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Barry Simon

Barry Simon

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To download copies of Barry’s papers for private use, click here. For Barry's Books on Amazon click here. Email [email protected]

I.B.M. Professor of Mathematics and Theoretical Physics, Emeritus

Online Selecta

Barry becomes a SIAM Fellow so a trifecta (with APS in 1981 and AMS in 2013)

David Zierler, Director of the Caltech Heritage Project did 14 hours of interviews with Barry with Audio Files on YouTube and a corrected transcript (which is quicker to process) at Caltech's website

From the 75th birthday (Zoom) conference: Video of Vingettes after the Scientific Talks

Barry elected to the U.S. National Academy of Sciences  NAS Press Release Caltech Press Release

Nature Interview with Barry
The mathematician who helped to reshape physics Nature 584 (2020) 20 (Aug 6, 2020) Online Downloadable PDF 

In 2019, Springer published Loewner's Theorem on Matrix Monotone Functions, Grundlehren der mathematischen Wissenschaften 354,  2019 [order page]

Barry wins AIP/APS Dannie  Heineman Prize for Mathematical Physcs AIP Announcement APS Full Prize List Caltech Press Release APS Page of All Winners

AMS Notices Articles in August and September 2016 issues,  Download: Full August (with cover of Barry), Part 1, Part 2, or combined   -- IAMP Bulletin Version Caltech Interview with Barry

Barry wins AMS Steele Prize for Lifetime Achievement!  AMS Announcement. Caltech Press Release. OP-SF Net Announcement. AMS Page of All Winners. AMS Notices Report on Prize

Barry's 70th birthday conference at Fields Institute (Toronto) and CRM (Montreal) -- August 22-September 1, 2016.  

From the 70th birthday conference: Video of Banquet Talks Poems (or approximations thereof) for Barry

In the second half of 2015, the AMS published Barry's 5 Volume A Comprehensive Course in Analysis all at the same time.  Here is a preview.  Here is the facebook page. Here is the order page.  You can download the Ultimate Companion here.  Here is a review from MAA Reviews and from Notices AMS     .

Barry wins Bolyai Prize.  Pictures from the Prize Ceremony.  Barry's acceptance talk Totik Article on.the prize Hungarain Academy Interview 

Barry wins Poincaré Prize. Citation  | Photos  | Laudatio

For the web page of Barry's book on convexity, click here.

For the web page of Barry's book on Szegö's theorem, click here.

For the web page of Barry's OPUC book, click here.

For Paul Nevai's review of Barry's OPUC book, click here

Corrected and extended 2nd printing of Schrödinger Operators with Application to Quantum Mechanics and Global Geometry by H. Cycon, R. Froese, W. Kirsch, and B. Simon is now available.

Click here for a complete list of B. Simon's publications with links to MathSciNet and articles.

For Barry's CV, click here  and for a pdf bibliography, click here

Click here for picture of Barry with Mike Reed (of Reed-Simon) at Reed's 65th birthday celebration, May 2007.

An historic picture from a conference, circa 1983

For Program, Pictures, Video from SimonFest (held March, 2006), click here.

For picture of Swansea Honorary Fellowship (with Aubrey Truman, taken July 2006), click here.

For pictures from Barry's Honarary degree cermony in Munich (and  the associated visit to Munich), click here

A picture from the mid-80's

A.B., Harvard College, 1966
Ph.D. in Physics, Princeton University, 1970
D.Sc.h.c., Technion-Israel Institute of Technology, 1999
Honorary Fellow, University of Wales Swansea, 2006
D.h.c., Ludwig-Maximilians-Universitat Munchen, 2014

Named Lectures
Milton Brockett Porter Lectures, Rice University, 2006
Sixth van Winter Memorial Lecture in Mathematical Physics, University of Kentucky, 2006-2007
The Wolfgang Wasow Memorial Lecture, University of Wisconsin at Madison, 2007
Sackler Lecture, Bohr Institute, University of Copenhagen, 2015
First Lars Ahlfors Lecture, Brigham Young University, 2016
University of Haifa Distinguished Lecture Series in Mathematics, 2018
Baylor Lectures Series in Mathematics, 2018
Lezioni Leonardesche, Milan, 2018
DeLong Lecture Series, University of Colorado, 2019-2020

