July 16 – 21 , 2017, Dagstuhl Seminar 17292

Topology, Computation and Data Analysis


Hamish Carr (University of Leeds, GB)
Michael Kerber (TU Graz, AT)
Bei Wang (University of Utah – Salt Lake City, US)

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In the last two decades, considerable effort has been made in a number of research communities into computational applications of topology. Inherently, topology abstracts functions and graphs into simpler forms, and this has obvious attraction for data analysis. This attraction is redoubled in the era of extreme data, in which humans increasingly rely on tools that extract mathematically well-founded abstractions.

Efforts to apply topology computationally to data, however, have largely been fragmented, with work progressing in a number of communities, principally computational topology and topological visualization. Of these, computational topology expands from computational geometry and algebraic topology to seek algorithmic approaches to topological problems, while topological data analysis and topological visualization seek to apply topology to data analysis, of graphs and networks in the first case and of (usually) simulated volumetric data in the second. The research in these communities can roughly be clustered into theory (what are the underlying mathematical concepts), applications (how are they used for data analysis), and computation (how to compute abstractions for real data sets). It is crucial to advances in this area that these three branches go hand-in-hand, and communication between theoretical, applied, and computational researchers is therefore indispensable. On the other hand, there is surprisingly little communication between the computational topology and topological visualization communities.

Our major goal is to soften this strict separation between computational topology and topological visualization by establishing new inter-community ties. We plan to bring together cross sections of both communities, including researchers with theoretical, applied, and computational backgrounds. By reducing redundancy and speeding cross-communication, we expect that this will provide a significant boost to both areas and even encourage them to merge into a singular more dynamic community.

The possible topics of this Dagstuhl Seminar include but are not limited to the theory and application of categorical approaches in topological data analysis, multidimensional persistent homology, singularity theory and fiber topology in multivariate data analysis, and scalable computation of topological invariants. We highly encourage participants to propose further topics, prior to or during the seminar. It will include research talks by leading scientists in these fields, and a number of breakout sessions, where smaller groups discuss topics of shared interest in both communities with the potential to trigger research of common interest.

  Creative Commons BY 3.0 DE
  Hamish Carr, Michael Kerber, and Bei Wang


  • Data Structures / Algorithms / Complexity


  • Computational topology
  • Topological data analysis

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