Disorder, growth and exclusion

Systems as diverse as the growth of bacterial colonies, the burning of paper, the displacement of magnetic walls or road traffic are all subject to the same theory. This theory, at the heart of which is the KPZ (Kardar Parisi Zhang) equation dating back to 1986, has seen spectacular advances over the last two decades.
After presenting some experimental results and numerical simulations of systems that can be described by the KPZ equation, the aim of the lecture was to introduce the main models (exclusion models, polymers in the presence of disorder, sedimentation models) that come under this theory, and to outline the main theoretical approaches for studying them.