I am professor at Graz University of Technology at the Institute of Geometry since 2015. Before that, I had postdoc positions at Max Planck Institute for Informatics, Saarbrücken, Stanford University, and the Institute of Science and Technology Austria. I graduated in 2009 at Max Planck Institute for Informatics under the supervision of Kurt Mehlhorn and Michael Sagraloff.

Research interests

My research focuses on the design, analysis and implementation of efficient algorithms in algebraic topology, computational geometry, real algebraic geometry, and symbolic computation, with the goal to bridge the gap between mathematical theory and application areas. My current emphasis lies on the theory of persistent homology and its applications in the analysis of scientific data.

Selected Publications

for a complete list, click here

Angel Javier Alonso, Michael Kerber, Tung Lam, Michael Lesnick: Delaunay Bifiltrations of Functions on Point Clouds. Symposium on Discrete Algorithms (SODA 2024), pp.4872-4891. Available at arXiv:2310.15902
Havard Bjerkevik, Magnus Botnan, Michael Kerber: Computing the interleaving distance is NP-hard. Foundations of Computational Mathematics 20, pp.1237-1271, 2020.
Aruni Choudhary, Michael Kerber, Sharath Raghvendra: Improved Topological Approximations by Digitization. Symposium on Discrete Algorithms (SODA 2019).
Michael Kerber, Dmitriy Morozov, Arnur Nigmetov: Geometry helps to Compare Persistence Diagrams. Journal of Experimental Algorithms 22, 2017.
Ulrich Bauer, Michael Kerber, Jan Reininghaus: Distributed Computation of Persistent Homology. Algorithm Engineering and Experiments (ALENEX 2014), pp.31-38.
Chao Chen, Michael Kerber: An Output Sensitive Algorithm for Persistent Homology. Computational Geometry: Theory and Applications 46 (4) pp. 435-447, 2013 - Special Issue on the 27th Annual Symposium on Computational Geometry.
Paul Bendich, Herbert Edelsbrunner, Michael Kerber: Computing Robustness and Persistence for Images. IEEE Transactions on Visualization and Computer Graphics 16 (2010), pp. 1251-1260.
Arno Eigenwillig, Michael Kerber, Nicola Wolpert: Fast and Exact Geometric Analysis of Real Algebraic Plane Curves. Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 2007), pp. 151-158.

PhD Students

I had/have the privilege to be co-supervised by the following people in their PhD project (pardon the categorical joke):

Aruni Choudhary (2013-2017): Approximation Algorithms for Vietoris-Rips and Cech filtrations. Afterwards postdoc at Freie Universität Berlin
Hannah Schreiber (2015-2019): Algorithmic Aspects in standard and non-standard Persistent Homology. Afterwards postdoc at St.Louis University
Arnur Nigmetov (2015-2020): Comparison of Topological Summaries. Afterwards postdoc at Lawrence Berkeley National Labs
René Corbet (2017-2020): Improvements to the pipeline of Multiparameter Persistence. Afterwards postdoc at KTH Stockholm
Bianca Dornelas (2019-2023): k-fold covers, sparsifications and simplicial collapses
Florian Russold (2021-)
Angel Javier Alonso Hernandez (2021-)
Jan Jendrysiak (2021-)
Matthias Söls (2022-)

Software

PHAT is collection of efficient implementations of persistent homology
DIPHA is another package for the efficient computation of persistent homology on distributed systems
HERA is an efficient implementation for computing bottleneck and Wasserstein distances of persistence diagrams.
SOPHIA is an efficient implementations for computing persistence diagrams of simplicial complexes connected by simplicial maps.
mpfree computes the minimal presentation of a free implicit representation.
Also check out the CGAL webpage, especially the algebraic kernel package

Other

Article (in German) about our research group (from 2020).

Teaching

see here