Math 553B: Configurations
Branko Grünbaum
Spring 1999, MWF 2:30-3:20
The study of configurations of "points" and "lines," subject to suitable
restrictions, can be interpreted at several levels of generality. In purely
geometric terms, configurations such as the ones named after Pappus and
Desargues not only are interesting in their own right, but are also important
as tools in proofs and in various aspects of axiomatics and of algebraization
of geometry. At the topological level, there are close relations of configurations
to oriented matroids, as well as to questions concerning special kinds
of complexes. At the combinatorial level, configurations are special kinds
of designs, which can provide examples for the more general theory as well
as lead to graph-theoretic results and to insights that do not generalize
to arbitrary designs. Questions of enumeration arise at each of the levels,
as do problems of characterization of topologically realizable combinatorial
configurations, or geometrically realizable topological ones. Finally,
the configuration spaces of various kinds of configurations (no pun intended)
are interesting and important from many points of view.
The course assumes only general mathematical maturity, and the standard
undergraduate courses.