Israel Michael Sigal

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Israel Michael Sigal (born August 31, 1945 in Kiev ) is a Russian-born Canadian-Israeli mathematician who deals with mathematical physics.

Life

Sigal graduated from Gorky State University in 1968 and received his PhD from Tel Aviv University in 1976 . In the Soviet Union he was a student of Felix Berezin . From 1976 to 1978 he was at the ETH Zurich , 1978 to 1981 at Princeton University and from 1981 a scientist at the Weizmann Institute . From 1984 he was a professor at the University of California, Irvine , and from 1985 at the University of Toronto . There he has held the Norman Stuart Robertson Chair in Applied Mathematics since 1998 .

plant

In 1987 he and Avy Soffer proved the asymptotic completeness in the quantum mechanical N-body scattering problem with short-range interactions. and later in 1993 for long-range interaction. With this they solved two of the list of problems in mathematical physics ( Simon problems ) that Barry Simon put forward in 1984. With Volker Bach and Jürg Fröhlich , he dealt with the strict mathematical treatment of non-relativistic quantum electrodynamics as well as the treatment of spectral problems with the renormalization group . Together with his doctoral student Randall Pyke, he proved the instability of temporally periodic, spatially localized solutions of nonlinear wave equations and general bounds for the periods of the solutions of nonlinear wave equations.Further, he dealt with the mathematical theory of quantum mechanical tunneling (with P. Hislop) and with large Coulomb systems, with evidence of the instability of large negatively charged ions. With his PhD student Stephen Gustafsen, he investigated the stability of magnetic eddies (vortices) in superconductors (described by the Ginsburg-Landau theory ), thereby proving a conjecture by Clifford Taubes and Arthur Jaffe , and he found effective dynamic laws for vortex motion. Together with Bach and Fröhlich, he proved that quantum mechanical systems, which are coupled to a thermal reservoir, approach the state of equilibrium again in the event of disturbances from the equilibrium.

Honors and memberships

In 1992 he was Jeffrey-Williams Lecturer at the Canadian Mathematical Society and in 1993 he received the John L. Synge Award . He is a Fellow of the Royal Society of Canada (1993). 1989 to 1991 was a fellow of the Killam Foundation.

In 1990 he was invited speaker at the International Congress of Mathematicians in Kyoto ( Quantum mechanics of many particle systems ) and he was invited speaker at the International Congress for Mathematical Physics in 1979 in Lausanne, 1981 in Berlin and 1986 in Marseille. He is a fellow of the American Mathematical Society .

Michael Loss (at ETH Zurich) and Izabella Laba are among his doctoral students .

Fonts

  • with Stephen J. Gustafson: Mathematical concepts of quantum mechanics , Springer Verlag, 2nd edition 2011
  • with Peter D. Hislop: Introduction to spectral theory: with applications to Schrödinger operators , Springer Verlag 1996
  • Scattering theory for many body quantum-mechanical systems: rigorous results , Lecture Notes in Mathematics 1011, Springer Verlag 1983
  • with Volker Bach, Jürg Fröhlich: Mathematical theory of nonrelativistic matter and radiation , Lett. Math. Phys., 34, 1995, pp. 183-201
  • Asymptotic Completeness, AMS Translations 175, 1996, pp. 183-201 (pdf)

Web links

Individual evidence

  1. ↑ Life data according to American Men and Women of Science , Thomson Gale 2004
  2. ^ Sigal, Soffer: N-particle scattering problem: asymptotic completeness for short range interactions , Annals of Mathematics, Volume 125, 1987, pp. 35-108
  3. ^ Sigal, Soffer, Asymptotic completeness for N-particle long range scattering, Journal of the Am. Math. Soc., Volume 7, 1994, pp. 307-334, pdf
  4. ^ Bach, Fröhlich, Sigal: Quantumelectrodynamics of confined non-relativistic particles , Advances in Mathematics, Volume 137, 1998, pp. 205-289
  5. ↑ Pyke, Sigal: Nonlinear wave and Schrödinger equations , Part 1: Instability of periodic and quasiperiodic solutions , Communications in Mathematical Physics, Volume 153, 1993, pp. 297-320
  6. ↑ Pyke, Sigal: onlinear wave equations: Constraints on periods and exponential bounds for periodic solutions , Duke Math. Journal, Volume 88, 1997, pp. 133-180
  7. ^ Gustafsen, Sigal: The stability of magnetic vortices , Comm. Math. Phys., Vol. 210, 2000, pp. 257-276
  8. ↑ Bach, Fröhlich, Sigal: Return to equilibrium , J. Math. Phys., Volume 41, 2000, pp. 3985-4060
  9. ^ Mathematics Genealogy Project
personal data
SURNAME Sigal, Israel Michael
BRIEF DESCRIPTION Israeli mathematician
DATE OF BIRTH August 31, 1945
PLACE OF BIRTH Kiev