I1671-N26: Transformations and Singularities

Joint Project between Austria (FWF) and Japan (JSPS)

FWF - Austrian Science Fund

JSPS - Japan Society for the Promotion of Science

Project leader (Austria): Udo Hertrich-Jeromin
Project leader (Japan): Yoshihiko Suyama
Funding period (Austria): 1 Jul 2014 - 31 Mar 2018 (approved 14 Mar 2014)

Field: Mathematics; Areas: Differential geometry, Singularity theory, Integrable systems, Discrete differential geometry


Transform Ellipsoid Ellipsoid and Christoffel transform
with ends at the umbilics

Abstract. Transformations of surfaces allow to construct new (families of) surfaces of the same kind. The concept of transformation is rather far-reaching: for example, the Weierstrass representation of minimal surfaces can be interpreted as a special case. Moreover, discrete (facetted) surfaces of the same kind naturally occur from repeated transformations.

Singularities are, most generally, the "bad points" of a theory, points at which the methods of a theory fail. This already constitutes a strong motivation for their study: the employed methods require extension, the studied objects reconsideration, and new viewpoints on the theory arise.

The aim of this project is to study the interplay between transformations and singularities. More precisely: we aim to

  • understand how transformations of particular surfaces behave (or fail to behave) at singularities; and
  • study how those transformations create (or annihilate) singularities, and what the nature of the occurring singularities is.

A good understanding of the interplay between transformations and singularities will shed further light on either theory. Moreover, new results and phenomena will arise from this interplay, for example, regarding "singularities" of facetted or paneled surfaces.


Opening workshop
Vienna 15-20 Sep 2014

Closing workshop
Toyko 19-23 Feb 2016


Birgit Slama (Secretary)

Volker Branding (AT)
Wolfgang Carl (AT)
Andreas Fuchs (AT)
Shoichi Fujimori (JP)
Udo Hertrich-Jeromin (AT)
Atsufumi Honda (JP)
Satoshi Kawakubo (JP)
Masatoshi Kokubu (JP)
Nozomu Matsuura (JP)
Christian Müller (AT)
Kosuke Naokawa (JP)
Wayne Rossman (JP)
Yoshihiko Suyama (JP)
Gudrun Szewieczek (AT)
Masaaki Umehara (JP)
Johannes Wallner (AT)
Kotaro Yamada (JP)
Masashi Yasumoto (JP)


FWF - Austrian Science Fund
JSPS - Japan Society for the Promotion of Science
TUW - Vienna University of Technology
JASEC - Japan-Austria Science Exchange Centre
DMG - Institute of Discrete Mathematics and Geometry

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