Topological and finite circle geometries and their automorphism groups

Host Faculty: Engineering
General Subject Area: Pure Mathematics
Project Level: PhD
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Circle geometries are incidence geometries that generalise classical geometries obtained from intersections of quadrics with planes in 3-dimensional projective space or intersections of cones over normal rational curves with planes in higher-dimensional projective space. Each circle geometry has a group associated with it, its autmorphism group. Following Felix Klein's Erlangen programme, one kind of project is to make assumptions on the circle geometry (what type of circle geometry, i.e. Mobius, Laguerre, Minkowski or orthogonal array plane, is it finite or topological or smooth, etc.) and on the automorphism groups (transitivity properties, existence of certain subgroups, dimension, etc.) and then determine which circle geometries can result. Another kind of project is to characterise certain circle geometries by configurational conditions or other properties.


Supervisor: Gunter Steinke

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