Convex and Discrete Geometry is an area of mathematics situated between analysis,
geometry and discrete mathematics with numerous relations to other areas. The book gives …

A positive definite quadratic form is called perfect, if it is uniquely determined by its
arithmetical minimum and the integral vectors attaining it. In this self-contained survey we …

Finding the densest sphere packing in d-dimensional Euclidean space R d is an outstanding
fundamental problem with relevance in many fields, including the ground states of molecular …

" Starting from classical arithmetical questions on quadratic forms, this book takes the reader
step by step through the connections with lattice sphere packing and covering problems. As …

Maximally random jammed (MRJ) sphere packing is a prototypical example of a system
naturally poised at the margin between underconstraint and overconstraint. This marginal …

Motivated by the search for best lattice sphere packings in Euclidean spaces of large
dimensions we study randomly generated perfect lattices in moderately large dimensions …

We consider a semi-random walk on the space X of lattices in Euclidean n-space which
attempts to maximize the sphere-packing density function Φ. A lattice (or its corresponding …

We make precise some properties of the Hermite function in relation with the Morse theory
introduced by Avner Ash in his papers 'On eutactic forms', Canad. J. Math. 29 (1977) 1040 …

Eine Kugelpackung im (Rn,(,)) ist eine Anordnung unendlich vieler (n− 1)-dimensionaler
Sphären, so dass sich diese Kugel höchstens berühren, aber nicht schneiden. Jedes Gitter …