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.
Recent & Upcoming (Selected Events)
- July 24-31 2016: ICME Hamburg. Invited Talk and exhibition (with S. Halverscheid) on Felix Klein and mathematical models during the thematic afternoon on Wednesday.
- Jule 20-23, 2016: Organiser of a Workshop at the "Imaginary Conference" on an Imaginary Book.
- June 28, 2016: Invited Talk/Workshop at ICERM (Providence, USA) on algebraic surfaces, their visualisations and 3D-models
- Oct. 27, 2015: Talk "On Alfred Clebsch and Cubic Surfaces." at the history of mathematics meeting at MFO, Oberwolfach, Germany
- March 13, 2014: Talk at Nancy (France) on cubic surface models. See MO-Labs.com for some of them.
- April 1, 2013: My new website MO-Labs.com on which I present some of the mathematical objects I have been producing.
- Sept. 29, 2012: Workshop on the question: How to use the new capabilities of 3d-printing for teaching purposes. AK MUI Meeting at Soest, Germany.
- Sept 20, 2012: Two workshops at the DMV-Tagung on: Neue mathematische 3d-Modelle für die Lehre.
- Sept. 14-15, 2012: A small exhibition on mathematical 3d-models for teaching during the conference on geometry teaching at Saarbrücken, Germany.
- August 2012: My new website MO-Labs.com has been released. You may now purchase some of my mathematical 3d-models online.
- June 23, 2012: Talk at the conference CADGME 2012, at Novi Sad, Serbia.
- June 12, 2012: Talk at the Mini-Workshop on the history of mathematical instruments, mashines, and models. Mainz, Germany.
- May 31, 2012: Opening of the exhibition Forms and Formulas at Lisboa, Portugal, on 300 square meters. I am one of the three curators. We show more than 60 of my 3d-printed mathematical models, together with other new and historical pieces!
- April 26, 2012: Invited talk at the IMAGINARY-Conference at Barcelona, Spain.
- April 24, 2012: Talk at the Didactics Colloquium at the Saarland University.
- April 4, 2012: Talk at the annual MNU meeting at Freiburg, Germany.
- March 2012: Talk at the annual meeting of the GDM at Weingarten, Germany.
- Nov. 10, 2011: Invited Talk at the ETH, Zürich, Switzerland.
- Oct. 11, 2011: Invited Talk at the Maths Institute at Lisbon, Portugal: Parabolas are Useful!
- Sept. 25, 2011: Talk on Zeros and Discriminants of Polynomials during the AkMUI Conference at Soest, Germany.
- Sept. 20, 2011: Workshop on Understanding Chaotic Behaviour using GeoGebra (in German) at the so-called Lehrertag of the annual DMV Meeting. Cologne, Germany. Material
- Sept. 1-4, 2011: Invited Talk at the conference Geometry from an Advanced Point of View at Aveiro, Portugal.
- March - July 2011: Visiting Professor at the university of Cologne (in German: Vertretung einer Professur).
- Nov. 6, 2010: Workshop Algebra in Bildern at the CASIO meeting called Teach and Talk, Nürnberg, Germany. PDF-Download.
- Sept. 27, 2010: Talk at the Oberseminar Südwest, Karlsruhe, Germany: Algebraische Geometrie in der Sekundarstufe I? (in German).
- Sept. 25, 2010: Talk and Workshop at AkMUI 2010, Soest, Germany: Algebraische Geometrie versus Analytische Geometrie in der Schule (in German).
- Sept. 12, 2010: Talk at AkGeo 2010, Marktbreit, Germany: Terme in Bildern in der Sekundarstufe I (in German).
- 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: http://Calendar.AlgebraicSurface.net