The nature of the glass transition, between liquid and solid glassy states, is one of the great unsolved mysteries of condensed-matter physics [1]. It is still not clear to what extent thermodynamics and kinetic factors play a role.  A recent fruitful way of investigating the atomic dynamics of liquids is instantaneous normal mode (INM) analysis, in which the "vibrational" eigenmodes are calculated for an instantaneous configuration of the liquid as if it were a solid [2]. In this way, a number of negative eigenvalue (energy), or imaginary frequency, modes appear.  Such modes are associated with unstable portions of the potential-energy surface and some of these modes have been associated with the cooperative flow motion characteristic of the liquid state above the glass-transition temperature, Tg [3]. However, this cannot be the whole picture since it is well known that, for vibrational excitations (as for electrons), states near band edges are spatially localized by structural disorder, and indeed imaginary-frequency INMs can also appear for solids where no diffusional flow occurs. Recently, a conjecture  about the disappearance of the extended (flow) unstable modes at the glass transition has been made [4]. The aim of this project is to investigate for the first time the localization-delocalization  transition by a multifractal analysis [5] in the negative-energy tail of the INM spectrum of a representative disordered system (e.g. silica [6]), to ascertain how many delocalized INM modes exist at a given degree of disorder (i.e. temperature),  to correlate these with the flow behaviour of the model liquid and thus conclude what happens with unstable delocalized (flow) modes around the glass transition. The multifractal codes and the instantaneous configurations of silica  around the glass transition are  available within the group.