Barry Martin Simon (born 16 April 1946) is an American mathematical physicist and was the

IBM International Business Machines Corporation (using the trademark IBM), nicknamed Big Blue, is an American Multinational corporation, multinational technology company headquartered in Armonk, New York, and present in over 175 countries. It is ...

professor of Mathematics and

Theoretical Physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ...

Caltech The California Institute of Technology (branded as Caltech) is a private university, private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small g ...

, known for his prolific contributions in

spectral theory In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operator (mathematics), operators in a variety of mathematical ...

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics ...

, and nonrelativistic

quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

(particularly Schrödinger operators), including the connections to atomic and molecular physics. He has authored more than 400 publications on mathematics and physics. His work has focused on broad areas of mathematical physics and

analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

covering:

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...

statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...

Brownian motion Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas). The traditional mathematical formulation of Brownian motion is that of the Wiener process, which is often called Brownian motion, even in mathematical ...

, random matrix theory, general nonrelativistic quantum mechanics (including N-body systems and

resonance Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximu ...

s), nonrelativistic quantum mechanics in

electric Electricity is the set of physical phenomena associated with the presence and motion of matter possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwel ...

and

magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...

s, the semi-classical limit, the singular continuous spectrum, random and ergodic Schrödinger operators,

orthogonal polynomials In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geom ...

, and non- selfadjoint spectral theory.

Early life

Barry Simon's mother was a school teacher, his father was an accountant. His ancestors were from

Odesa Odesa, also spelled Odessa, is the third most populous List of cities in Ukraine, city and List of hromadas of Ukraine, municipality in Ukraine and a major seaport and transport hub located in the south-west of the country, on the northwestern ...

and

Grodno Grodno, or Hrodna, is a city in western Belarus. It is one of the oldest cities in Belarus. The city is located on the Neman, Neman River, from Minsk, about from the Belarus–Poland border, border with Poland, and from the Belarus–Lithua ...

. His grandfather got the new surname, Simon, at

Ellis Island Ellis Island is an island in New York Harbor, within the U.S. states of New Jersey and New York (state), New York. Owned by the U.S. government, Ellis Island was once the busiest immigrant inspection and processing station in the United State ...

; his original surname was Slopak. Simon attended James Madison High School in

Brooklyn Brooklyn is a Boroughs of New York City, borough of New York City located at the westernmost end of Long Island in the New York (state), State of New York. Formerly an independent city, the borough is coextensive with Kings County, one of twelv ...

. Simon is an observant Jew.

Career

During his high school years, Simon started attending college courses for highly gifted pupils at

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

. In 1962, Simon won a MAA mathematics competition. ''

The New York Times ''The New York Times'' (''NYT'') is an American daily newspaper based in New York City. ''The New York Times'' covers domestic, national, and international news, and publishes opinion pieces, investigative reports, and reviews. As one of ...

'' reported that in order to receive full credits for a faultless test result he had to make a submission with MAA. In this submission he proved that one of the problems posed in the test was ambiguous. In 1962, Simon entered

Harvard Harvard University is a private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher lear ...

with a stipend. He became a Putnam Fellow in 1965 at 19 years old. He received his AB in 1966 from

Harvard College Harvard College is the undergraduate education, undergraduate college of Harvard University, a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Part of the Harvard Faculty of Arts and Scienc ...

and his PhD in

Physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

in 1970, supervised by Arthur Strong Wightman. His dissertation dealt with ''Quantum mechanics for Hamiltonians defined as quadratic forms''. Following his doctoral studies, Simon took a professorship at Princeton for several years, often working with colleague Elliott H. Lieb on the Thomas– Fermi Theory and Hartree– Fock Theory of

atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...

s in addition to

phase transition In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic Sta ...

s and mentoring many of the same students as Lieb. He eventually was persuaded to take a post at

, from which he retired in the summer of 2016.

Honors and awards

*1974: Invited Speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

in Vancouver *1981: Elected fellow of the

American Physical Society The American Physical Society (APS) is a not-for-profit membership organization of professionals in physics and related disciplines, comprising nearly fifty divisions, sections, and other units. Its mission is the advancement and diffusion of ...

*1990: Elected correspondent member of the Austrian Academy of Sciences *2005: Elected fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

*2012: Elected fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

*2012: Awarded the

Henri Poincaré Prize The Henri Poincaré Prize is awarded every three years since 1997 for exceptional achievements in mathematical physics and foundational contributions leading to new developments in the field. It is named after the French mathematician Henri Poincar ...

*2015: Awarded the Bolyai Prize of the Hungarian Academy of Sciences *2016: Awarded the Steele Prize for Lifetime achievements *2018:

Dannie Heineman Prize for Mathematical Physics Dannie Heineman Prize for Mathematical Physics is an award given each year since 1959 jointly by the American Physical Society and American Institute of Physics. It is established by the Heineman Foundation in honour of Dannie Heineman. As of 201 ...

from the

*2019: Elected to the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...

