Nodal Surfaces
A large part of my work is connected to (hyper-)surfaces with many singularities. The main question in this subject is: What is the maximum number μ(d) of isolated singularities on a surface of degree d in projective three-space?
Up to now, this question is only answered for d <= 6. In this section, we give known bounds on μ(d) and provide images and animations of known examples.
For another website on this topic, see Stephan Endraß's site.
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Recent & Upcoming
- March 2010: Invited talk at the Saga Workshop 2010, Auron, France: Visualization of Real Algebraic Curves and Surfaces with Singularities.
- February 2010: Talk at the Convex Algebraic Geometry Workshop at Banff, Canada: Visualizing Convex Algebraic Geometry
- July 2009: Talk at the university of Hannover, Germany: Real surfaces with real singularities and applications (in didactics and architecture)
- May 2009: Talk at the architecture department of the technical university at Cottbus, Germany: Algebraic Geometry in Architecture?
- Feb. 18, 2009: Talk at the Otto-Hahn-Gymnasium at Saarbrücken (Germany): Von Pythagoras zu aktueller algebraischer Geometrie (PDF)
- Nov. 3 - Nov. 7, 2008: at the Maths Research Institute at Oberwolfach (Germany): Organizer of a teachers' training course on the use of algebraic curves and surfaces in school (in German).
- Oct. 24. - Nov. 16, 2008: Ausstellung IMAGINARY 2008 in der K4-Galerie in Saarbrücken.
- Sept. 2008 at Kassel (Germany): Talk at the AKMUI meeting.
- Sept 2008 at Erlangen (Germany): Talk at the DMV Conference. I am also one of the organizers of a Mini-Symposium there.
- Sept 2008 at Oslo (Norway): Talk at the CMA seminar.
- August 2008 at Saarbrücken: Talk at the Kulturmeilen-Fest: Über die Schönheit der Geometrie(in German). PDF-Download. Mathematische Animationen zum Vortrag: Barth-Fläche, Enriques-Flächen, meine 99-nodale Fläche.
- January 2008: Our paper on surfaces with many solitary points on arxiv.org.
- December 2007 at Paris (France): Invited Talk at MACIS 2007: Visualization Challenges in Real Algebraic Geometry
- 2006, December 1: Together with Hans-Christian Graf von Bothmer, I present an advent calendar of geometrical animations: www.Calendar.AlgebraicSurface.net
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