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?).
Group Leader
Administrative Support
Team
Current Projects
Embeddings of simplicial complexes | Topological Tverbergtype problems and multiple self-intersections of maps | Discrete isoperimetric inequalities and higher-dimensional expanders
Publications
Brunck FR, Kwan MA. 2024. Books, Hallways, and social butterflies: A note on sliding block puzzles. Mathematical Intelligencer. View
Lopushanski M, Ivanov G. 2024. A constructive algorithm for building rectifiable curves in weakly convex sets. AIP Conference Proceedings. ICCMSE: International Conference of Computational Methods in Sciences and Engiineering vol. 3030, 080002. View
Filakovský M, Nakajima TV, Opršal J, Tasinato G, Wagner U. 2024. Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs. 41st International Symposium on Theoretical Aspects of Computer Science. STACS: Symposium on Theoretical Aspects of Computer Science, LIPIcs, vol. 289, 34. View
Ivanov G, Naszódi M. 2024. Quantitative Steinitz theorem: A polynomial bound. Bulletin of the London Mathematical Society. 56(2), 796–802. View
Dymond M, Kaluza V. 2024. Divergence of separated nets with respect to displacement equivalence. Geometriae Dedicata. 218, 15. View
ReX-Link: Uli Wagner
Career
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
