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| Author(s): |
Fabrício Caluza Machado
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2017-02-21 |
| Examining board members: |
Fernando Mario de Oliveira Filho;
Sandra Augusta Santos;
Frank Vallentin
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| Advisor: | Fernando Mario de Oliveira Filho |
| Abstract | |
The kissing number of Rn is the maximum number of pairwise-nonoverlapping unit spheres that can simultaneously touch a central unit sphere. In this thesis we study methods to bound from above the size of such configurations using optimization techniques, like duality and semidefinite programming. The main result achieved is the computation of better bounds for the kissing number in dimensions 9 to 23; a result possible due to the exploitation of symmetries in the polynomials present in the bound proposed by Bachoc and Vallentin (2008), leading to the consideration of smaller semidefinite programs. Finally, the studied bound is extended to a bigger class of problems. (AU) | |
| FAPESP's process: | 14/16058-0 - Semidefinite programming bounds for kissing numbers |
| Grantee: | Fabrício Caluza Machado |
| Support Opportunities: | Scholarships in Brazil - Master |