Developments in Mathematics Finite Geometries

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. This is a graduate-level book aimed at experienced researchers as well as beginning graduate students in finite geometry, incidence geometry, design theory, coding theory and combinatorics. The 21 articles arise from the Fourth Isle of Thorns Conference on Finite Geometries, held in July 2000. The book contains new high-level results at the forefront of the field as well as authoritative surveys. The articles are written so that beginning graduate students can appreciate them. Among the surveys by the invited speakers are P.J. Cameron ("Fixed Points and cycles"), C.E. Praeger ("Implications of line-transitivity for designs"), B. Schmidt, ("Exponent bounds", which explains recent results on difference sets), and several papers with H. Van Maideghem as co-author on generalized polygons. The editors also contribute: A. Blokhuis, D. Jungnickel, and B. Schmidt ("On a class of symmetric divisible designs which are almost projective planes"), and D. Luyckx and J.A. Thas discuss the geometry of the quadric in six dimensions. There is also a lengthy and complete survey by J.W.P. Hirschfeld and L. Storme ("The packing problem in statistics, coding theory and finite projective spaces: update 2001"). Researchers as well as beginning graduate students in the areas of finite geometry, incidence geometry, design theory, coding theory and combinatorics should appreciate the surveys and original papers by leaders in these fields.