http://www.dagstuhl.de/17292

July 16 – 21 , 2017, Dagstuhl Seminar 17292

Topology, Computation and Data Analysis

Organizers

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

For support, please contact

Annette Beyer for administrative matters

Andreas Dolzmann for scientific matters

Documents

List of Participants
Shared Documents
Dagstuhl Seminar Wiki
Dagstuhl Seminar Schedule [pdf]

(Use seminar number and access code to log in)

Motivation

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.

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

Classification

  • Data Structures / Algorithms / Complexity

Keywords

  • Computational topology
  • Topological data analysis

Book exhibition

Books from the participants of the current Seminar 

Book exhibition in the library, ground floor, during the seminar week.

Documentation

In the series Dagstuhl Reports each Dagstuhl Seminar and Dagstuhl Perspectives Workshop is documented. The seminar organizers, in cooperation with the collector, prepare a report that includes contributions from the participants' talks together with a summary of the seminar.

 

Download overview leaflet (PDF).

Publications

Furthermore, a comprehensive peer-reviewed collection of research papers can be published in the series Dagstuhl Follow-Ups.

Dagstuhl's Impact

Please inform us when a publication was published as a result from your seminar. These publications are listed in the category Dagstuhl's Impact and are presented on a special shelf on the ground floor of the library.

NSF young researcher support