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Michael Kerber
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Research Interests
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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.
Publications (in reverse chronological order)
- Herbert Edelsbrunner, Michael Kerber: Dual Complexes of Cubical Subdivisions of R^n. Discrete and Computational Geometry 47 (2012), pp.393-414 (pdf) © Springer, 2012.
- Herbert Edelsbrunner, Michael Kerber: Alexander Duality for Functions: the Persistent Behavior of Land and Water and Shore. arXiv:1109.5052
- Gavin Brown, Michael Kerber, Miles Reid: Fano 3-folds in codimension 4, Tom and Jerry, Part I. Accepted for Compositio Mathematica. Available at arXiv:1009.4313
- Michael Kerber, Michael Sagraloff: A Worst-case Bound for Topology Computation of Algebraic Curves. Journal of Symbolic Computation 47 (2012), pp.239-258. Available at arXiv:1104.1510
- Michael Kerber, Michael Sagraloff: Efficient Real Root Approximation. Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation (ISSAC 2011), pp. 209-216 (pdf, ps) Supplementary material: pdf, ps
© ACM, 2011. This is the authors' version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ISSAC'11: International Symposium on Symbolic and Algebraic Computation Proceedings
An improved version of the result is available as Root Refinement for Real Polynomials arXiv:1104.1362
- Chao Chen, Michael Kerber: An Output Sensitive Algorithm for Persistent Homology. Proceedings of the 27th Annual Symposium on Computational Geometry, pp. 207-215 (SoCG 2011) (pdf, ps)
© ACM, 2011. This is the authors' version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in the Proceedings of the 2011 Annual Symposium on Computational Geometry (SoCG'11)
- Eric Berberich, Michael Hemmer, Michael Kerber: A Generic Algebraic Kernel for Non-linear Geometric Applications. Proceedings of the 27th Annual Symposium on Computational Geometry, pp. 179-186 (SoCG 2011) (pdf, ps)
© ACM, 2011. This is the authors' version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in the Proceedings of the 2011 Annual Symposium on Computational Geometry (SoCG'11)
- Eric Berberich, Dan Halperin, Michael Kerber, Roza Pogalnikova: Deconstructing Approximate Offsets. Proceedings of the 27th Annual Symposium on Computational Geometry (SoCG 2011), pp. 187-196 (pdf, ps)
© ACM, 2011. This is the authors' version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in the Proceedings of the 2011 Annual Symposium on Computational Geometry (SoCG'11)
An extended abstract of this work was presented at the 26th European Workshop on Computational Geometry (EuroCG 2010) (pdf)
- Chao Chen, Michael Kerber: Persistent Homology Computation With a Twist. 27th European Workshop on Computational Geometry (EuroCG 2011). (pdf)
- Herbert Edelsbrunner, Michael Kerber: Covering and packing with spheres by diagonal distortion in R^n. Rainbow of Computer Science - Essays Dedicated to Hermann Maurer on the Occasion of His 70th Birthday, eds. C. Calude, G. Rozenberg and A. Salomaa, LNCS 6570, pp. 20-35. (pdf)
- Michael Kerber, Michael Sagraloff: A Note on the Complexity of Real Algebraic Hypersurfaces. Journal on Graphs and Combinatorics 27 (3) pp. 419-430 (pdf)
© Springer, 2011. The original publication is available at www.springerlink.com
An extended abstract of this work was presented at 7th Japan Conference on Computational Geometry and Graphs (JCCGG'09) (pdf, ps)
- Paul Bendich, Herbert Edelsbrunner, Michael Kerber: Computing Robustness and Persistence for Images. IEEE Transactions on Visualization and Computer Graphics 16 (2010), pp. 1251-1260 (pdf) © IEEE 2010
- Paul Bendich, Herbert Edelsbrunner, Michael Kerber, Amit Patel: Persistent Homology under Non-uniform Error. Invited paper for the 35th International Symposium on Mathematical Foundations of Computer Science (MFCS 2010), LNCS 6281, pp. 12-23 (pdf)
© Springer, 2010. The original publication is available at www.springerlink.com - Eric Berberich, Efi Fogel, Dan Halperin, Michael Kerber, Ophir Setter: Arrangements on Parametric Surfaces II: Concretizations and Applications. Mathematics in Computer Science 4 (1), pp.67-91 (pdf) © Birkhäuser 2010
