Explore the completion of the space of Lagrangians for the spectral distance and its applications in a conference talk recorded during the thematic meeting "From smooth to C⁰ symplectic geometry: topological aspects and dynamical implications" at the Centre International de Rencontres Mathématiques in Marseille, France. Delve into results related to conformal dynamics, singular Hamiltonian systems, and connections with sheaf theory. Discover the Audiovisual Mathematics Library's features, including chapter markers, keywords, enriched video content with abstracts and bibliographies, and multi-criteria search options for a comprehensive mathematical learning experience.