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

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 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

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

• Editorial Responsibilities
  • Editor, Communications in Mathematical Physics, for Schrödinger Operators and Atomic Physics, 1979-2014
  • Advisory Board, Communications in Mathematical Physics, 2015-
  • Editor, Inverse Problems and Imaging
  • Editor, Journal of Approximation Theory
  • Editor, Journal of Evolution Equations
  • Editor, Journal of Operator Theory
  • Editor, Journal of Spectral Theory
  • Editor, Cambridge Tracts in Mathematics, New Mathematical Monographs, Cambridge Studies in Advanced Mathematics
  • Advisory Board, Springer Graduate Texts in Mathematics

• My LA Times Op-Ed piece on High School Teaching
• My LA Times Dialog on K-12 Mathematics Teaching
• LA Times article during my service in the "Math Wars"
  

• 2014 Orthodox Jewish Allstars (including Barry) 
  
• Video of 5 Allstars (including Barry)
• Barry chosen for James Madison High School Wall of Distinction,  2016 (previous honorees include Ruth Ginsburg, Bernie Sanders, Chuck Schummer and "Judge" Judy Sheindlin); acceptance speech

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

Math Department Home Page