Explore the spectral metric on the space of Lagrangians and its completion in this 48-minute lecture by Claude Viterbo from École Normale Supérieure. Delve into the topological and geometric aspects of the completion of Lagrangian space for the spectral metric, examining its connections to symplectic topology and sheaf theory through quantization. Gain insights into this advanced mathematical topic presented at the Institut des Hautes Etudes Scientifiques (IHES).