The physics of disordered systems and its applications

The theory of disordered systems is undoubtedly the branch of statistical physics that has developed the most in recent years, with spin-offs in fields such as mathematics, biology and optimization. Using simple examples, this year's lecture (2020-2021) will attempt to explain the main ideas and applications.

The aim of this two-year lecture is to describe both the wide variety of problems involved in the physics of disordered systems (localization, transport in the presence of impurities, random fields, spin glasses, interface trapping) and the main theoretical approaches developed over the last few decades (products of random matrices, method of replicas, renormalization, probabilistic methods...) to study them. Over the past thirty years, these methods have made it possible to tackle many other questions outside physics, such as optimization, neural networks and species evolution.