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

In the second half of 2015, the AMS will publish Barry's 5 Volume A Comprehensive Course in Analysis all at the same time. Here is a preview <In Preparation>.

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
hereCorrected 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.

To subscribe to B. Simon's electronic preprint mailing list, click
here.

For Barry's CV, 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 pcitures 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

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

Mathematical physics, especially Schrödinger operators

*Szego's Theorem and Its Descendants: Spectral Theory for L*, M.B. Porter Lectures, Princeton University Press, Princeton, NJ, 2011^{2}Perturbations of Orthogonal Polynomials*Convexity, An Analytic Viewpoint,*Cambridge University Press, Cambridge, UK, 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

*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]

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
- 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

- 2014 Orthodox Jewish Allstars (including Barry)

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