Other Honors
1965 Putnam Competition Winner (top six group)
Sloan Foundation Fellow, 1972-76
Medal of International Academy of Atomic and Molecular Science, 1981
Fellow, American Physical Society, 1981
Stampacchia Prize, 1982
Guggenheim Fellowship, 1988-1989
Corresponding Member, Austrian Academy of Sciences, 1990
Fellow, American Academy of Arts and Sciences, 2005
Poincare Prize, IAMP, 2012
Fellow, American Mathematical Society, 2013 (initial class)
Simons Foundation Fellowship in Matheamtics, 2013
Bolyai Prize of the Hungarian Academy of Sciences, 2015
Steele Prize for Lifetime Acheivment, AMS, 2016
James Madison High School Wall of Distinction, 2016 (previous honorees include Ruth Ginsburg, Bernie Saunders, Chuck Schummer and "Judge" Judy Sheindlin)
Dannie Heineman Prize in Mathematical Physics, AIP/APS, 2018
Member, National Academy of Sciences, 2019
Fellow, Society for Industrial and Applied Mathematics (SIAM)  2023

B. Simon's Graduate Students (and some of their theses)

B. Simon's "Mentees"

Research Interests

Mathematical physics, especially Schrödinger operators and Spectral Theory of Orthogonal Polynomials

Selected Recent Publications

  • (with J. Christiansen and M. Zinchenko) Asymptotics of Chebyshev Polynomials, I. Subsets of R., Inv. Math, 208 (2017), 217-245
  • A Comprehensive Course in Analysis, Five Volumes, AMS, USA, 2015
  • Loewner's Theorem on Matrix Monotone Functions, Springer, Grundlehren der mathematischen Wissenschaften 354,  (2019)
  • (with A. Avila and Y. Last) Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with a.c. spectrum, Analysis & PDE 3 (2010), 81-108
  • (with D. Damanik and R. Killip) Perturbations of orthogonal polynomials with periodic recursion coefficients, Annals of Math. 171 (2010), 1931-2010

Selected Older Publications

  • Resonances in n-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory, Annals of Math. 97 (1973), 247-274
  • (with M. Reed) Methods of Modern Mathematical Physics, Vol. I: Functional Analysis, Academic Press, 1972; Vol. II: Fourier Analysis, Self-Adjointness, Academic Press, 1975; Vol. III: Scattering Theory, Academic Press, 1978; Vol. IV: Analysis of Operators, Academic Press, 1977
  • (with F. Guerra and L. Rosen) The P(\phi)_2 quantum theory as classical statistical mechanics, Annals of Math. 101 (1975), 111-259
  • (with E. Lieb) The Thomas-Fermi theory of atoms, molecules and solids, Advances in Math. 23 (1977), 22-116
  • (with J. Fröhlich and T. Spencer) Infrared bounds, phase transitions and continuous symmetry breaking, Commun. Math. Phys. 50 (1976), 79-85
  • (with P. Perry and I. Sigal) Spectral analysis of multiparticle Schrödinger operators, Annals of Math. 114 (1981), 519-567
  • (with M. Aizenman) Brownian motion and Harnack's inequality for Schrödinger operators, Commun. Pure Appl. Math. 35 (1982), 209-273
  • Semiclassical analysis of low lying eigenvalues, II. Tunneling, Annals of Math. 120 (1984), 89-118
  • Holonomy, the quantum adiabatic theorem and Berry's phase, Phys. Rev. Lett. 51 (1983), 2167-2170
  • (with T. Wolff) Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians, Commun. Pure Appl. Math. 39 (1986), 75-90
  • Operators with singular continuous spectrum: I. General operators, Annals of of Math. 141 (1995), 131-145
  • The classical moment problem as a self-adjoint finite difference operator, Advances in Math. 137 (1998), 82-203
  • (with Y. Last) Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators, Invent. Math. 135 (1999), 329-367
  • A new approach to inverse spectral theory, I. Fundamental formalism, Annals of Math. 150 (1999), 1029-1057
  • (with F. Gesztesy) A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure, Annals of Math. 152 (2000), 593-643
  • (with R. Killip) Sum rules for Jacobi matrices and their applications to spectral theory, Annals of Math. 158 (2003), 253-321
  • Orthogonal Polynomials on the Unit Circle, Part 1: Classical Theory, AMS Colloquium Publications, Vol. 54.1, American Mathematical Society,   Providence, RI, 2005 [webpage]
  • Orthogonal Polynomials on the Unit Circle, Part 2: Spectral Theory, AMS Colloquium Publications, Vol. 54.2, American Mathematical Society, Providence, RI, 2005 [webpage]
  • Szegö's Theorem and Its Descendants: Spectral Theory for L2 Perturbations of Orthogonal Polynomials, M.B. Porter Lectures, Princeton University Press, Princeton, NJ, 2011 [webpage]
  • (with D. Damanik) Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegö asymptotics, Invent. Math. 165 (2006), 1-50

Barry with a Calculus student's most powerful weapons 

Non-Caltech Items

Go to the Directory for mailing address, fax and telephone numbers, and e-mail address.

B. Simon's complete list of publications and co-authors

B. Simon's papers available from the arXiv.

Click here to get a listing of B. Simon's papers from the AMS MathSciNet with links to Mathematical Reviews.
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Schedule of mathematical physics seminars at Caltech