Graduiertenkolleg: Methods for Discrete Structures

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Monday Lecture and Colloquium

Monday, December 3, 2012

Freie Universität Berlin
Institut für Informatik
Takustr. 9
14195 Berlin
room 005

Lecture - 14:15

Martin Henk - Magdeburg

Successive minima inequalities

We survey on some classical and new inequalities involving Minkowski's successive minima lambda_i(K) of a (o-symmetric) convex body K\subset R^n, where lambda_i(K) is the smallest positive number lambda such that lambda K contains at least i linearly independent lattice points of Z^n. Minkowski proved bounds for the volume of K in terms of the successive minima, and here we want to discuss possible extensions/generalizations of these inequalities when the volume is replaced by the lattice point enumerator or when the successive minma are subject to certain restrictions.

Colloquium - 16:00

Hao Chen - Freie Universität Berlin

Distance geometry for kissing spheres

A kissing sphere is a sphere that is tangent to a given reference ball. With a Möbius invariant distance function, we develop a distance geometry for kissing spheres. Two fundamental problems, the embeddability problem and the distance completion problem, will be studied in detail. An interesting fact is that the distance matrix for kissing spheres also plays the role of Cayley-Menger matrix, which allows us to prove analogues of results in Euclidean distance geometry. In some sense, our new distance geometry generalizes the classical Euclidean distance geometry.

Letzte Aktualisierung: 23.11.2012