Abstract: A problem purely motivated by how geometry emerges from the quantum formalism gives rise to a slightly noncommutative structure and a spectral model of gravity coupled with matter which fits with experimental knowledge. Biosketch: French mathematician Alain Connes is a professor at the Collège de France, IHES, and a Distinguished Professor at Ohio State University, USA. He is the recipient of mathematics’ top award, the Fields Medal (1982), as well as the Crafoord Prize (2001). His work in operator algebras has application in a number of areas, including number theory and particle physics. The Colloqium will be livestreamed from the ICTP website at the date/time indicated at: http://video.ictp.it/livestream