Yakov Eliashberg Explained

Yakov Eliashberg
Birth Date:11 December 1946
Birth Place:Leningrad, USSR
Fields:Mathematics
Workplaces:Stanford University
Alma Mater:St. Petersburg State University
Thesis Title:Surgery of Singularities of Smooth Mappings
Thesis Year:1972
Doctoral Advisor:Vladimir Rokhlin
Doctoral Students:
Known For:Homotopy principle
Awards:Oswald Veblen Prize in Geometry (2001)
Heinz Hopf Prize (2013)
Crafoord Prize (2016)
Wolf Prize in Mathematics (2020)
BBVA Foundation Frontiers of Knowledge Award (2023)

Yakov Matveevich Eliashberg (also Yasha Eliashberg; Russian: link=no|Яков Матвеевич Элиашберг; born 11 December 1946) is an American mathematician who was born in Leningrad, USSR.

Education and career

Eliashberg received his PhD, entitled Surgery of Singularities of Smooth Mappings, from Leningrad University in 1972, under the direction of Vladimir Rokhlin.

Due to the growing anti-Semitism in the Soviet Union, from 1972 to 1979 he had to work at the Syktyvkar State University in the isolated Komi Republic. In 1980 Eliashberg returned to Leningrad and applied for a visa, but his request was denied and he became a refusenik until 1987. He was cut off from mathematical life and was prevented to work in academia, but due to a friend's intercession, he managed to secure a job in industry as the head of a computer software group.[1] [2] [3]

In 1988 Eliashberg managed to move to the United States, and since 1989 he has been Herald L. and Caroline L. Ritch professor of mathematics at Stanford University.[4] Between 2001 and 2002 he was Distinguished Visiting professor at the Institute of Advanced Studies.[5]

Awards

Eliashberg received the "Young Mathematician" Prize from the Leningrad Mathematical Society in 1972.[6] He was an invited speaker at the International Congress of Mathematicians in 1986,[7] 1998[8] and 2006 (plenary lecture).[9] In 1995 he was a recipient of the Guggenheim Fellowship.[10]

In 2001 Eliashberg was awarded the Oswald Veblen Prize in Geometry from the AMS for his work in symplectic and contact topology,[11] in particular for his proof of the symplectic rigidity[12] and the development of 3-dimensional contact topology.[13]

In 2002 Eliashberg was elected to the National Academy of Sciences of the US[14] and in 2012 he became a fellow of the American Mathematical Society.[15] He also was a member of the Selection Committee in mathematical sciences of the Shaw Prize.[16] He received a Doctorat Honoris Causa from the ENS Lyon in 2009[17] and from the University of Uppsala in 2017.[18]

In 2013 Eliashberg shared with Helmut Hofer the Heinz Hopf Prize from the ETH, Zurich, for their pioneering research in symplectic topology.[19] In 2016 Yakov Eliashberg was awarded the Crafoord Prize in Mathematics from the Swedish Academy of Sciences for the development of contact and symplectic topology and groundbreaking discoveries of rigidity and flexibility phenomena.[20]

In 2020 he received the Wolf Prize in Mathematics (jointly with Simon K. Donaldson).[21] [22] He was elected to the American Academy of Arts and Sciences in 2021.[23] For 2023 he was awarded the BBVA Foundation Frontiers of Knowledge Award in Basic Sciences (jointly with Claire Voisin).[24]

Research

Eliashberg's research interests are in differential topology, especially in symplectic and contact topology.

In the 80's he developed a combinatorial technique which he used to prove that the group of symplectomorphisms is

l{C}0

-closed in the diffeomorphism group.[25] This fundamental result, proved also in a different way by Gromov,[26] is now called the Eliashberg-Gromov theorem, and is one of the first manifestation of symplectic rigidity.

In 1990 he discovered a complete topological characterization of Stein manifolds of complex dimension greater than 2.[27]

Eliashberg classified contact structures into "tight" and "overtwisted" ones.[28] Using this dichotomy, he gave the complete classification of contact structures on the 3-sphere. Together with Thurston, he developed the theory of confoliations, which unifies foliations and contact structures.[29]

Eliashberg worked on various aspects of the h-principle, introduced by Mikhail Gromov, and he wrote in 2002 an introductory book on the subject.[30]

Together with Givental and Hofer, Eliashberg pioneered the foundations of symplectic field theory.

He supervised 41 PhD students as of 2022.

