Barry Simon

Barry Simon
Simon in 2015
Born	16 April 1946 (1946-04-16) (age 78) New York City
Alma mater	AB, Harvard University PhD, Princeton University
Title	Professor
Spouse	Martha Simon
Awards	Henri Poincaré Prize (2012) Bolyai Prize (2015) Leroy P. Steele Prize (2016) Caltech
Doctoral advisor	Arthur Wightman
Doctoral students	Percy Deift Alexander Kiselev Antti Kupiainen

Barry Martin Simon (born 16 April 1946) is an American

During his high school years, Simon started attending college courses for highly gifted pupils at Columbia University. In 1962, Simon won a MAA mathematics competition. The New York Times 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.^[5][2]

In 1962, Simon entered

His status is legendary in mathematical physics and he is renowned for his ability to write scientific manuscripts "in five percent of the time ordinary mortals need to write such papers."[8]

A former graduate student of Simon's, in a tale revealing of his brilliance, once stated:

Barry has always been remarkable for his vast knowledge of mathematics, so it was many years before I can recall ever telling him a published theorem he didn't already know. One day I saw Barry in Princeton shortly after a meeting and told him about an old inequality for

PDEs, which, as I could tell from his intent look, was new to him. I said, "It seems to be useful. Do you want to see the proof?" His response "No, that's OK." Then he went to the board and wrote down a flawless proof on the spot.^[9]

• 1974: Invited Speaker at the International Congress of Mathematicians in Vancouver^[10]
• 1981: Elected fellow of the American Physical Society^[11]
• 1990: Elected correspondent member of the Austrian Academy of Sciences^[12]
• 2005: Elected fellow of the American Academy of Arts and Sciences^[13]
• 2012: Elected fellow of the American Mathematical Society^[14]
• 2012: Awarded the Henri Poincaré Prize^[2]
• 2015: Awarded the Bolyai Prize of the Hungarian Academy of Sciences^[15]
• 2016: Awarded the
  Steele Prize for Lifetime achievements^[2]
• 2018: Dannie Heineman Prize for Mathematical Physics from the American Physical Society^[16]
• 2019: Elected to the National Academy of Sciences^[17]

Selected publications

Articles

• Simon, Barry (1973). "Resonances in n-Body Quantum Systems With Dilatation Analytic Potentials and the Foundations of Time-Dependent Perturbation Theory". The Annals of Mathematics. 97 (2): 247.
  doi:10.2307/1970847
  . (over 700 citations)
• Guerra, F.; Rosen, L.; Simon, B. (1975). "The P(φ)₂ Euclidean Quantum Field Theory as Classical Statistical Mechanics". The Annals of Mathematics. 101 (1): 111-259.
  doi:10.2307/1970988
  .
• Lieb, Elliott H; Simon, Barry (1977). "The Thomas-Fermi theory of atoms, molecules and solids". Advances in Mathematics. 23 (1): 22–116.
  doi:10.1016/0001-8708(77)90108-6
  . (over 700 citations)
• ISSN 0010-3616
  .
• Perry, P.;
  doi:10.2307/1971301
  .
• Simon, Barry (1982). "Schrödinger semigroups". Bulletin of the American Mathematical Society. 7 (3): 447–526.
  ISSN 0273-0979
  . (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)
• Simon, Barry (1983-12-12). "Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase". Physical Review Letters. 51 (24): 2167–2170.
  ISSN 0031-9007
  . (over 2050 citations)
• Avron, J. E.; Seiler, R.; Simon, B. (1983-07-04). "Homotopy and Quantization in Condensed Matter Physics". Physical Review Letters. 51 (1): 51–53.
  ISSN 0031-9007
  . (over 600 citations)
• Simon, Barry (1984). "Semiclassical Analysis of Low Lying Eigenvalues, II. Tunneling". The Annals of Mathematics. 120 (1): 89-118.
  doi:10.2307/2007072
  .
• Simon, Barry;
  ISSN 0010-3640
  .
• Simon, Barry (1995). "Operators with Singular Continuous Spectrum: I. General Operators". The Annals of Mathematics. 141 (1): 131-145.
  doi:10.2307/2118629
  .

• Quantum mechanics for hamiltonians defined as quadratic forms. Princeton University Press, Princeton NJ 1971,
  ISBN 0-691-08090-9
  .
• with Michael C. Reed: Methods of Modern Mathematical Physics. 4 vols. Academic Press, New York, NY etc. 1972–1978;
  • vol. 1: Functional Analysis. 1972,
    ISBN 0-12-585001-8
    ;
  • vol. 2: Fourier Analysis, Self-Adjointness. 1975,
    ISBN 0-12-585002-6
    ;
  • vol. 3: Scattering Theory. Academic Press, 1979,
    ISBN 0-12-585003-4
    ;
  • vol. 4: Analysis of Operators. Academic Press, 1978,
    ISBN 0-12-585004-2
    .
• The ${\displaystyle P(\Phi )_{2}}$ Euclidean (Quantum) Field Theory. Princeton University Press, Princeton NJ 1974,
  ISBN 0-691-08144-1
  .
• 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,
  ISBN 0-691-08180-8
  , 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,
  ISBN 0-8218-3582-3
  ).
• Trace Ideals and their applications (= London Mathematical Society. Lecture Note Series. 35). Cambridge University Press, Cambridge etc. 1979,
  ISBN 0-8218-3581-5
  ).
• with Hans L. Cycon, Richard G. Froese, and Werner Kirsch: Schrödinger Operators. Springer, Berlin etc. 1987,
  ISBN 978-3-540-16758-7
  ).
• The Statistical mechanics of lattice gases. vol. 1. Princeton University Press, Princeton NJ 1993,
  ISBN 0-691-08779-2
  .
• 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,
    ISBN 0-8218-3446-0
    ;
  • vol. 2: Spectral theory. 2005,
    ISBN 0-8218-3675-7
    .
• Convexity. An analytic viewpoint (= Cambridge Tracts in Mathematics. 187). Cambridge University Press, Cambridge etc. 2011,
  ISBN 1-107-00731-3.^[18]
• Szegő´s theorem and its descendants. Spectral theory for ${\displaystyle L^{2}}$ perturbations of orthogonal polynomials. Princeton University Press, Princeton NJ 2011,
  ISBN 978-0-691-14704-8
  .
• A Comprehensive Course in Analysis. 4 vols. with vol. 2 published in 2 parts, American Mathematical Society, Providence RI 2015,
  ISBN 978-1-4704-1098-8
  .
  • vol. 1: Real Analysis.[19]
  • 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,
  ISBN 978-3-030-22421-9^[20]

• Simon problems

References