Project 10: "Subdivision in nonlinear geometries"

This project is running since 2010.

Principal investigator: Johannes Wallner
Graz University of Technology, Austria.
Mentor for: Moßhammer; Boiko, Frei.

Associated scientist: Michael Kerber (since 2015)
Graz University of Technology, Austria.
Mentor for: del Guidice, Huening, Vogel.

DK Students

  • Second phase of the doctoral program:
  • Svenja Hüning (Germany, since April 2016)
  • Email: huening@tugraz.at
    Mentors: Michael Kerber, Birgit Vogtenhuber
  • First phase of the doctoral program:
  • Oliver Ebner (Austria; July 2010–July 2012)
    Personal homepage; Email: o.ebner@tugraz.at
    Mentors: Rainer Burkard, Wolfgang Woess.
    PhD Defense: July 20, 2012.
    Referees: Ph. Grohs (Zürich), K. Jetter (Stuttgart), J. Wallner.
    Examiners: Ph. Grohs (Zürich), J. Wallner.

Associated Students

  • Second phase of the doctoral program:
  • Leonardo Alese (Italy; since November 2015)
    Email: alese@tugraz.at
    Mentors: Peter Grabner, Daniele D'Angeli.

  • Caroline Moosmüller (Austria; since November 2013)
    Email: moosmueller@tugraz.at
    Mentors: Mihyun Kang, Roswitha Rissner.
  • First phase of the doctoral program:
  • Wolfgang Carl (Austria; since December 2012)
    Personal homepage; Email: carl@tugraz.at
    Mentors: Mihyun Kang, Franz Lehner.

  • Florian Lehner (Austria; July 2011–July 2014)
    Personal homepage; Email: f.lehner@tugraz.at
    Mentors: Wilfried Imrich, Bettina Klinz, Wolfgang Woess.
    PhD Defense: July 4, 2014.
    Referees: W. Imrich (Leoben), S. Klavzar (Ljubljana), J. Wallner.
    Examiners: W. Imrich (Leoben), S. Klavzar (Ljubljana).

Project description (pdf-file)

A main focus of Wallner's work is nonlinear subdivision processes and discrete multiscale representations of data, which for started as a collaboration with Nira Dyn on proximity inequalities and their implications on the continuity and smoothness of limit curves produced by geometric, necessarily nonlinear, subdivision processes. Wallner's research group at TU Graz aims at a systematic theory of univariate and multivariate geometric subdivision rules defined in nonlinear geometries (Riemannian manifolds, Lie groups, Euclidean space minus obstacles). Other topics of research are the numerical processing of 3D geometry data, discrete differential geometry, semidiscrete surfaces, and lately especially the application of geometric methods to freeform architectural design. Wallner is a member of FWF research network S92 on industrial geometry.