Configuracions de punts d'energia mínima a l'esfera

Abstract

[en] In 1904, the Nobel Prize in Physics J.J. Thomson, raised the following problem: how to distribute electrons on a spherical surface with the minimal energy. One hundred years later, the problem remains open. In 1998, S. Smale, Fields Medal, proposed a list of eighteen unsolved mathematical problems for the 21st century. The seventh is closely connected with Thomson’s question. In the study of the minimal energy configurations on the sphere or on other surfaces there is still a great deal to do. The researchers discovered connections with coding theory, physics of superconductors, the atomic theory... and the research continues. The objective of this work is bibliographic: to study some of the theoretical basis and questions about optimal spherical configurations of points. Gradually, the approximations we present are more accurate. However, the answer is still far beyond our reach.