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

Barry wins Poincaré Prize.   Citation  |  Photos  |  Laudatio

An historic picture from a conference, circa 1983

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

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

Click here for a complete list of B. Simon's publications with links to MathSciNet and articles.
To subscribe to B. Simon's electronic preprint mailing list, click here.

For Barry's CV, click here.

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

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

A picture from the mid-80's

A.B., Harvard College, 1966
Ph.D. in Physics, Princeton University, 1970

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

B. Simon's "Mentees"

Research Interests

Mathematical physics, especially Schrödinger operators

Selected Recent Publications

• Szego's Theorem and Its Descendants: Spectral Theory for L² Perturbations of Orthogonal Polynomials, M.B. Porter Lectures, Princeton University Press, Princeton, NJ, 2011
• (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
• (with D. Damanik) Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szego asymptotics, Invent. Math. 165 (2006), 1-50
• (with R. Killip) Sum rules for Jacobi matrices and their applications to spectral theory, Annals of Math. 158 (2003), 253-321
  
  

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
• 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]
  

Courses Taught

Barry with a Calculus student's most powerful weapons 

• Winter 2010–2011: Ma 111b - Analysis, II
• Spring 2010–2011: Ma 110c - Analysis, I

Non-Caltech Items

• Editorial Responsibilities
• Editor, Communications in Mathematical Physics, for Schrödinger Operators and Atomic Physics
• 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

• My LA Times Op-Ed piece on High School Teaching
• My LA Times Dialog on K-12 Mathematics Teaching

• My Position on the Bible Codes
• Mathematicians' Statement on the Bible Codes

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

For paper submissions to Communications in Mathematical Physics, please submit to CommMathPhys@caltech.edu.

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