Barry Simon

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Barry Simon

Barry Martin Simon (born April 16, 1946 in New York City ) is a leading American mathematical physicist and analyst.

life and work

Simon's father was an auditor and his mother a teacher. In 1962, as a high school student in Brooklyn, he won a national mathematics test from the MAA (Mathematical Association of America) and attended courses for the gifted at Columbia University as a student. In 1962 he began studying at Harvard on a scholarship. In 1965, at the age of 19, he was a Putnam Fellow (after winning the competition of the same name) and graduated from Harvard University in 1966. He was studied at Princeton University in 1970 by Arthur Strong Wightman on Quantum mechanics for Hamiltonians defined as quadratic forms doctorate, which was published shortly afterwards as a book.

Simon was then a professor at Princeton for a long time (where Wightman, Valentine Bargmann , Freeman Dyson and Elliott Lieb were at the time, who with Simon made Princeton one of the centers of mathematical physics worldwide) before joining Caltech in 1980 as a Simon Fairchild Distinguished Scholar went, where he became professor in 1981 and has been "IBM Professor of Mathematics and Theoretical Physics" since 1984. He has been Professor Emeritus since 2016.

Simon is the author of over 300 publications on a wide spectrum of mathematical physics and analysis, in particular the theory of the spectrum of Schrödinger operators with applications to atoms and molecules, atoms in electric and magnetic fields, convergence of perturbation series and semiclassical border crossing, stochastic systems (e.g. Schrödinger equation with quasi-periodic or random potentials, random matrices), Thomas-Fermi and Hartree-Fock theory of atoms (partly in collaboration with Elliott Lieb, his colleague in Princeton in the 1970s) and many-body systems in non-relativistic quantum mechanics , mathematical statistical mechanics (theory of phase transitions, etc.), orthogonal polynomials and mathematical (“constructive”) quantum field theory . His four-volume textbook on mathematical physics with Michael Reed is a standard work.

In 1984 he put up a list of 15 problems in mathematical physics ( Simon problems ), which he updated in 2000 (two were added, around five had been solved in the meantime).

Honors and memberships

In 1974 he was invited speaker at the International Congress of Mathematicians in Vancouver (Approximation of Feynman Integrals and Markov fields by spin systems). In 2012 he received the Henri Poincaré Prize and in 2015 the Bolyai Prize . He also received the Stampacchia Prize in 1982 and the medal of the International Academy of Atomic and Molecular Science in 1981. He has been a Fellow of the American Mathematical Society since 2013 and of the American Physical Society since 1981 . In 2016 he received the Leroy P. Steele Prize for Lifetime Achievement from the AMS, for 2018 he was awarded the Dannie Heineman Prize for Mathematical Physics from the APS. He has several honorary doctorates ( Technion in Haifa, University of Wales Swansea , Ludwig Maximilians University Munich ).

From 1972 to 1976 he was a Sloan Research Fellow , 1988/89 Guggenheim Fellow and 2013 Simons Foundation Fellow. In 1990 he became a corresponding member of the Austrian Academy of Sciences . He is a Fellow of the American Academy of Arts and Sciences (2005) and a member of the National Academy of Sciences (2019).

Others

His PhD students include Percy Deift , Alexander Kiselev, and Robert B. Israel .

He has been married to a math teacher Martha Katzin, who did her PhD at Princeton, since 1971, and has five children. As an Orthodox Jew, he is also known for his commitment to refuting so-called “Torah Codes”. With Woody Leonhard he also wrote some computer books for young people ("Mother of All" series) and wrote for PC Magazine in the 1990s.

