Algebra Seminar

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.