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 …

The physics of the glass transition and amorphous materials continues to attract the attention
of a wide research community after decades of effort. Supercooled liquids and glasses have …

We combine the swap Monte Carlo algorithm to long multi-CPU molecular dynamics
simulations to analyze the equilibrium relaxation dynamics of model supercooled liquids …

About sixty years ago, the anomalous magnetic response of certain magnetic alloys drew
the attention of theoretical physicists. It soon became clear that understanding these …

Jamming is a ubiquitous phenomenon that appears in many soft matter systems, including
granular materials, foams, colloidal suspensions, emulsions, polymers, and cells—when …

We compute the typical number of equilibria of the generalized Lotka-Volterra equations
describing species-rich ecosystems with random, nonreciprocal interactions using the …

Rich out-of-equilibrium collective dynamics of strongly interacting large assemblies emerge
in many areas of science. Some intriguing and not fully understood examples are the glassy …

We analyze in a closed form the learning dynamics of stochastic gradient descent (SGD) for
a single layer neural network classifying a high-dimensional Gaussian mixture where each …

The similarity in mechanical properties of dense active matter and sheared amorphous
solids has been noted in recent years without a rigorous examination of the underlying …

This perspective article reviews arguments that glass-forming liquids are different from those
of standard liquid-state theory, which typically have a viscosity in the mPa· s range and …