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 stochastic block model (SBM) is a random graph model with planted clusters. It is widely
employed as a canonical model to study clustering and community detection, and provides …

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 …

The problem of optimizing over random structures emerges in many areas of science and
engineering, ranging from statistical physics to machine learning and artificial intelligence …

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 …

Recent years witnessed the development of powerful generative models based on flows,
diffusion, or autoregressive neural networks, achieving remarkable success in generating …

The ability to prepare a physical system in a desired quantum state is central to many areas
of physics such as nuclear magnetic resonance, cold atoms, and quantum computing. Yet …

This book provides an introduction to the mathematical and algorithmic foundations of data
science, including machine learning, high-dimensional geometry, and analysis of large …

An intelligent agent interacting with the real world will encounter individual people, courses,
test results, drugs prescriptions, chairs, boxes, etc., and needs to reason about properties of …

With quantum computing technologies nearing the era of commercialization and quantum
supremacy, machine learning (ML) appears as one of the promising'killer'applications …