This is an extended version of my Nobel Lecture, delivered on December 8, 2021. I will
recall the genesis of the concept of multiple equilibria in natural sciences. I will then describe …

Despite decades of work, gaining a first-principles understanding of amorphous materials
remains an extremely challenging problem. However, recent theoretical breakthroughs have …

The low-frequency vibrational and low-temperature thermal properties of amorphous solids
are markedly different from those of crystalline solids. This situation is counterintuitive …

Deep learning has been immensely successful at a variety of tasks, ranging from
classification to artificial intelligence. Learning corresponds to fitting training data, which is …

Unusual features of the vibrational density of states D (ω) of glasses allow one to rationalize
their peculiar low-temperature properties. Simulational studies of D (ω) have been restricted …

Glassy solids exhibit a wide variety of generic thermomechanical properties, ranging from
universal anomalous specific heat at cryogenic temperatures to nonlinear plastic yielding …

Low-frequency vibrational modes play a central role in determining various basic properties
of glasses, yet their statistical and mechanical properties are not fully understood. Using …

In 1989, Sir Sam Edwards made the visionary proposition to treat jammed granular materials
using a volume ensemble of equiprobable jammed states in analogy to thermal equilibrium …

We report an analytical study of the vibrational spectrum of the simplest model of jamming,
the soft perceptron. We identify two distinct classes of soft modes. The first kind of modes are …

A remarkable feature of disordered solids distinct from crystals is the violation of the Debye
scaling law of the low-frequency vibrational density of states. Because the low-frequency …