The goal of this project is to contribute to the design and execution of a precise experimental test of a theory for the glass and jamming transitions. Indeed, the last few years have witnessed a considerable advance in the microscopic description of glassy systems: an intrinsic relation between these two transitions has been uncovered. The phase diagram was obtained, finding that the jamming transition is located inside the glass phase and corresponds to a transition from entropic rigidity to mechanical rigidity. This last year has brought new breakthroughs: the jamming critical exponents can be computed with the theory, which suggests a precise test in a lab. The testing of these new progresses in theory requires an integrated research program joining theory and experiment, an opportunity that is emerging in Paris, by the collaboration of the group of F. Zamponi (supervisor of this action and one of the co-authors of the main last theoretical results) with the nearby experimental group leaded by O. Dauchot. Hereby, I present this project with the aim of being part of this exciting opportunity.