Explore a comprehensive overview of structural properties in smooth symplectic mapping class groups and delve into open questions about their C⁰ counterparts in this conference talk. Gain insights into key proof ingredients and recent developments initiated by Alexandre Jannaud. 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. Access this video and other talks by renowned mathematicians through CIRM's Audiovisual Mathematics Library, featuring chapter markers, keywords, enriched content with abstracts and bibliographies, and multi-criteria search functionality.