The completion of the set of Lagrangians and applications to dynamics -- Based on lectures by C. Viterbo

These lectures introduce the completion of the set of Lagrangian submanifolds of a symplectic manifold with respect to the spectral metric. The paper establishes basic properties through the notion of γ-support and presents applications to conformally symplectic dynamics, generalizing the concept of Birkhoff attractor. It also mentions other applications and highlights open questions, demonstrating potential in understanding complex dynamical systems.