Finite Geometries -

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Résumé :
When? These are the proceedings of Finite Geometries, the Fourth Isle of Thorns Conference, which took place from Sunday 16 to Friday 21 July, 2000. It was organised by the editors of this volume. The Third Conference in 1990 was published as Advances in Finite Geometries and Designs by Oxford University Press and the Second Conference in 1980 was published as Finite Geometries and Designs by Cambridge University Press. The main speakers were A. R. Calderbank, P. J. Cameron, C. E. Praeger, B. Schmidt, H. Van Maldeghem. There were 64 participants and 42 contributions, all listed at the end of the volume. Conference web site http://www. maths. susx. ac. uk/Staff/JWPH/ Why? This collection of 21 articles describes the latest research and current state of the art in the following inter-linked areas: ? combinatorial structures in finite projective and affine spaces, also known as Galois geometries, in which combinatorial objects such as blocking sets, spreads and partial spreads, ovoids, arcs and caps, as well as curves and hypersurfaces, are all of interest; ? geometric and algebraic coding theory; ? finite groups and incidence geometries, as in polar spaces, gener? alized polygons and diagram geometries; ? algebraic and geometric design theory, in particular designs which have interesting symmetric properties and difference sets, which play an important role, because of their close connections to both Galois geometry and coding theory.

Sommaire:
Point-line geometries with a generating set that depends on the underlying field.- On a class of symmetric divisible designs which are almost projective planes.- Generalized elliptic cubic curves, Part 1.- Fixed points and cycles.- RWPRI geometries for the alternating group A8.- A characterization of truncated Dn-buildings as flag-transitive PG.PG*-geometries.- Group-theoretic characterizations of classical ovoids.- A general framework for subexponential discrete logarithm algorithms in groups of unknown order.- Generalized quadrangles and pencils of quadrics.- The Desarguesian plane of order thirteen.- Two characterizations of the Hermitian spread in the split Cayley hexagon.- Epimorphisms of generalized polygons, Part 2: some existence and non-existence results.- The packing problem in statistics, coding theory and finite projective spaces: update 2001.- The geometric approach to linear codes.- Flocks and locally hermitian 1-systems of Q(6, q).- Diagrams for embeddings of polygons.- The Law-Penttila q-clan geometries.- Implications of line-transitivity for designs.- Exponent bounds.- On symmetries and translation generalized quadrangles.- Complete caps in projective space which are disjoint from a subspace of codimension two.- Participants.- Talks.