SoSe 13: Ergänzungsmodul Forschungsseminar"Sphere packing"
Günter Ziegler
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Inhalt:
How can we arrange a collection of disjoint unit spheres so that they: (a) don't overlap, except at their boundaries; (b) the interior of the spheres cover as much of some ambient space (e.g., d-dimensional Euclidean space) as possible? This is the so-called Sphere Packing question, and for the 2-dimensional Euclidean plane, the answer is classical; for 3-dimensions the resolution of the "Kepler Conjecture" by Hales in 2005 provides the answer. In other dimensions and for many other natural shapes, only bounds are known.
In this seminar, we'll look at sphere packings and the methods used to establish bounds about them. Along the way, we'll see not only geometric ideas, but, linear and semi-definite programming and lattices, among other objects.
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Litertur:
The books "Sphere Packings" by Chuanming Zong and "Kugelpackungen von Kepler bis Heut" by Max Leppmeier contain a lot of the topics we'll look at, though other references will be used as well.
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Inhalt:
How can we arrange a collection of disjoint unit spheres so that they: (a) don't overlap, except at their boundaries; (b) the interior of the spheres cover as much of some ambient ...
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