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Edelsbrunner Group

Algorithms, Computational Geometry, and Computational Topology

Understanding the world in terms of patterns and relations is the undercurrent in computational geometry and topology, the broad research area of the Edelsbrunner group.

While geometry measures shapes, topology focuses its attention on how the shapes are connected. These shapes may be three-dimensional (an artistic sculpture or a cave in a mountain), it may be four-dimensional (a galloping horse or a flexing protein), or it may even have many more than four dimensions (the configuration space of a robot or the expression pattern of a cancer). The Edelsbrunner group approaches the two related subjects of geometry and topology from a computational point of view. The computer aids in this study and it is used to make the insights useful in applications and workable for non-specialists. The group believes in a broad approach that does not sacrifice depth, including the development of new mathematics, the design of new algorithms and software, and the application in industry and other areas of science. Candidate areas for fruitful collaborations include 3D printing, structural molecular biology, neuroscience, and, more generally, data analysis.


Current Projects

Discretization in geometry and dynamics | Topological data analysis in information space


Edelsbrunner H, Garber A, Ghafaris M, Heiss T, Saghafiant M, Wintraecken M. 2024. Brillouin zones of integer lattices and their perturbations. SIAM Journal on Discrete Mathematics. 38(2), 1784–1807. View

Attali D, Kourimska H, Fillmore CD, Ghosh I, Lieutier A, Stephenson ER, Wintraecken M. 2024. Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of euclidean spaces and of Riemannian manifolds. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 11:1-11:19. View

Edelsbrunner H, Nikitenko A. 2024. Average and expected distortion of Voronoi paths and scapes. Discrete and Computational Geometry. View

Kourimska H, Lieutier A, Wintraecken M. 2024. The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 69. View

Edelsbrunner H, Pach J. 2024. Maximum Betti numbers of Čech complexes. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 53. View

View All Publications

ReX-Link: Herbert Edelsbrunner


Since 2009 Professor, Institute of Science and Technology Austria (ISTA)
2004 – 2012 Professor of Mathematics, Duke University, Durham, USA
1999 – 2012 Arts and Sciences Professor for Computer Science, Duke University, Durham, USA
1996 – 2013 Founder, Principal, and Director, Raindrop Geomagic
1985 – 1999 Assistant, Associate, and Full Professor, University of Illinois, Urbana-Champaign, USA
1981 – 1985 Assistant, Graz University of Technology, Austria
1982 PhD, Graz University of Technology, Austria

Selected Distinctions

ISI Highly Cited Researcher
2018 Wittgenstein Award
2014 Fellow of the European Association for Theoretical Computer Science
2014 Member, Austrian Academy of Sciences (ÖAW)
2012 Corresponding Member of the Austrian Academy of Sciences
2008 Member, German Academy of Sciences Leopoldina
2006 Honorary Doctorate, Graz University of Technology
2005 Member, American Academy of Arts and Sciences
1991 Alan T. Waterman Award, National Science Foundation

Additional Information

View Edelsbrunner website
Mathematics at ISTA

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