Combinatorics Seminar - Oswin Aichholzer

16:15-18:00

Speaker: Oswin Aichholzer

Title: Order Types, Rotation Systems, and Crossing Numbers of K_n

Abstract: In the area of crossing  numbers we ask for minimizing the number of edge intersections in a drawing of a graph.
There is a rich variety of crossing number problems: Which graphs do we consider, what exactly is a drawing of a graph, and how are intersections counted?
In this talk we will concentrate on the crossing number of complete graphs embedded in the plane as either geometric
or simple drawing. We will have a closer look at two useful combinatorial concepts for these representations: order types for the
geometric case, and rotation systes for the topological case.