A brief introduction to Combinatorial Geometry

DATE:Tuesday, April 5, 2022
TIME:17:00 (s.t.) – 18:00
VENUE:FAV 02 (HH EG 03, Favoritentraße 9 - 11, 1040 Vienna)


Point, lines, and circles are some of the fundamental entities from geometry. In this talk we discuss the underlying combinatorics of point configurations and their dual structures: arrangements of lines and arrangements of great-circles. By slightly relaxing the geometric restrictions ("lines" dont have to be straight and "circles" dont have to be round), we obtain so-called pseudopoint configurations, arrangements of pseudolines and (great-)pseudocircles, respectively. While the original settings cannot be axiomized via finitely many forbidden subconfigurations, we can indeed find such a purely combinatorial describtion for the relaxed "pseudo" setting which allows us to make investigations using computer assistance, and in particular, using SAT attacks. Last but not least, we discuss so-called simple topological drawings, which have the same combinatorial properties as straight-line drawings. Since on top of each point set, we can place a straight-line drawing of the complete graph, simple topological drawings can be seen as a further generalization of point configurations (they indeed also generalize pseudopoint configurations).


Stefan Szeider

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