Michael Huber

Abstract:   Among the properties of homogeneity of incidence geometries flag-transitivity obviously is a particularly important and natural one. Consequently, in the last decades also flag-transitive Steiner t-designs (i.e. flag-transitive t-(v, k, 1) designs) have been investigated. In a big common effort, Buekenhout, Delandtsheer, Doyen, Kleidman, Liebeck and Saxl essentially characterized all flag-transitive Steiner 2-designs. Their result, which was announced in 1990, makes use of the classification of the finite simple groups.
    However, for Steiner t-designs with parameters t = 3, 4 such characterizations remained challenging open problems for about 40 years.
    This talk presents the complete classifications of all flag-transitive Steiner t-designs with t = 3, 4. Our result relies on the classification of the finite doubly transitive permutation groups. The occurring examples and the most interesting parts of the proofs shall be illustrated.