Monday, October 29, 2007
Technische Universität Berlin
Fak. II, Institut für Mathematik
Str. des 17. Juni 136
10623 Berlin
room MA 041
Lecture - 14:15
Abstract:
Among the properties of homogeneity of incidence structures
flag-transitivity obviously is a particularly important and natural
one. Consequently, in the last decades flag-transitive Steiner
t-designs (i.e. flag-transitive t-(v,k,1) designs) have been
investigated, whereas only by the use of the classification of
the finite simple groups has it been possible in recent years to
essentially characterize all flag-transitive Steiner 2-designs.
However, despite the finite simple group classification, for Steiner
t-designs with parameters t > 2 such characterizations have remained
challenging long-standing open problems.
This talk presents the complete classification of all flag-transitive
Steiner t-designs with t > 2. The result, which relies on the classification
of the finite doubly transitive permutation groups, generalizes work
by J. Tits (1964) and H. Lüneburg (1965). Besides group theory the
proofs also involve incidence geometric, combinatorial and number
theoretical arguments.
The occurring examples and an outline of the proof with the most
interesting parts shall be illustrated.
Colloquium - 16:00
Abstract:
This talk will be about the problem of finding spanning trees of a
graph, where the goal is to maximize the number of leaves. I will give an
overview of recent results on this problem: fast fixed parameter tractable
algorithms, approximation algorithms, and lower bounds for the number of
leaves that can be obtained in various graph classes.