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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
Colloquium - 16:00
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.