Victor Ivrii

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Victor Ivrii
Born (1949-10-01) 1 October 1949 (age 71)
Alma materNovosibirsk State University,
AwardsFellow of the Royal Society of Canada 1998,
Killam Research Fellow, 2002-2004
Fellow of American Mathematical Society, 2012.
Scientific career
InstitutionsMagnitogorsk Technical University
École Polytechnique
University of Toronto
Doctoral advisorSergey Sobolev

Victor Ivrii (Russian: Виктор Яковлевич Иврий),[1] FRSC (born 1 October 1949)[2] is a Soviet, Canadian mathematician who specializes in analysis, microlocal analysis, spectral theory and partial differential equations. He is a professor at the University of Toronto Department of Mathematics.

He was an invited speaker at International Congress of Mathematicians, Helsinki—1978 and Berkeley—1986.[3]

Education and Degrees[edit]

He graduated from Physical Mathematical School at Novosibirsk State University in 1965, received his University Diploma (equivalent to MSci) in 1970 and PhD in 1973 in Novosibirsk State University. He defended his Doktor nauk thesis in St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences in 1982.[4]

Scientific Contributions[edit]

Weakly hyperbolic equations[edit]

His first main works were devoted to the well-posedness of the Cauchy problem for weakly hyperbolic equations. In particular he discovered a necessary (later proven to be sufficient) condition for Cauchy problem to be well-posed no matter what the lower terms in the equation are.[5]

Propagation of singularities[edit]

In a series of papers he explored propagation of singularities of symmetric hyperbolic systems inside of the domain and near the boundary. He was invited to give a talk at ICM—1978, Helsinki but was not granted an exit visa by the Soviet authorities;[6] however his talk [7] was published in the Proceedings of the Congress.

Asymptotic distribution of eigenvalues[edit]

His work in propagation of singularities logically guided him to the theory of asymptotic distribution of eigenvalues (a subject he has been studying ever since). V. Ivrii's debut in this field was a proof of Weyl conjecture (1980). Then he developed a rescaling technique which allowed to consider domains and operators with singularities. He again was invited give a talk at ICM—1986, Berkeley but again was not granted an exit visa by the Soviet authorities. His talk [8] was read by Lars Hörmander and published in the Proceedings of the Congress.

V. Ivrii wrote three research monographs,[9][10] and,[11] all published by Springer-Verlag.

Multiparticle quantum theory[edit]

The methods developed by V. Ivrii were very useful for the rigorous justification of Thomas-Fermi theory. Together with Israel Michael Sigal he justified the Scott correction term for molecules.[12] Later V. Ivrii justified the Dirac and Schwinger correction terms.


Awards and honors[edit]


  1. ^ Персоналии: Иврий Виктор Яковлевич
  2. ^
    Victor Ivrii was born October 1, 1949 in Sovetsk, USSR
  3. ^ ICM Plenary and Invited Speakers
  4. ^ V. Ivrii' C.V.
  5. ^ V. Ya. Ivrii, V M Petkov, Necessary conditions for the Cauchy problem for non-strictly hyperbolic equations to be well-posed, Russian Math. Surveys, 1974, 29 (5), 1–70
  6. ^ International Congress of Mathematicians#Soviet participation
  7. ^ "Propagation of singularities of solutions of symmetric hyperbolic systems" (PDF). Archived from the original (PDF) on 2012-05-23. Retrieved 2011-12-25.
  8. ^ "Estimates for the number of negative eigenvalues of the Schrödinger operator with singular potentials" (PDF). Archived from the original (PDF) on 2012-05-23. Retrieved 2011-12-25.
  9. ^ Precise Spectral Asymptotics for Elliptic Operators Acting in Fiberings over Manifolds with Boundary, 1984, 238pp
  10. ^ Microlocal Analysis and Precise Spectral Asymptotics, 1998, 731pp
  11. ^ Microlocal Analysis, Sharp Spectral Asymptotics and Applications, 2019,
  12. ^ V. Ivrii, M. I. Sigal. Asymptotics of the ground state energies of Large Coulomb systems, Annals of Mathematics 138 (1993), 243-335.
  13. ^ fr:Liste des membres de la Société royale du Canada (1997-2005)
  14. ^ fr:Liste des boursiers Killam, par ordre alphabétique I
  15. ^ List of Killam Research Fellows[permanent dead link]
  16. ^ List of Fellows of the American Mathematical Society, retrieved 2013-01-26.

External links[edit]