# Lecture by Helena Bergold (Fern Universität Hagen): Topological Drawings meet Classical Theorems of Convex Geometry

In this talk we discuss classical theorems from Convex Geometry such as Carathéodory's Theorem in a more general context of topological drawings of complete graphs. In a (simple) topological drawing the edges of the graph are drawn as simple closed curves such that every pair of edges has at most one common point. Triangles of topological drawings can be viewed as convex sets. This gives a link to convex geometry. Our main result is a generalization of Kirchberger's Theorem that is of purely combinatorial nature. For this we introduce a structure called ''generalized signotopes'' which are a combinatorial generalization of topological drawings. We discuss further properties of generalized signotopes. Joint work with Stefan Felsner, Manfred Scheucher, Felix Schröder and Raphael Steiner.

### Time & Location

Feb 08, 2021 | 02:15 PM

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