MATHEMATICS AND COMPUTER SCIENCE

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.

Group Leader



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Team

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Arseniy Akopyan

Postdoc

+43 2243 9000 0

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Ranita Biswas

Postdoc

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Adam Brown

Postdoc

+43 664 88326267 0


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Sebastiano Cultrera di Montesano

PhD Student

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Ondrej Draganov

PhD Student

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Teresa Heiss

PhD Student


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Farid Karimipour

Postdoc

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Zuzka Masárová

PhD Student

+43 2243 9000 4777

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Anton Nikitenko

Postdoc


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Georg Osang

PhD Student

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Elizabeth Stephenson

PhD Student

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Hubert Wagner

Postdoc

+43 2243 9000 3302


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Mathijs Wintraecken

Postdoc

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Katharina Ölsböck

PhD Student


Current Projects

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


Publications

Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 538, 261–289. View

Vegter G, Wintraecken M. 2019. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. The 31st Canadian Conference in Computational Geometry. CCCG: Canadian Conference in Computational Geometry 275–279. View

Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 73, 1–15. View

Boissonnat J-D, Lieutier A, Wintraecken M. 2019. The reach, metric distortion, geodesic convexity and the variation of tangent spaces. Journal of Applied and Computational Topology. View

Akopyan A, Izmestiev I. 2019. The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. View

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Career

since 2009 Professor, IST Austria
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
2018 ERC Advanced Grant
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

Download CV
View Edelsbrunner website
Open Mathematics at IST Austria website




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