Monday, October 22, 2007
Technische Universität Berlin
Fakultät II, Institut für Mathematik
Str. des 17. Juni 136,
room MA 041
Lecture - 14:15
Abstract:
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
Abstract:
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.