In this review article we discuss connections between the physics of disordered systems,
phase transitions in inference problems, and computational hardness. We introduce two …

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

From the winner of the Turing Award and the Abel Prize, an introduction to computational
complexity theory, its connections and interactions with mathematics, and its central role in …

We consider the problem of finding nearly optimal solutions of optimization problems with
random objective functions. Such problems arise widely in the theory of random graphs …

Local algorithms on graphs are algorithms that run in parallel on the nodes of a graph to
compute some global structural feature of the graph. Such algorithms use only local …

We consider the algorithmic problem of finding a near ground state (near optimal solution) of
a p-spin model. We show that for a class of algorithms broadly defined as Approximate …

We prove, under an assumption on the critical points of a real-valued function, that the
symmetric Ising perceptron exhibits thefrozen 1-RSB'structure conjectured by Krauth and …

Boolean satisfiability (k-SAT) is one of the most studied optimization problems, as an
efficient (that is, polynomial-time) solution to k-SAT (for k≥ 3) implies efficient solutions to a …

We study the Ising pure $ p $-spin model for large $ p $. We investigate the landscape of the
Hamiltonian of this model. We show that for any $\gamma> 0$ and any large enough $ p …

We study the problem of determining the capacity of the binary perceptron for two variants of
the problem where the corresponding constraint is symmetric. We call these variants the …