Wednesday June 29 2016
Scuola Normale Superiore
École Normale Supérieure, Paris
In 1854, in his treatise on the Laws of Nature, George Boole had stated a clear goal : « to investigate the fundamental laws of those operations of the mind by which reasoning is performed ». This led him to study the foundations of logic and of probabilities. A century later, Claude Shannon opened the way to a mathematical understanding of information and of its communication. The fields of research initiated by these two giants play a major role in contemporary science, and in particular in the handling of large amounts of data, and in the extraction of information out of these data. However, in large-size problems, collective phenomena of the type studied in statistical physics, like phase transitions, start to play a major role. This talk will study the importance of phase transitions in some core problems of Boolean logics and of information theory, with a special focus on the importance of glassy phases.