Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, October 23, 2007, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Marek Sulovský

Curves and Arrangements

I will present one or two discrete geometric results dealing with curves in the plane. First of them is a recent upper bound O(n^(2-1/2s)) [Chan '05] on the complexity of k-levels in an arrangement of s-intersecting curve segments in the plane (where k-level is a closure of the set of all points lying on some of the curve segments, which have exactly k curve segments below them). Although the proof of this result is very simple, a better than quadratic bound has not been known for a long time.

If time permits, I will also talk about the upper bound on the complexity of k-level in an arrangement of lines, which is O(n^(4/3)) [Dey '98] and try to explain, how a theorem about singularities of curves can be used to prove this upper bound.

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