Selected publications

Articles

* (over 700 citations) * * (over 700 citations) * * * (over 1500 citations) *(with M. Aizenman
Brownian motion and Harnack's inequality for Schrödinger operators
Commun. Pure Appl. Math. 35 (1982), 209–273 (over 600 citations) * (over 2050 citations) * (over 600 citations) * * *

Books

* ''Quantum mechanics for hamiltonians defined as quadratic forms.'' Princeton University Press, Princeton NJ 1971, . * with Michael C. Reed: ''Methods of Modern Mathematical Physics.'' 4 vols. Academic Press, New York, NY etc. 1972–1978; ** vol. 1: ''Functional Analysis.'' 1972, ; ** vol. 2: ''Fourier Analysis, Self-Adjointness.'' 1975, ; ** vol. 3: ''Scattering Theory.'' Academic Press, 1979, ; ** vol. 4: ''Analysis of Operators.'' Academic Press, 1978, . * ''The

P(\Phi)_2

Euclidean (Quantum) Field Theory.'' Princeton University Press, Princeton NJ 1974, . * as editor with Elliott H. Lieb and Arthur S. Wightman: ''Studies in mathematical physics. Essays in Honor of Valentine Bargmann.'' Princeton University Press, Princeton NJ 1976, , contributions by Barry Simon: ** pp. 305–326: ''On the number of bound states of two body Schrödinger operators – a review.'
online PDF; 377 kB.
** pp. 327–349: ''Quantum dynamics: from automorphism to hamiltonian.'
online PDF; 573 kB.
* ''Functional integration and quantum physics'' (= ''Pure and Applied Mathematics.'' 86). Academic Press, New York NY etc. 1979, ISBN 0-12-644250-9 (2nd edition: American Mathematical Society, Providence RI 2005, ). * ''Trace Ideals and their applications'' (= ''London Mathematical Society. Lecture Note Series.'' 35). Cambridge University Press, Cambridge etc. 1979, (2nd edition: (= ''Mathematical Surveys and Monographs.'' 120). American Mathematical Society, Providence RI 2005, ). * with Hans L. Cycon, Richard G. Froese, and Werner Kirsch: ''Schrödinger Operators.'' Springer, Berlin etc. 1987, (corrected and extended 2nd printing: Springer 2008, ). * ''The Statistical mechanics of lattice gases.'' vol. 1. Princeton University Press, Princeton NJ 1993, . * ''Orthogonal polynomials on the unit circle'' (= ''American Mathematical Society Colloquium Publications.'' 54, 1–2). 2 vols. American Mathematical Society, Providence RI 2005; ** vol. 1: ''Classical theory.'' 2005, ; ** vol. 2: ''Spectral theory.'' 2005, . * ''Convexity. An analytic viewpoint'' (= ''Cambridge Tracts in Mathematics.'' 187). Cambridge University Press, Cambridge etc. 2011, . * ''Szegő´s theorem and its descendants. Spectral theory for

L^2

perturbations of orthogonal polynomials.'' Princeton University Press, Princeton NJ 2011, .
''A Comprehensive Course in Analysis''
4 vols. with vol. 2 published in 2 parts, American Mathematical Society, Providence RI 2015, . ** vol. 1: ''Real Analysis.'' ** vol. 2A: ''Basic Complex Analysis.'' ** vol. 2B: ''Advanced Complex Analysis.'' ** vol. 3: ''Harmonic Analysis.'' ** vol. 4: ''Operator Theory.''
''Loewner's theorem on monotone matrix functions''
Springer, 2019,

References

External links

* * ttps://scholar.google.com/citations?user=OM0D_3wAAAAJ&oi=ao Publications and citationsat

Google Scholar Google Scholar is a freely accessible web search engine that indexes the full text or metadata of Academic publishing, scholarly literature across an array of publishing formats and disciplines. Released in Beta release, beta in November 2004, th ...

* * (KBS Fest at ISI Bangalore) * * * * * * Caltech Heritage Project, interviews from 2021 & 2022 ** (interview Thursday Nov. 18, 2021) ** ** (interview Friday Nov. 26, 2021) ** ** (interview Thursday Dec. 2, 2021) ** ** (interview Thursday Dec. 9, 2021) ** ** (interview Wednesday Dec. 15, 2021) ** ** (interview Thursday Dec. 23, 2021) ** (interview March 7, 2022) {{DEFAULTSORT:Simon, Barry 1946 births Living people 20th-century American mathematicians 21st-century American mathematicians 21st-century American physicists Jewish American physicists Harvard University alumni Princeton University alumni Princeton University faculty California Institute of Technology faculty Putnam Fellows Fellows of the American Mathematical Society American mathematical physicists Operator theorists James Madison High School (Brooklyn) alumni Mathematicians from New York (state) Members of the United States National Academy of Sciences Fellows of the American Physical Society 21st-century American Jews