Despite a great deal of effort, the basic issues in understanding glass/liquid and more general jamming transitions remain unsettled. From the theoretical point of view progress, has been hampered by the absence of a model which displays a transition with the basic features detected in experiments and is simple enough to be analysed. In this seminar we present the first example of short range finite dimensional models for which such an ideal glass transition can be proven to occur: at and above a critical density, a finite fraction of the system is frozen and relaxation times diverge faster than any power law (similar to Vogel-Fulcher law) when approaching the critical density from below. Furthermore, we will show that this transition is related to a new type of percolation transition displaying mixed first order/critical properties: the mass of the infinite cluster is discontinuous and at the same time there is a diverging correlation length.

SPhT, CEA/Saclay