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 …

Many questions of fundamental interest in today's science can be formulated as inference
problems: some partial, or noisy, observations are performed over a set of variables and the …

The combination of the compactness of networks, featuring small diameters, and their
complex architectures results in a variety of critical effects dramatically different from those in …

The mechanisms by which modularity emerges in complex networks are not well understood
but recent reports have suggested that modularity may arise from evolutionary selection. We …

We study the satisfiability of randomly generated formulas formed by M clauses of exactly K
literals over N Boolean variables. For a given value of N the problem is known to be most …

An instance of a random constraint satisfaction problem defines a random subset 𝒮 (the set
of solutions) of a large product space XN (the set of assignments). We consider two …

We consider the problem of coloring the vertices of a large sparse random graph with a
given number of colors so that no adjacent vertices have the same color. Using the cavity …

Current quantum computing devices have different strengths and weaknesses depending
on their architectures. This means that flexible approaches to circuit design are necessary …

Physical processes have inspired many optimization heuristics. Most famously, variants of
simulated annealing and genetic algorithms are widely used tools for the exploration of …

Glassy systems are characterized by an extremely sluggish dynamics without any simple
sign of long range order. It is a debated question whether a correct description of such …