Lattices and Spherical Designs

This reports on recent developments in the theory of lattices mainly founded by Boris Venkov. A lattice in Euclidean space is called strongly perfect, if the vectors of minimal norm in the lattice form a spherical 4-design.

These are very interesting lattices, since they are certain local maxima of the density function. The relation to spherical designs opens new methods to construct locally densest lattice either via a full classification of all strongly perfect lattices of a given dimension or by proving that particular lattices are strongly perfect using modular forms and representation theory of finite groups.

The url of this page is http://qseries.org/fgarvan/quadformsconf/workshop-program/nebe.html.
Created by F.G. Garvan (fgarvan@math.ufl.edu) on Saturday, February 28, 2009.
Last update made Sat Feb 28 21:49:35 EST 2009.

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