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Wagner Group

Discrete and Computational Geometry and Topology

How and when can a geometric shape be embedded in n-dimensional space without self-intersections? What restrictions does it place on the shape? These and other questions in combinatorial and computational geometry and topology are central to the Wagner group’s research program.

A simplicial complex is a description of how to represent a geometric shape by gluing together points, edges, triangles, and their n-dimensional counterparts in a “nice” way. Simplicial complexes are a natural way to represent shapes for the purposes of computation and algorithm design, and the Wagner group explores both their topological properties, such as embeddability, as well as what can be proved about their combinatorics – e.g. bounds on the number of simplices – given a particular geometric or topological constraint. More generally, they take classically topological questions and consider them from a combinatorial point of view, and conversely, they use techniques and ideas from topology to approach questions in combinatorics. They are moreover interested in the computational aspects of such problems, in particular questions of decidability (does an algorithm exist?) and complexity (if so, what are the costs in terms of time or space?).

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Current Projects

Embeddings of simplicial complexes | Topological Tverbergtype problems and multiple self-intersections of maps | Discrete isoperimetric inequalities and higher-dimensional expanders


Arroyo Guevara AM, Klute F, Parada I, Vogtenhuber B, Seidel R, Wiedera T. 2022. Inserting one edge into a simples drawing is hard. Discrete and Computational Geometry. View

Wild P. 2022. High-dimensional expansion and crossing numbers of simplicial complexes. Institute of Science and Technology (ISTA). View

Fulek R, Kynčl J. 2022. The Z<inf>2</inf> -Genus of Kuratowski minors. Discrete and Computational Geometry. View

Krokhin A, Opršal J. 2022. An invitation to the promise constraint satisfaction problem. ACM SIGLOG News. 9(3), 30–59. View

Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2022. On compatible matchings. Journal of Graph Algorithms and Applications. 26(2), 225–240. View

View All Publications

ReX-Link: Uli Wagner


since 2018 Professor, Institute of Science and Technology Austria (ISTA)
2013 – 2018 Assistant Professor, Institute of Science and Technology Austria (ISTA)
2012 – 2013 SNSF Research Assistant Professor, Institut de Mathématiques de Géométrie et Applications, EPFL, Lausanne, Switzerland
2008 – 2012 Senior Research Associate, Institute of Theoretical Computer Science, ETH Zurich, Switzerland
2006 – 2008 Postdoctoral Researcher, Institute of Theoretical Computer Science, ETH Zurich, Switzerland
2004 – 2006 Postdoc, Einstein Institute for Mathematics, The Hebrew University of Jerusalem, Israel
2004 Postdoc, Univerzita Karlova, Prague, Czech Republic
2003 Postdoc, Mathematical Sciences Research Institute, Berkeley, USA
2004 PhD, ETH Zurich, Switzerland

Selected Distinctions

2018 Best Paper Award at the Symposium on Computational Geometry (SoCG)
2014 Best Paper Award at the Symposium on Computational Geometry (SoCG)
2012 Research Assistant Professorship Grant of Swiss National Science Foundation (SNSF)
2012 Best Paper Award at Symposium of Discrete Algorithms (SODA)
2004 Richard Rado Prize

Additional Information

Download CV
Mathematics at ISTA

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