Abstract Radon theorem

So far Radon and Helly theorems have been very useful when dealing with convex sets. In this talk I will describe how one can use topology and Ramsey theory to extend the Radon theorem to much broader setting.

Several years ago, we provided a general framework that allows them to be used in more general settings, however the obtained bounds were enormous. In this talk I will present several results that in some cases dramatically improve the bounds. I will also sketch some problems in Ramsey theory and related areas, whose solution is needed to make further progress.

This talk is based on the results I have obtained during my stay at IST Austria.