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 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.
- Steinke GF. (2019) A characterization of the known finite Minkowski planes in terms of Klein–Kroll types with respect to G -translations. Journal of Geometry 110(2) http://dx.doi.org/10.1007/s00022-019-0475-1.
- Creutz B., Ho D. and Steinke GF. (2018) On automorphism groups of toroidal circle planes. Journal of Geometry 109(1) http://dx.doi.org/10.1007/s00022-018-0420-8.
- Steinke GF. (2018) A family of two-dimensional laguerre planes of Kleinewillinghöfer type II.A.2. Journal of the Australian Mathematical Society 105(3): 366-379. http://dx.doi.org/10.1017/S1446788717000398.