Research

I mainly work on the triangulation of manifolds (manifold meshing). Other interest include the application of computational topology to cosmology.

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Papers:

• The reach, metric distortion, geodesic convexity and the variation of tangent spaces
  HAL preprint (accepted for SoCG 2018)
  Jean-Daniel Boissonnat, André Lieutier, and Mathijs Wintraecken
  
  
• Triangulating stratified manifolds I: a reach comparison theorem
  HAL preprint
  Jean-Daniel Boissonnat, and Mathijs Wintraecken
  
  
• Local criteria for triangulation of manifolds
  HAL preprint (accepted for SoCG 2018)
  Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh, and Mathijs Wintraecken
  
  
• Coxeter triangulations have good quality
  HAL preprint
  Abstract to be presented at EuroCG2018
  Aruni Choudhary, Siargey Kachanovich, and Mathijs Wintraecken
  
  
• Anisotropic triangulations via discrete Riemannian Voronoi diagrams
  Proceedings version , The full version
  Mael Rouxel-Labbé, Mathijs Wintraecken and Jean-Daniel Boissonnat
  SoCG 2017


• Bounds on the angle between tangent spaces and the metric distortion for C² manifolds with given positive reach
  Page 241
  Mathijs Wintraecken
  EUROCG 2017


• The Topology of the Cosmic Web in Terms of Persistent Betti Numbers.
  ArXiv version Journal version (monthly notices of the royal astronomical society)
  Pratyush Pranav, Herbert Edelsbrunner, Rien van de Weygaert, Gert Vegter, Michael Kerber, Bernard J.T. Jones, Mathijs Wintraecken


• Discretized Riemannian Delaunay triangulations.
  The full version, the Hal version (This version coincides with the version accepted for the Proceedings of the 25th International Meshing Roundtable) Journal version
  M. Rouxel-Labbé, M. Wintraecken and J.-D. Boissonnat
  


• Barycentric coordinate neighbourhoods in Riemannian manifolds.
  ArXiv version
  Ramsay Dyer, Gert Vegter and Mathijs Wintraecken


• Optimal Triangulation of Saddle Surfaces.
  Journal version , ArXiv version
  Dror Atariah, Günter Rote, and Mathijs Wintraecken
  Contributions to Algebra and Geometry


• Riemannian simplices and triangulations.
  Journal version , arXiv version, and talk for SOCG
  Ramsay Dyer, Gert Vegter and Mathijs Wintraecken
  Geometriae Dedicata


• On the Optimal Triangulation of Convex Hypersurfaces, Whose Vertices Lie in Ambient Space.
  Journal version , and local version
  M.H.M.J.Wintraecken and G. Vegter
  Mathematics in Computer Science


• A geometrical take on invariants of low-dimensional manifolds found by integration.
  Journal version , local version, talk, and an erratum (in preparation)
  G. Vegter and M.H.M.J Wintraecken
  Topology and its Applications


• Probing Dark Energy with Alpha Shapes and Betti Numbers
  ArXiv version
  Rien van de Weygaert, Pratyush Pranav, Bernard J.T. Jones, E.G. Patrick Bos, Gert Vegter, Herbert Edelsbrunner, Monique Teillaud, Wojciech A. Hellwing, Changbom Park, Johan Hidding, and Mathijs Wintraecken

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Theses:

My phd thesis and further information on my advisors and assessment committee can be found here.

My Master thesis in Mathematics is titled `Confluence of singular fibers on rational elliptic surfaces' and was written under the advisorship of Hans Duistermaat. This is a short version and this is the talk.