Qualifications & Memberships
My research interests are in topological and finite geometry and their connections to groups. I am the leading expert in the theory of topological circle planes and for Laguerre and Minkowski planes. I pioneered the cut-and-paste method for the construction of topological geometries beginning with the first examples of 2-dimensional projective planes whose collineation groups consist only of the identity. In the area of Laguerre planes I discovered the first non-classical models of 4-dimensional Laguerre planes. This brought to an end a 20-year long search and opened the door for further investigations of such planes and related geometries, such as 6-dimensional generalized quadrangles. I further introduced elation Laguerre planes, a particularly nice and well-behaved class of Laguerre planes that have the potential to play a role in the theory of Lagurre planes that is analogous to the one of translation planes in the theory of projective planes. In the area of Minkowski planes I introduced a standard representation of 4-dimensional Minkowski planes which significantly reduced the verification of the various defining topological properties of 4-dimensional Minkowski planes and I constructed the first examples of 4-dimensional non-classical Minkowski planes thus concluding a 30-year long search for such planes.
- Steinke GF. (2021) A note on the dembowksi-prohaska conjecture for finite inversive planes. Australasian Journal of Combinatorics 79: 527-541.
- Steinke GF. (2021) The classification of Kleinewillinghöfer types of 2-dimensional Laguerre planes. Aequationes Mathematicae http://dx.doi.org/10.1007/s00010-021-00780-3.
- Creutz B., Ho D. and Steinke GF. (2019) Three-dimensional connected groups of automorphisms of toroidal circle planes. Advances in Geometry http://dx.doi.org/10.1515/advgeom-2019-0031.
- Steinke G. (2019) A new family of 2-dimensional Laguerre planes that admit PSL2(R) × R as a group of automorphisms. Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial 17(1): 53-75. http://dx.doi.org/10.2140/iig.2019.17.53.
- Steinke G. and Stroppel M. (2019) Generalized quadrangles, Laguerre planes and shift planes of odd order. Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial 17(1): 47-52. http://dx.doi.org/10.2140/iig.2019.17.47.