相关论文: The work of Elliott Lieb

This article is dedicated to Elliott Lieb in celebration of his 90th birthday. I recount briefly some history of our joint work on the existence of the thermodynamic limit for Coulomb systems and discuss, even more briefly, two open…

A fundamental paper of Elliott Lieb from 1973 has been the basis for much beautiful work on matrix inequalities by many people over the following years. We review a well-connected set of these developments. Some new proofs are provided.

This is a report on the work of Robert Langlands, following his award of the Abel Prize in 2018. It includes his contributions to the general areas of Representation Theory, Automorphic Forms, Number Theory and Arithmetic Geometry. We have…

Mel Levy and Elliott Lieb are two of the most prominent researchers who have dedicated their efforts to the investigation of fundamental questions in many-electron theory. Their results have not only revolutionized the theoretical approach…

We review some topics in the theory of symmetric decreasing rearrangements with a particular focus on Lieb's fundamental contributions. Topics covered include the Brascamp--Lieb--Luttinger theorem, the sharp Young and…

Mathematical physics has many facets, of which we shall briefly give a (very partial) description, centered around those of main interest for Elliott and us (Moshe Flato and I). In our case these aspects had as a corollary a variety of…

The Lieb-Oxford bound, a nontrivial inequality for the indirect part of the many-body Coulomb repulsion in an electronic system, plays an important role in the construction of approximations in density functional theory. Using the…

The Nobel prize in physics for 2022 was given for performing Bell experiments with varying degree of sophistication. The interpretation of this experiment is discussed by first recalling Bell's simple argument behind his inequalities, in…

We review some recent progress on Lieb-Thirring inequalities, focusing on direct methods to kinetic estimates for orthonormal functions and applications for many-body quantum systems.

This is an extended version of my 2018 Heinemann prize lecture describing the work for which I got the prize. The citation is very broad so this describes virtually all my work prior to 1995 and some afterwards. It discusses work in…

Michel Talagrand (Centre National de la Recherche Scientifique, France) has been awarded the prestigious Abel Prize for 2024 for his work in probability theory, functional analysis, and statistical physics. In this note, we introduce the…

This is an exposition of the contributions of L\'aszl\'o Lov\'asz to mathematics and computer science written on the occasion of the bestowal of the Abel Prize~2021 to him. Our survey, of course, cannot be exhaustive. We sketch remarkable…

Review of Stability of Matter in Quantum Mechanics, by Elliott H. Lieb and Robert Seiringer, Cambridge University Press, Cambridge, 2010, xv+293 pp, ISBN 978-0-521-19118-0.

This article is an account of the scientific work of Hugo Duminil-Copin at the time of his award in 2022 of the Fields Medal "for solving longstanding problems in the probabilistic theory of phase transitions in statistical physics,…

We investigate and prove Lieb-Oxford bounds in one dimension by studying convex potentials that approximate the ill-defined Coulomb potential. A Lieb-Oxford inequality establishes a bound of the indirect interaction energy for electrons in…

A simple and completely general representation of the exact exchange-correlation functional of density-functional theory is derived from the universal Lieb-Oxford bound, which holds for any Coulomb-interacting system. This representation…

We give a brief review of the main results of the theory of elliptic hypergeometric functions -- a new class of special functions of mathematical physics. We prove the most general univariate exact integration formula generalizing Euler's…

We review some older and more recent results concerning the energy and particle distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic in nature: they describe properties of many-particle systems in the…

The ideas and results that are in the background of the 2022 Nobel Prize in physics had an immense impact on our understanding of reality. Therefore, it is crucial that these implications reach also the general public, not only the…

Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, inparticular, are important for the construction of improved density functionals. Here we investigate one…