In this paper, the history, present status, and future of density-functional theory (DFT) is
informally reviewed and discussed by 70 workers in the field, including molecular scientists …

In this review, we present the theoretical foundations and first-principles frameworks to
describe quantum matter within quantum electrodynamics (QED) in the low-energy regime …

Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …

In this introductory chapter we first give a brief historical review of optimal transport, then we
recall some basic definitions and facts from measure theory and Riemannian geometry, and …

Over the past five years, multi-marginal optimal transport, a generalization of the well known
optimal transport problem of Monge and Kantorovich, has begun to attract considerable …

We study the decentralized distributed computation of discrete approximations for the
regularized Wasserstein barycenter of a finite set of continuous probability measures …

We study the complexity of approximating the multimarginal optimal transport (MOT)
distance, a generalization of the classical optimal transport distance, considered here …

While in principle exact, Kohn–Sham density functional theory—the workhorse of
computational chemistry—must rely on approximations for the exchange–correlation …

We study multi-marginal optimal transport problems from a probabilistic graphical model
perspective. We point out an elegant connection between the two when the underlying cost …

Wasserstein barycenters correspond to optimal solutions of transportation problems for
several marginals, and as such have a wide range of applications ranging from economics …