Low temperature glassy systems: Present understanding, open problems and future developments

Jamming of hard spheres is a new critical phenomenon whose exponents are different from those of the other known transitions. These exponents have been recently computed in a mean field approximation whose limits of validity are not known. Even if their values are in very good agreement with the ones obtained by accurate numerical simulations, the deep reasons for this success are not understood. In this paper, after a brief presentation of the state of the art on the glass transition and jamming, I will discuss how this breakthrough can be the starting point of possible progresses in the following directions: the computation of the upper critical dimension for jamming, harmonic oscillations for soft spheres at low temperature, off-equilibrium behavior and quantum glassy effects.