Graduiertenkolleg: Methods for Discrete Structures

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Monday Lecture and Colloquium

Monday, October 22, 2007

Technische Universität Berlin
Fakultät II, Institut für Mathematik
Str. des 17. Juni 136,
room MA 041

Lecture - 14:15

Gabor Fejes Toth, Budapest

Methods, results and open problems in the theory of packing and covering

This will be a survey on packing and covering with emphasis on problems in low dimensions. It will be shown, how different types of cells can be used to estimate the packing and covering densities, and how weighting technics can reduce global problems to local ones. The use of mean value and continuity arguments for proving existence theorems will be illustrated on some examples. Also some open problems will be presented.

Colloquium - 16:00

Nikolaus Witte - TU Berlin

Zonotopes with large 2D-cuts

There are d-dimensional zonotopes with n zones for which a 2-dimensional central sections with about n^(d-1) (\Omega(n^{d-1})) vertices. For d=3 this was known, with examples provided by the "Ukrainian easter eggs" by Eppstein et al. Our result is asymptotically optimal for all fixed d>=2.

Letzte Aktualisierung: 07.10.2008