Math Research

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

  • history of caustics
  • history of algebraic geometry in the 19th century
  • 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

Some Milestones of my Research

History of Mathematics and Mathematical 3d-Models

Clebsch's diagonal cubic with two planes -

Didactics of Mathematics and E-Learning

Cross widget communication within an e-learning system

  • 2018 (with S. Halverscheid): Felix Klein’s Mathematical Heritage seen through 3d Models. In: The Legacy of Felix Klein, pp. 131-152, Springer.
  • 2016 (with S. Karkalas and M. Mavrikis): Towards analytics for educational interactive e-Books: The case of the reflective designer analytics platform (RDAP), in: Proceeding LAK ’16 Proceedings of the Sixth International Conference on Learning Analytics & Knowledge (see article on the web)
  • 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”, in: ICME 13 Proceedings (pdf)
  • 2016 (with U. Kortenkamp): Bausteine in digitalen Lernumgebungen vernetzen: Technologie zur Gestaltung und Analyse von kreativen Lernprozessen, in: Proceedings of the GDM Tagung 2016 (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 -

  • 2011 (with G. Barczik and D. Lordick): Algebraic Expansions: Broadening the Scope of Architectural Design through Algebraic Surfaces
    in: Computational Design Modelling: Proceedings of the Design Modelling Symposium Berlin 2011
  • 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).