## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Tuesday, December 16, 2008, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Rom Pinchasi (Technion, Israel)

## Some new results related to the 'halving lines problem'

We introduce several interrelated results concerning with halving lines of a set of $n$ points in the plane and measure concentration in the plane. We will be motivated by the following result:

For every $\epsilon>0$ there exists $\alpha(\epsilon)>0$ such that for every continuous probability measure $\mu$ in the plane one can find two lines that cross at an angle of $\alpha(\epsilon)$ such that the measure $\mu$ of each of the two quadrants of angle $\pi-\alpha(\epsilon)$ is at least $1/2-\epsilon$.

We will provide lower bounds for the maximum possible value of $\alpha(\epsilon)$ and show how this problem is related to the halving lines problem. We will also present some new results concerning halving lines.

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