Glass and vitrification
The nature of the glass transition is one of the frontier questions in Statistical and Condensed Matter Physics; collective structural relaxation processes distributed over many decades in time develop. While the mode coupling theory made considerable progress in simple liquids, novel glass states and glass-to-glass transition remain to be explored.
The nature of low-temperature excitations in amorphous solids also remains an active field of research, where we recently showed that disordered harmonic oscillators constitute a minimal microscopic model that suffices to explain all vibrational anomalies.