- Michael Kerber: Geometric Algorithms for Algebraic Curves and Surfaces. PhD Thesis, Saarland University, 2009 (pdf, ps)
- Michael Sagraloff, Michael Kerber, Michael Hemmer: Certified Complex Root Isolation via Adaptive Root Separation Bounds. 9th Asian Symposium on Computer Mathematics (ASCM'09) (pdf)
- Eric Berberich, Michael Kerber, Michael Sagraloff: An Efficient Algorithm for the Stratification and Triangulation of Algebraic Surfaces. Computational Geometry: Theory and Applications 43 (3) pp. 257-278 - Special Issue on 24th Annual Symposium on Computational Geometry
- Michael Kerber: On the Complexity of Reliable Root Approximation. 11th International Workshop on Computer Algebra in Scientific Computing (CASC'09). LNCS 5743, pp. 155-167 (pdf, ps)
© Springer, 2009. The original publication is available at www.springerlink.com - Michael Kerber: Division-Free Computation of Subresultants Using Bezout Matrices. International Journal of Computer Mathematics 86 (12) pp. 2186-2200, 2009
- Eric Berberich, Michael Kerber, Michael Sagraloff: Exact Geometric-Topological Analysis of Algebraic Surfaces. Proceedings of the twenty-fourth Annual Symposium on Computational Geometry (SoCG 08), pp. 164-173
(pdf, ps)
© ACM, 2008. This is the authors' version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in the Proceedings of the twenty-fourth Annual Symposium on Computational Geometry (SoCG'08) http://doi.acm.org/10.1145/1377676.1377703
An extended abstract of this work was presented at the 24th European Workshop on Computational Geometry (pdf, ps).
- Pavel Emeliyanenko, Michael Kerber: Visualizing and Exploring Planar Algebraic Arrangements - a Web Application. Video presented at the 24th Annual Symposium on Computational Geometry (SoCG'08)
- Eric Berberich, Michael Kerber: Exact arrangements on Tori and Dupin cyclides. Proceedings of the 2008 ACM Symposium on Solid and Physical Modeling (SPM 2008), pp. 59-66
(pdf, ps)
© ACM, 2008. This is the authors' version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in the Proceedings of the ACM Solid and Physical Modelling Symposium (SPM 2008) http://doi.acm.org/10.1145/1364901.1364912
An extended abstract of this work was presented at the 24th European Workshop on Computational Geometry (pdf, ps).
- Arno Eigenwillig, Michael Kerber: Exact and Efficient 2D-Arrangements of Arbitrary Algebraic Curves. Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2008), pp. 122-131 (pdf, ps).
© SIAM 2008. The provided download is an author-prepared version of the article. - 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 (pdf, ps).
© ACM, 2007. This is the authors' version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in the Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation (ISSAC 2007). http://doi.acm.org/10.1145/1277548.1277570 - Michael Kerber: Analysis of Real Algebraic Plane Curves. Diploma Thesis, Saarbrücken 2006 (pdf, ps).
Positions
November 2009 - present: Postdoc at the Institute of Science and Technology (IST) Austria
January - July 2010: Visiting Postdoc at Duke University, Computer Science Department
March - June 2005: Research Associate at University of Warwick, Mathematics Institute
Education
- October 2006 - October 2009
PhD student in Computer Science at the Max-Planck-Institut für Informatik
Title of PhD thesis: Geometric Algorithms for Algebraic Curves and Surfaces (pdf, ps) (referees: Kurt Mehlhorn (supervisor), Laureano Gonzalez-Vega, Chee Yap) - October 2001 - September 2006:
Studies in Computer Science at the Universität des Saarlandes, Saarbrücken, Germany and the Max-Planck-Institut für Informatik
Title of Diploma Thesis: Analysis of Real Algebraic Plane Curves (pdf, ps) (supervisors: Arno Eigenwillig, Kurt Mehlhorn, Nicola Wolpert) - June 2000:
Abitur at the Gymnasium am Stadtgarten, Saarlouis
Software
- Check out the xalci webdemo for plotting arrangements of algebraic curves and watch the video about it
- Also check out the CGAL webpage, especially the algebraic kernel package
Private
Visit my former and my current table tennis club
Check my emails online (the password is ***********).
