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. (2017) Modified classical flat Minkowski planes. Advances in Geometry 17(3): 379-396. http://dx.doi.org/10.1515/advgeom-2017-0026.
- Steinke GF. (2016) Finite Minkowski planes of type 20 with respect to homotheties. Finite Fields and Their Applications 39: 83-95. http://dx.doi.org/10.1016/j.ffa.2016.01.007.
- Steinke GF. (2016) On kleinewillingh¨ofer types of finite laguerre planes with respect to homotheties. Australasian Journal of Combinatorics 66(3): 425-435.
- Steinke GF. (2015) Flat Laguerre planes admitting 4-dimensional groups of automorphisms that fix a parallel class. Aequationes Mathematicae 89(5): 1359-1388. http://dx.doi.org/10.1007/s00010-014-0315-1.
- Steinke GF. and Stroppel MJ. (2015) Simple groups acting two-transitively on the set of generators of a finite elation Laguerre plane. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 56(1): 285-298. http://dx.doi.org/10.1007/s13366-013-0169-z.