Gia Dvali (LMU-MPI & NYU) gives a talk at the MCMP Colloquium (14 January, 2015) titled "Corpuscular structure of geometry". Abstract: We review some recent ideas on quantum-corpuscular structure of gravitational metric backgrounds, such as black holes and cosmological spaces. We show how this picture sheds light on seemingly-mysterious properties, such as, black hole information processing and evaporation, as well as how it excludes eternal de Sitter space. This picture sheds a very different light on notion of "holography" and cosmological constant problem.