Conférence de l'École de Physique des Houches

Einstein's theory states that the geometry of space is a dynamic object identified with gravitation. At the same time, the ideas of quantum mechanics indicate that all the ingredients of physical reality must be "quantized": geometry emerges perhaps from more fundamental constituents, and becomes what is sometimes called "quantum geometry". In this presentation, Marcos Mariño will introduce the context and physical motivation behind the idea of quantum geometry, as well as the new conceptual and mathematical tools needed to describe it.