The Elliott Lieb 90th Anniversary Volume

Elliott Lieb, one of the most influential mathematical physicists worldwide, is 90 years old and this anniversary is celebrated with the publication of the collected volume The Physics and Mathematics of Elliott Lieb, edited by Rupert L. Frank, Ari Laptev, Mathieu Lewin, and Robert Seiringer. In addition, this publication coincides with the Gauss Prize awarded to Lieb at the recent International Congress of Mathematicians 2022, the 2022 American Physical Society Medal for Exceptional Achievement in Research, as well as a high-profile anniversary meeting at Harvard University in his honour.

Together with his various coauthors, Elliott Lieb has produced outstanding research in both mathematics and physics for over six decades, and continues to do so to the present day. For an overview of his work, the Gauss Prize citation and laudatio found at the website of the International Mathematical Union are a good source of information

The two-volume work The Physics and Mathematics of Elliott Lieb includes around 50 chapters, by distinguished authors, which give an extensive account of Lieb’s impact on a very broad range of topics and the resulting subsequent developments. As the editors write in their preface:

"The goal of this book is to demonstrate the impact of Elliott’s work on a very broad range of topics in mathematics and physics. Many chapters are directly concerned with Elliott’s work and the resulting subsequent developments, while others are only loosely connected to it. We have tried to cover most of the areas Elliott has made groundbreaking contributions to, but we have certainly not managed to cover all of them, despite the 1300 pages of these two volumes."

Many contributions are of an expository character and are accessible to a non-expert audience of researchers in mathematics, physics and chemistry. A non-exhaustive list of topics covered includes the problem of stability of matter, quantum many-body systems, density functional theory, topics in statistical mechanics, entropy inequalities and matrix analysis, functional inequalities and sharp constants.

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