Major publications

Books

Notes and References

  1. Web site: 2020-01-13 . Yakov Eliashberg . 2022-08-08 . Wolf Foundation . en-US.
  2. Web site: Schulman . Julia . Hsieh . Michael . 2021-02-11 . Coffin Problems: Soviet Anti-Semitism Buried Rising Jewish Scientists . 2022-08-08 . Tablet Magazine.
  3. Book: New perspectives and challenges in symplectic field theory . 2009 . American Mathematical Society . Miguel Abreu, François Lalonde, Leonid Polterovich . 978-0-8218-4356-7 . Providence, R.I. . 370387862.
  4. Web site: Yakov Eliashberg . 2022-08-09 . mathematics.stanford.edu . en.
  5. Web site: 2019-12-09 . Yakov Eliashberg . 2022-08-08 . www.ias.edu . en.
  6. Web site: SPb. Math. Society: the awards . 2022-08-09 . Saint Petersburg Mathematical Society.
  7. Book: Proceedings of the International Congress of Mathematician 1986 . . 1986 . Gleason . Andrew M. . Andrew M. Gleason . 1 . Berkeley . 531–539.
  8. Book: Proceedings of the International Congress of Mathematician 1998 . . 1998 . Louis . Alfred K. . 2 . Berlin . 327–338 . Schneider . Peter . Peter Schneider (mathematician).
  9. Book: Proceedings of the International Congress of Mathematician 2006 . . 2007 . Sanz-Solé . Marta . Marta Sanz-Solé . 1 . Madrid . 217–246 . Soria . Javier . Varona . Juan Luis . Verdera . Joan.
  10. Web site: Yakov Eliashberg . 2022-08-08 . John Simon Guggenheim Memorial Foundation . en-US.
  11. 2001 Veblen Prize . . 48 . 4 . 408–410.
  12. Book: Eliashberg, Ya M. . Proc. of the International Congress of Mathematicians, 1986 . 1986 . 531–539 . Combinatorial methods in symplectic geometry.
  13. Eliashberg . Yakov . 1992 . Contact 3-manifolds twenty years since J. Martinet's work . Annales de l'Institut Fourier . 42 . 1–2 . 165–192 . 10.5802/aif.1288 . 0373-0956. free .
  14. Web site: Yakov Eliashberg . 2022-08-08 . www.nasonline.org.
  15. http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society
  16. Web site: Award Presentation Ceremony 2012 The Shaw Prize . 2022-08-08 . www.shawprize.org . en.
  17. Web site: Mangin . Fabienne . 2019 . La remise des insignes de Docteur 'Honoris Causa', une tradition au sein de l'ENS de Lyon . The presentation of the insignia of doctor "Honoris Causa", a tradition within the ENS of Lyon . 2022-08-08 . alumni.ens-lyon.fr . fr.
  18. Web site: Piehl . Jakob . Honorary Doctors of the Faculty of Science and Technology - Uppsala University, Sweden . 2022-08-08 . www.uu.se . en.
  19. Web site: Laureates 2013 . 2022-08-08 . math.ethz.ch . en.
  20. Web site: The Crafoord Prizes in Mathematics and Astronomy 2016 .
  21. Web site: University . Stanford . 2020-01-17 . Yakov Eliashberg awarded Wolf Prize in Mathematics . 2022-08-08 . Stanford News . en.
  22. Kehoe . Elaine . 2020-06-01 . Donaldson and Eliashberg Awarded 2020 Wolf Prize . . 67 . 6 . 1 . 10.1090/noti2109 . 225820459 . 0002-9920. free .
  23. Web site: Yakov Eliashberg . 2022-08-08 . American Academy of Arts & Sciences . en.
  24. https://www.frontiersofknowledgeawards-fbbva.es/ BBVA Foundation Frontiers of Knowledge Award 2023
  25. Eliashberg . Ya. M. . 1987-07-01 . A theorem on the structure of wave fronts and its applications in symplectic topology . Functional Analysis and Its Applications . en . 21 . 3 . 227–232 . 10.1007/BF02577138 . 121961311 . 1573-8485.
  26. Book: Partial Differential Relations . 1986 . en . 10.1007/978-3-662-02267-2. Gromov . Mikhael . 978-3-642-05720-5 .
  27. Eliashberg . Yakov . 1990-03-01 . Topological characterization of stein manifolds of dimension >2 . International Journal of Mathematics . 01 . 1 . 29–46 . 10.1142/S0129167X90000034 . 0129-167X.
  28. Eliashberg . Y. . 1989-10-01 . Classification of overtwisted contact structures on 3-manifolds . Inventiones Mathematicae . en . 98 . 3 . 623–637 . 10.1007/BF01393840 . 1989InMat..98..623E . 121666486 . 1432-1297. 1404.6157 .
  29. Book: Eliashberg . Y. . Confoliations . Thurston . William P. . 1998 . . 0-8218-0776-5 . Providence, R.I. . 37748408 . William Thurston.
  30. Book: Eliashberg . Y. . Introduction to the h-principle . Mishachev . N. . 2002 . 0-8218-3227-1 . Providence, Rhode Island . 49312496.

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