Mostly Finite Geometries

Based on the proceedings of the conference held at the University of Iowa, in honour and celebration of the mathematician T.G. Ostrom's 80th birthday, this text focuses on finite geometries as well as topological geometries in the infinite case, some of which originate with ideas of finite geometric objects. It includes information about flocks of quadratic cones and related geometric and combinatorial structures.

Guest lectures: Remarks concerning linear systems with parallelism; on the classification of 4-dimensional flexible projective planes; replaceable nests; flocks of Laguerre planes and associated geometries; ovoids and translation planes from lattices. Contributed articles: the construction of generalized m-gons from blueprints; variations on a theme of Dembowski; on a theorem of Hering and two-transitive ovals with a fixed external line; inductively minimal flag-transitive geometries; transitive autotopism groups and the generalized twisted field planes; a family of non-Buekenhout unitals in the Hall planes; 4-caps in orthogonal spaces; a remark on a theorem of T.G. Ostrom; a note on the Aschbacher biplanes of order 11; Arc subgroups of Planar Singer groups; structure theory for point-Baer and line-Baer collineations in affine planes; flocks of quadratic and semi-elliptic cones; the generalized Kantor-Knuth flocks; spreads corresponding to flocks of quadratics; a new infinite family of extended generalized quadrangles; virtual derivation; some generalized quadrangles in characteristic 2; some p-ranks related to geometric structures; building a cyclic q-clan; hyper-reguli in projective space of dimension 5; parallelisms of PG(3,3) invariant under a collineation of order 5; classical spaces that interact with spreads; Coset representation of homogeneous geometrical structures; division algebras three-dimensional over algebraic number fields.