Jürgen Richter-Gebert -Technische Universität München

Using Cinderella.2 in mathematical explorations, education and research

Abstract: The new version of the interactive geometry software Cinderella offers functionality that goes far beyond the treatment of elementary geometry. In particular the programme includes modules for

• transformations and transformation groups
• fractals
• physics simulation
• external and internal scripting

Colloquium - 16:00

Stephan Hell -Technische Universität Berlin

On a topological fractional Helly theorem

Abstract: Helly's theorem is a classical theorem in convex geometry: For every finite family F of convex sets in d-dimensional Euclidean space in which every d or fewer sets have a common point we have a point common to the whole family. The fractional Helly theorem for convex sets is a deep extension of Helly's theorem.

In my talk I start with a survey on recent fractional Helly theorems using different approaches. Then I present a new topological fractional Helly theorem: We show that finite families of open sets (and of subcomplexes of finite cell complexes) in d-dimensional Euclidean space have fractional Helly number k, where k depends on the dimension d and the homological intersection complexity of the family.