
School of Mathematics and Statistics
Helge Tverberg
University of Bergen
On Radon's Theorem and its many generalizations.
Friday 17th November, 121pm, Carslaw 275.
In 1921 the Austrian mathematician Johann Radon published(as a
lemma), an innocentsounding result : Any set of d+2 points
in dspace can be split in two parts in such a way that the
corresponding two convex hulls have a nonempty 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.
