An analysis of well-rounded lattices

• Grant number: 18/12702-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2018
• End date: September 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Carina Alves
• Grantee: William Lima da Silva Pinto
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

Signal constellations having lattice structure are considered good for signal transmission, since the linear structure of the lattices is highly simplifies the decoding task. A good part of lattice research is directed by the search for an answer the following question: how do we dispose spheres of the same radius in Rn without overlap, so as to cover as much space as possible? Another problem similar is the kissing number problem. The kissing number problem arose in a discussion between Isaac Newton and David Gregory in 1964. The question was to find out how many identical spheres can be arranged so that they all touch a similar central sphere. Spherical configurations that give good kissing numbers always come from well-rounded lattice. With this motivation, the proposal of this project is to do a study of well-rounded lattices in dimension bigger or equal to 2.