Books by Simon

  • Quantum mechanics for Hamiltonians defined as quadratic forms. Princeton University Press, Princeton NJ 1971, ISBN 0-691-08090-9 .
  • with Michael C. Reed : Methods of Modern Mathematical Physics. 4 volumes. Academic Press, New York, NY et al. 1972–1978;
  • The Euclidean (Quantum) Field Theory. Princeton University Press, Princeton NJ 1974, ISBN 0-691-08144-1 .
  • as editor with Elliott H. Lieb, Arthur S. Wightman: Studies in mathematical physics. Essays in Honor of Valentine Bargmann. Princeton University Press, Princeton NJ 1976, ISBN 0-691-08180-8 , therein by Simon:
  • Functional integration and quantum physics (= Pure and Applied Mathematics. 86). Academic Press, New York NY et al. 1979, ISBN 0-12-644250-9 (2nd edition: American Mathematical Society, Providence RI 2005, ISBN 0-8218-3582-3 ).
  • Trace Ideals and their applications (= London Mathematical Society. Lecture Note Series. 35). Cambridge University Press, Cambridge et al. 1979, ISBN 0-521-22286-9 (2nd edition: (= Mathematical Surveys and Monographs. 120). American Mathematical Society, Providence RI 2005, ISBN 0-8218-3581-5 ).
  • with Hans L. Cycon, Richard G. Froese, Werner Kirsch: Schrödinger Operators. Springer, Berlin et al. 1987, ISBN 3-540-16758-7 (Corrected and extended 2nd Print: ibid. 2008, ISBN 978-3-540-16758-7 ).
  • The Statistical Mechanics of Lattice Gases. Volume 1. Princeton University Press, Princeton NJ 1993, ISBN 0-691-08779-2 .
  • Orthogonal polynomials on the unit circle (= American Mathematical Society Colloquium Publications. 54, 1-2). 2 volumes. American Mathematical Society, Providence RI 2005;
  • Convexity. An analytic viewpoint (= Cambridge Tracts in Mathematics. 187). Cambridge University Press, Cambridge et al. 2011, ISBN 1-107-00731-3 .
  • Szegő's theorem and its descendants. Spectral theory for perturbations of orthogonal polynomials. Princeton University Press, Princeton NJ 2011, ISBN 978-0-691-14704-8 .
  • A comprehensive course in Analysis. 4 (in 5) volumes (Vol. 1: Real Analysis. Vol. 2 A: Basic complex Analysis. Vol. 2 B: Advanced complex Analysis. Vol. 3: Harmonic Analysis. Vol. 4: Operator Theory. ). American Mathematical Society, Providence RI 2015, ISBN 978-1-4704-1098-8 .

Articles (selection)

  • Resonances in n-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory. In: Annals of Mathematics . Vol. 97, No. 2, 1973, pp. 247-274, doi : 10.2307 / 1970847 .
  • with Francesco Guerra , Lon Rosen: The Euclidean quantum field theory as classical statistical mechanics. In: Annals of Mathematics. Vol. 101, No. 1, 1975, pp. 111-259, doi : 10.2307 / 1970988 .
  • with Jürg Fröhlich , Thomas C. Spencer : Infrared bounds, phase transitions and continuous symmetry breaking. In: Communications in Mathematical Physics . Vol. 50, No. 1, 1976, pp. 79-85, doi : 10.1007 / BF01608557 .
  • with Elliott H. Lieb : The Thomas-Fermi theory of atoms, molecules and solids. In: Advances in Mathematics . Vol. 23, No. 1, 1977, pp. 22-116, doi : 10.1016 / 0001-8708 (77) 90108-6 .
  • with Peter Perry, Israel M. Sigal: Spectral Analysis of N-Body Schrödinger Operators. In: Annals of Mathematics. Vol. 114, No. 3, 1981, pp. 519-567, doi : 10.2307 / 1971301 .
  • with Michael Aizenman : Brownian motion and Harnack inequality for Schrödinger operators. In: Communications on Pure and Applied Mathematics. Vol. 35, No. 2, 1982, pp. 209-273, doi : 10.1002 / cpa . 3160350206 .
  • Holonomy, the quantum adiabatic theorem and Berry's Phase. In: Physical Review Letters . Vol. 51, No. 24, 1983, pp. 2167-2170, doi : 10.1103 / PhysRevLett.51.2167 .
  • Semiclassical analysis of low lying eigenvalues, II. Tunneling. In: Annals of Mathematics. Vol. 120, No. 1, 1984, pp. 89-118, doi : 10.2307 / 2007072 .
  • with Tom Wolff: Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians. In: Communications on Pure and Applied Mathematics. Vol. 39, No. 1, 1986, pp. 75-90, doi : 10.1002 / cpa . 3160390105 .
  • Operators with singular continuous spectrum: I. General operators. In: Annals of Mathematics. Vol. 141, No. 1, 1995, pp. 131-145, doi : 10.2307 / 2118629 .
  • The classical moment problem as a self-adjoint finite difference operator. In: Advances in Mathematics. Vol. 137, No. 1, 1998, pp. 82-203, doi : 10.1006 / aima.1998.1728 .
  • with Yoram Last: Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger Operators. In: Inventiones Mathematicae . Vol. 135, No. 2, 1999, pp. 329-367, doi : 10.1007 / s002220050288 .
  • A new approach to inverse spectral theory, I. Fundamental formalism. In: Annals of Mathematics. Vol. 150, No. 3, 1999, pp. 1029-1057, doi : 10.2307 / 121061 .
  • with Fritz Gesztesy : A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure. In: Annals of Mathematics. Vol. 152, No. 2, 2000, pp. 593-643, doi : 10.2307 / 2661393 .
  • with Rowan Killip: Sum rules for Jacobi matrices and their applications to spectral theory. In: Annals of Mathematics. Vol. 158, No. 1, 2003, pp. 253-321, JSTOR 3597158 .
  • with David Damanik: Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegő asymptotics. In: Inventiones Mathematicae. Vol. 165, No. 1, 2006, pp. 1-50, doi : 10.1007 / s00222-005-0485-5 .

