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



On this site:

Team

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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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Hana Dal Poz Kourimska

Postdoc

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Ondrej Draganov

PhD Student

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Chris Fillmore

PhD Student


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Teresa Heiss

PhD Student

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Farid Karimipour

Postdoc

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Zuzka Masárová

Postdoc

+43 2243 9000 4777


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Anton Nikitenko

Postdoc

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Morteza Saghafian

Predoctoral Visiting Scientist

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Elizabeth Stephenson

PhD Student


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Mathijs Wintraecken

Postdoc


Current Projects

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


Publications

Akopyan A, Schwartz R, Tabachnikov S. 2020. Billiards in ellipses revisited. European Journal of Mathematics. View

Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 93. View

Akopyan A, Bobenko AI, Schief WK, Techter J. 2020. On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry. View

Osang GF, Rouxel-Labbé M, Teillaud M. 2020. Generalizing CGAL periodic delaunay triangulations. Leibniz International Proceedings in Informatics. ESA: Annual European Symposium on Algorithms, LIPIcs, vol. 173. View

Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry. 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
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
Open Mathematics at IST Austria website




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