Improved bounds for the kissing number and related geometrical parameters

• Grant number: 15/05648-4
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: September 01, 2015
• End date: February 29, 2016
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Theory of Computation
• Principal Investigator: Fernando Mario de Oliveira Filho
• Grantee: Fabrício Caluza Machado
• Supervisor: Frank Vallentin
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: University of Cologne (UoC), Germany
• Associated to the scholarship: 14/16058-0 - Semidefinite programming bounds for kissing numbers, BP.MS

Abstract

The kissing number problem asks for the maximum number of nonoverlapping unit balls that can simultaneously touch a central unit ball in Rn. Providing good upper bounds for the kissing number in a given dimension is a challenging optimization task; the best bounds currently known have been obtained via semidefinite programming by Bachoc and Vallentin. Fabrício has recently studied this bound and related methods.The goal of this project is not only to learn new tools and techniques, but to try to obtain new results such as improved bounds. The host for the internship, prof. Frank Vallentin, has been behind some of the most recent developments in the application of optimization methods to geometrical problems like the kissing number problem, and as such the environment will be ideal for the development of this project. (AU)