# Noon lecture

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On 09.01.2020 at 12:30 in S6, there is the following noon lecture:

# Topological Drawings meet SAT Solvers and Classical Theorems of Convex Geometry

## Manfred Scheucher

## TU Berlin

## Abstract

In a simple topological drawing of the complete graph K_n, vertices are mapped to points in the plane, edges are mapped to simple curves connecting the corresponding end points, and each pair of edges intersects at most once, either in a common vertex or in a proper crossing.

We discuss an axiomatization of simple drawings and for various sub-classes and present a SAT model. With the aid of modern SAT solvers, we investigate some famous and important classical theorems from Convex Geometry (such as Caratheodory's, Helly's, Kirchberger's Theorem, and the Erdös-Szekeres Theorem) in the context of simple drawings.

This is joint work with Helena Bergold, Stefan Felsner, Felix Schröder, and Raphael Steiner.

Research is in progress.

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