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Publications

Preprints

Most of my articles are available in PDF format, see below. Here are those which have not appeared yet:

• In preparation: A List of Challenges for Real Algebraic Surface Visualization Software.

Refereed Papers in Journals/Proceedings

• 2009 (with G. Barczik, D. Lordick): Algebraic Geometry in Architectural Design, to appear in eCAADe 2009. Download: PDF
• 2009 (with Erwan Brugallé): Surfaces with Many Solitary Points, (see also: arxiv.org/0801.4283), p. 123-134 in: Geom. Dedicata Vol. 141. 2009
• 2009: A List of Challenges for Real Algebraic Plane Curve Visualization Software, p. 137-164 in: Nonlinear Computational Geometry, edited by I. Emiris and F. Sottile and T. Theobald, IMA Volume 151, Springer.Downloads: Article as PDF. Explicit list of polynomials for challenges in low degrees
• 2008 (with S. Breske and D. van Straten): Real Line Arrangements and Surfaces with Many Real Nodes, (see also: arxiv.org/math.AG/0507234), p. 47-54 in: R. Piene, B. Jüttler, Geometric Modeling and Algebraic Geometry (Springer).
• 2007 (with Hans-Christian Graf von Bothmer, Josef Schicho, Christiaan van de Woestijne): The Casas-Alvero conjecture for infinitely many degrees, (see also: arxiv.org/math.AC/0605090), p. 224-230 in: J. Algebra, Vol. 316, No 1.
• 2006: Dessins d'Enfants and Hypersurfaces with Many Aj-Singularities, (see also: arxiv.org/math.AG/0505022), p. 607-622 in: J. Lond. Math.Soc. (2), Vol. 74
• 2006: A Septic with 99 real Nodes, (see also: arxiv.org/math.AG/0409348), p. 299-313 in: Rend. Sem. Mat. Univ. Pad., Vol. 116.
• 2006 (with S. Holzer): Illustrating the Classification of Real Cubic Surfaces, p. 119-134 in: M. Elkhadi, B. Mourrain, R. Piene, Algebraic Geometry and Geometric Modelling (Springer).
  Download: PDF.
• 2002 (with D. van Straten): A Visual Introduction to Cubic Surfaces using SPICY, in: M. Joswig, N. Takayama: Algebra, Geometry and Software Systems(Springer).
  Download: PDF.

Non-Refereed Papers

• 2008: Eine Fläche mit vielen reellen Singularitäten - zum Titelbild, S. 269, in: DMV-Mitteilungen 04/2008.
• 2008: Der Schwalbenschwanz - zum Titelbild, S. 182, in: DMV-Mitteilungen 03/2008.
• 2008 (with A. Sarti): Eine K3-Fläche - zum Titelbild, in: DMV-Mitteilungen 02/2008.
• 2008: Eine singuläre kubische Fläche - zum Titelbild, in: DMV-Mitteilungen 01/2008.
• 2005: A Sextic with 35 Cusps, in: Active DVD in occation of the MEGA 2005 conference at Alghero, see also: arxiv.org/math.AG/0502520. (Shortly after having completed this paper, I realized that one can get 36 cusps using B. Segre's old method (see Dessins d'Enfants...), so I never tried to publish this article. But notice that the method could be useful in other situations.).

Theses

• Ph.D. Thesis (2005): Hypersurfaces with Many Singularities -- History, Constructions, Algorithms, Visualization.
• Diploma Thesis (2001): Kubische Flächen und die Coblesche Hexaederform (in German).
• Thèse de Maitrise (1997): Les groupes libres et leurs sous-groupes (in French)

Popular Scientific Articles

• 2009: 33 Explanations accompanying Surfaces in the software Surfer, published on www.Imaginary2008.de, edited by G.-M. Greuel (Mathematisches Forschungsinstitut Oberwolfach).
• 2008: Weltrekordflächen - Flächen mit vielen Singularitiäten, published on www.Imaginary2008.de, edited by G.-M. Greuel (Mathematisches Forschungsinstitut Oberwolfach): article to explain parts of the interactive exhibition Imaginary 2008, organized together with the Oberwolfach Institute of Mathematics. The German pdf is available from the AlgebraicSurface.net website: http://algebraicsurface.net/data/AlgFlVieleSings.pdf
• 2007: 33 Erläuterungen zu Flächen in der Software Surfer (in German), published on www.Imaginary2008.de, edited by G.-M. Greuel (Mathematisches Forschungsinstitut Oberwolfach).
• 2004: Eine Fläche mit 99 Singularitäten, in: MONOID 80. Fachbereich Mathematik und Informatik Mainz, available from www.mathematik.uni-mainz.de/monoid/

Lecture Notes

All lecture notes below are preliminary versions:

• Winter Term 2008/09 - Winter Term 2009/10 (with F.-O. Schreyer, in German, 4 hours per week, 3 semesters): Mathematics for Computer Scientists 1-3.
• Summer Term 2008: Dynamic Geometry (in German, 4 hours per week). Attention! This text can only be read together with Barth's geometry lecture notes! See the teaching section for details.
• Winter Term 2007/08: Dynamic Geometry (in German, 2 hours per week). See the teaching section for details.
• Summer Term 2007: Algebraic Topology (in German, 2 hours per week). See the teaching section for details.