Barry Simon

California Institute of Technology


Primary Section: 11, Mathematics
Secondary Section: 13, Physics
Membership Type: Member (elected 2019)

Biosketch

Barry Simon is a mathematical physicist and analyst. He is known for his research in a variety of areas of mathematical physics including contributions to non-relativistic quantum mechanics, quantum field theory and statistical mechanics. He is also recognized for his work on the spectral theory of orthogonal polynomials. His more than 400 research papers and 20 books are highly cited. He was born in Brooklyn, NY, holds an AB from Harvard and PhD from Princeton (supervised by Arthur Wightman), both in Physics. After receiving his degree in 1970, he was on the faculty jointly in mathematics and physics at Princeton for twelve years. Since 1981, he has been at Caltech, where he is currently the IBM Professor of Mathematics and Theoretical Physics, Emeritus. He has supervised 30 Ph.D. theses and mentored many young scientists. His honors include being a Putnam exam winner, three honorary doctorates, the 2012 Poincaré Prize of IAMP, 2016 AMS Steele Prize for Lifetime Achievement in Mathematics and 2018 Dannie Heineman Prize in Mathematical Physics from the APS. He is a member of the National Academy of Sciences (US), a fellow of the American Academy of Arts and Sciences and a corresponding member of the Austrian Academy of Sciences.

Research Interests

Barry Simon's research has encompassed many areas of mathematical physics and functional analysis, especially spectral theory. An early interest concerned eigenvalue perturbation theory where he was a pioneer on summability methods for divergent perturbation series and on the complex scaling theory of resonances. Among his results relevant to atomic and molecular physics are his proof with Lieb that Thomas-Fermi theory is exact in the infinite charge limit and work with Avron and Herbst on quantum theory in magnetic field including the discovery of diamagnetic inequalities. In the theory of N-body quantum systems, he developed Deift-Simon wave operators and, with Perry and Sigal, N-body Mourre estimates. In constructive field theory, he developed the use of statistical mechanical methods with Guerra and Rosen. He developed the only rigorous proof of non-abelian continuous symmetry breaking in classical spin systems (with Fröhlich and Spencer) and quantum spin systems (with Dyson and Lieb). He was a pioneer in what is called Berry's phase (a term he coined) and was the first to understand the underlying geometric notions. He developed much of the framework for almost periodic Schrödinger operators and, with Wolff, a basic criterion for localization. He led what has been called the singular continuous revolution in spectral theory. Starting with his work with Killip on an analog of Szegó's theorem for orthogonal polynomials on the real line, he oversaw the introduction of spectral theory methods in the study of orthogonal polynomials.

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