literature

  • Fritz Gesztesy, Percy Deift, Cherie Galvez, Peter Perry, Wilhelm Schlag (Eds.): Spectral theory and mathematical physics. A commemorative publication in Honor of Barry Simon's 60th birthday. A Conference on Spectral Theory and Mathematical Physics in Honor of Barry Simon's 60th Birthday, March 27-31, 2006, California Institute of Technology, Pasadena, California (= Proceedings of Symposia in Pure Mathematics. 76, 1-2). 2 volumes. American Mathematical Society, Providence RI 2007.
  • Fritz Gesztesy: From Mathematical Physics to Analysis: A Walk in Barry Simon's Mathematical Garden. In: Notices of the American Mathematical Society . Vol. 63, No. 7, 2016, doi : 10.1090 / noti1403 .

Web links

Remarks

  1. ↑ with an error-free test result after submitting an entry for an ambiguous question, which even got him into the New York Times
  2. ↑ Eric Weisstein: Simon's Problems
  3. ↑ Simon: Fifteen Problems in Mathematical Physics. In: Willi Jäger, Jürgen Moser, Reinhold Remmert (eds.): Perspectives in Mathematics. Anniversary of Oberwolfach 1984. Birkhäuser, Basel et al. 1984, ISBN 3-7643-1624-1 , pp. 423-454.
  4. ^ Simon: Schrödinger Operators in the twentieth-first century. In: Athanassios Fokas, Alexander Grigoryan, Thomas Kibble, Boguslav Zegarlinski (eds.): Mathematical Physics 2000. Imperial College Press, London 2000, ISBN 1-86094-230-X , pp. 283-288.
  5. ↑ Bolyai Prize goes to Barry Simon ( Memento of the original from December 22, 2015 in the Internet Archive ) Info: The archive link has been inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. Communication from the Hungarian Academy of Sciences (mta.hu); Retrieved April 12, 2015  @1@ 2Template: Webachiv / IABot / mta.hu
  6. ^ Members of the OeAW: Barry Simon. Austrian Academy of Sciences, accessed on November 14, 2017 .
  7. ↑ Announcing Jew in the City's 2014 Orthodox Jewish All Stars !!
personal data
SURNAME Simon, Barry
ALTERNATIVE NAMES Simon, Barry M.
BRIEF DESCRIPTION American mathematician and physicist
DATE OF BIRTH April 16, 1946
PLACE OF BIRTH New York City