Lattice packings: an upper bound on the number of perfect lattices

Abstract

We consider an algorithmic approach by Voronoi to solve the lattice packing problem in any fixed dimension. After a visual introduction that makes clear why we should be interested in enumerating so-called perfect lattices, we continue with proving an upper bound on the number of them. This proof will mostly use geometric properties of perfect lattices and we conclude by a volumetric argument.

Date
Feb 21, 2020
Location
Simons Institute, Berkeley
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Wessel van Woerden
PhD student in Cryptology

My research interests include cryptanalysis and everything related to lattices and algorithms.