World's Best Scientists 2026 revealed!
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Mathematics
USA
2026

D-Index & Metrics

Mathematics

D-Index
122
Citations
80654
World Ranking
10
National Ranking
7

Physics

D-Index
102
Citations
66988
World Ranking
1518
National Ranking
798

Research.com Recognitions

  • 2026 - Research.com Mathematics in United States Leader Award
  • 2025 - Research.com Mathematics in United States Leader Award
  • 2022 - Research.com Mathematics in United States Leader Award
  • 2019 - Member of the National Academy of Sciences
  • 2018 - Dannie Heineman Prize for Mathematical Physics, American Physical Society and American Institute of Physics
  • 2016 - Steele Prize for Lifetime Achievement
  • 2013 - Fellow of the American Mathematical Society
  • 2012 - Henri Poincaré Prize, International Association of Mathematical Physics
  • 2005 - Fellow of the American Academy of Arts and Sciences
  • 1988 - Fellow of John Simon Guggenheim Memorial Foundation

Overview

Barry Simon is affiliated with the California Institute of Technology in the United States. Their research primarily focuses on mathematics, with a significant emphasis on mathematical physics, applied mathematics, and several intersecting subfields. The scientist's work spans a range of subjects including spectral theory in mathematical physics, mathematical functions and polynomials, and random matrices and applications.

The scientist has contributed to the fields of mathematical physics and theoretical and computational physics, with additional interests in quantum mechanics, graph theory, and analytic number theory. Their scientific output includes publications in various venues, highlighting sustained engagement with both preprint platforms and peer-reviewed journals.

  • Recent papers include "Twelve tales in mathematical physics: An expanded Heineman prize lecture" (2022) published in the Journal of Mathematical Physics
  • "The strong Gauss-Lucas theorem and analyticity of correlation functions via the Lee-Yang theorem" (2022) in the Journal of Mathematical Physics
  • "Widom Factors and Szego-Widom Asymptotics, a Review" (2022) in Operator theory
  • "Periodic Boundary Conditions for Periodic Jacobi Matrices on Trees" (2020) in arXiv (Cornell University)
  • "Remembrances of Harold Widom" (2022) in Notices of the American Mathematical Society

  • Frequent collaborators have included Jacob S. Christiansen, Maxim Zinchenko, Ари Лаптев, Pavel Kurasov, and Serguei Naboko.

  • Major publication venues for the scientist's work are arXiv (Cornell University), Journal of Mathematical Physics, Notices of the American Mathematical Society, Operator theory, and Journal of Mathematical Sciences.

The scientist has also contributed to the literature through book publications, with titles released by notable publishers:

  • Analysis as a Tool in Mathematical Physics (Springer Nature, 2020)
  • Analysis as a Tool in Mathematical Physics: In Memory of Boris Pavlov (California Institute of Technology, 2020)

Awards received by the scientist reflect recognition by various mathematical and physical societies. These include the Dannie Heineman Prize for Mathematical Physics awarded jointly by the American Physical Society and American Institute of Physics in 2018, the Steele Prize for Lifetime Achievement in 2016, and election as a Member of the National Academy of Sciences in 2019.

  • Fellow of the American Mathematical Society (2013)
  • Henri Poincaré Prize, International Association of Mathematical Physics (2012)
  • Fellow of the American Academy of Arts and Sciences (2005)
  • Fellow of John Simon Guggenheim Memorial Foundation (1988)

Best Publications

  • Methods of Modern Mathematical Physics

    Michael Reed;Barry Simon

  • Trace ideals and their applications

    Barry Simon

  • Schrodinger Operators: With Application to Quantum Mechanics and Global Geometry

    H. L. Cycon;Barry Simon

  • Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase

    Barry Simon

  • Functional integration and quantum physics

    Barry Simon

  • Orthogonal polynomials on the unit circle

    Barry Simon

  • The P(φ)[2] Euclidean (quantum) field theory

    Barry Simon

  • Methods of modern mathematical physics. III. Scattering theory

    M. Reed;B. Simon

  • Analysis of Operators

    Michael Reed;Barry Simon

  • The statistical mechanics of lattice gases

    Barry Simon

  • The Thomas-Fermi theory of atoms, molecules and solids

    Elliott H Lieb;Barry Simon

  • Coupling constant analyticity for the anharmonic oscillator

    Barry Simon;A Dicke

  • Schrödinger operators with magnetic fields. I. general interactions

    J. Avron;I. Herbst;B. Simon

  • Resonances in n-Body Quantum Systems With Dilatation Analytic Potentials and the Foundations of Time-Dependent Perturbation Theory

    Barry Simon

  • Schrödinger Semigroups

    Unknown

  • Homotopy and Quantization in Condensed Matter Physics

    J. E. Avron;R. Seiler;B. Simon

  • The Statistical Mechanics of Lattice Gases, Volume I

    Barry Simon

  • The bound state of weakly coupled Schrödinger operators in one and two dimensions

    Barry Simon

  • Brownian motion and harnack inequality for Schrödinger operators

    Michael Aizenman;B. Simon

  • Quantum Mechanics for Hamiltonians Defined as Quadratic Forms

    Barry Martin Simon

  • Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions

    Freeman J. Dyson;Elliott H. Lieb;Barry Simon

Frequent Co-Authors

Fritz Gesztesy
Fritz Gesztesy Baylor University
Elliott H. Lieb
Elliott H. Lieb Princeton University
David Damanik
David Damanik Rice University
Ira Herbst
Ira Herbst University of Virginia
Rowan Killip
Rowan Killip University of California, Los Angeles
Svetlana Jitomirskaya
Svetlana Jitomirskaya University of California, Irvine
Helge Holden
Helge Holden Norwegian University of Science and Technology
Rupert L. Frank
Rupert L. Frank California Institute of Technology
Edward Davies
Edward Davies King's College London
Alexander Kiselev
Alexander Kiselev Duke University

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