Frank Klinker


Research interests

One focus of my work is on a particular relation between differential geometry and physics: geometric supersymmetry. This expression describes the various connections between differential geometry and supersymmetry. Undoubtedly, representation theory and spin geometry are two important mathematical fields within this topic.

In this context, I am interested in (pseudo)-Riemannian geometry, geometric analysis, combinatorics, geometric algebras, geometry of supermanifolds, deformation of geometric structures, Yang-Mills theory, supergravity, string theory, and deformation quantization.

In general, my research interest is on the various relations between mathematics on the one hand and natural sciences, engineering and economics on the other hand.

Moreover, I like to apply mathematics to problems and questions that arise from practical applications; for example electrical engineering, automation engineering, finance and markets, or economics in general. So feel free to contact me if you are in need of advice for your mathematical problem.

Cooperations with Industry and Business


  • C. Eggert, ThyssenKrupp Rothe Erde GmbH, Dortmund, Germany (Geometric analysis of AC circuits)
  • R. Gäer, Schniewindt GmbH & Co. KG., Neuenrade, Germany (Geometric analysis of AC circuits)
  • W. Kranz, Kranz Software Engineering, Dortmund, Germany (Applied data smoothing)
  • R. Moorbrink, A. Trog, Franz Högemann GmbH, Garrel, Germany (Optimization of production processes)
  • S. Pohlschröder, Pohlschröder Property Consulting, Dortmund, Germany (Calculation and optimization of trend signals)
  • C. Reineke, ehem. Deutsche Telekom AG, Dortmund, Germany (Applied algebraic problems, geometric analysis of AC circuits)
  • Rentokil GmbH, Regionalfiliale Dortmund, Germany (Static calculations in warehouse logistics)

Cooperations with Schools


  • T. Günther, S. Knipper, F.-G. Schürmann, Marie-Curie-Gymnasium, Bönen (Geometric and analytic aspects of touching circles, approximation of water rocket dynamics)
  • C. Schickert, Marie-Curie-Gymnasium, Bönen (Geometric and analytic aspects of touching curves)

Projects

  • Geometric and analytic aspects of touching curves. (Joint work with T. Günther, S. Knipper, C. Schickert, F.-G. Schürmann)
  • Ist das Glas halbvoll oder halbleer: Eine analytische Betrachtung. (Joint work with C. Reineke)
  • On the classification of homogeneous supergravity backgrounds.
  • Properties of small eigenvalues of the Dirac operator on quaternionic Kähler manifolds and their eigenspaces.
  • The geometric treatment of supersymmetry on homogeneous supermanifolds.

Organized Conferences

March 16-19, 2015. TU Dortmund University: International Conference Geometric and Algebraic Methods in Mathematical Physics (GAMMP 2015)