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 …

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 …

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

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 …

We provide a theoretical description of dynamical heterogeneities in glass-forming liquids,
based on the premise that relaxation occurs via local rearrangements coupled by elasticity …

It is now well established that glasses feature quasilocalized nonphononic excitations—
coined “soft spots”—, which follow a universal ω 4 density of states in the limit of low …

It is now well established that structural glasses possess disorder-and frustration-induced
soft quasilocalized excitations, which play key roles in various glassy phenomena. Recent …

We revisit the concept of marginal stability in glasses and determine its range of applicability
in the context of an avalanche-type response to slow external driving. We argue that there is …

We introduce a numerical scheme to evolve functional elastic materials that can accomplish
a specified mechanical task. In this scheme, the number of solutions, their spatial …