Explore a mathematical lecture on stochastic differential equations (SDEs) driven by degenerate noises and their applications to networks of oscillators. Delve into the controllability approach presented by Renaud RAQUEPAS from Université Grenoble-Alpes, France. Learn about key concepts including couplings, exponential mixing, controllability dilemma, and solid controllability. Gain insights into the main results and their implications for understanding complex systems. This 43-minute talk, part of the School and Workshop on Mixing and Control, covers essential topics such as introduction, background, notation, and the Xhat concept, providing a comprehensive overview of this advanced mathematical field.