University of Sydney
School of Mathematics and Statistics
University of Bergen
On Radon's Theorem and its many generalizations.
Friday 17th November, 12-1pm, Carslaw 275.
In 1921 the Austrian mathematician Johann Radon published(as a
lemma), an innocent-sounding result : Any set of d+2 points
in d-space can be split in two parts in such a way that the
corresponding two convex hulls have a non-empty intersection. The
proof is simple, just a rewriting of the affine dependence which
must exist between the points.
In this talk I shall describe some of the many results and open,
natural, problems which Radon's Theorem has led to. These are
mostly of a geometric nature, but also very difficult topological
and purely combinatorial problems arise when the concept of
convexity is generalized.