Math Research

 

Most of my research is on algebra, geometry, history, or their interactions, often related to computers in one way or another:

  • mathematical models and sculptures – their history and mathematics,
  • geometrical modelling, in particular of non-linear surfaces,
  • (hyper-) surfaces with many singularities,
  • computational algebraic geometry and computer algebra,
  • e-learning software tools for mathematics,
  • didactics of mathematics – geometry, algebra, 3d-printing for teaching, using 3d-models in teaching.

Some of my research is listed on researchgate.net.

Some Milestones of my Research

History of Mathematics and Mathematical Models

Clebsch's diagonal cubic with two planes - OliverLabs.net

  • 2017: Straight lines on models of curved surfaces. In: The Mathematical Intelligencer, Springer, see the article online.
  • 2015: On Alfred Clebsch and Cubic Surfaces, p. 2798-2800 in: Oberwolfach report No. 47/2015.

Didactics of Mathematics and E-Learning

Cross widget communication within an e-learning system

  • 2016 (with M. El-Demerdash, J. Trgalova, J.-F. Nicaud): Collaborative Design of Educational Digital Resources for Promoting Creative Mathematical Thinking, conference paper for the “International Congress of Mathematical Education” (pdf)
  • 2016: Bausteine in digitalen Lernumgebungen vernetzen: Technologie zur Gestaltung und Analyse von kreativen Lernprozessen (pdf)
  • 2011: Terme in Bildern (20 Seiten), in: Tagungsband des GDM-Arbeitskreises Geometrie.

Applications of Mathematics

screenshot from our paper on algebraic geometry and architecture - OliverLabs.net

  • 2009 (with G. Barczik and D. Lordick): Algebraic Geometry in Architectural Design. In: Proceedings of the 27th eCAADe, Istanbul, Turkey.
  • 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.

Pure Mathematics (Algebra and Geometry)

World Record Septic with 99 singularities by Oliver Labs

Mathematical Software

Screenshot of the cubic surface illustration software by Oliver Labs

  • 2014-16: several publications within the European project Mathematical Creativity Squared, in particular I was the deliverable manager of three so-called widget catalogues (written with other team members), see the website of the MC2 project
  • 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).
  • 2002 (with D. van Straten): A Visual Introduction to Cubic Surfaces using SPICY, in: M. Joswig, N. Takayama: Algebra, Geometry and Software Systems (Springer).