Yakov Eliashberg

Yakov Eliashberg (Russian: Яков Матвеевич Элиашберг; born 11 December 1946) is an American mathematician who was born in Leningrad, USSR.

Yakov Eliashberg, Crafoord Prize Laureate in Mathematics 2016 at the Royal Swedish Academy of Sciences in Stockholm Sweden May 2016
Yakov Eliashberg, Crafoord Prize Laureate in Mathematics 2016 at the Royal Swedish Academy of Sciences in Stockholm Sweden May 2016
Yakov Eliashberg
Yakov Eliashberg in 1988.
Born (1946-12-11) 11 December 1946
Leningrad, USSR
NationalityAmerican
Alma materSt. Petersburg State University
Known forhis work in symplectic topology and h-principle
AwardsOswald Veblen Prize in Geometry (2001)
Heinz Hopf Prize (2013)
Crafoord Prize (2016)
Wolf Prize in Mathematics (2020)
Scientific career
FieldsMathematics
InstitutionsStanford University
Doctoral advisorVladimir Rokhlin[1]
Doctoral students

He received his Ph.D. from Leningrad University in 1972 under the direction of Vladimir Rokhlin.[2] From 1972 to 1979 he taught at the Syktyvkar State University of Komi Republic of Russia and from 1980 to 1987 worked in industry as the head of a computer software group. In 1988 Eliashberg moved to the United States, and since 1989 he has been a professor of mathematics at Stanford University.

Awards

Eliashberg received the Leningrad Mathematical Society Prize in 1972. In 1986[3], 1998[4] and 2006 (plenary lecture)[5] he was an invited speaker at the International Congress of Mathematicians. He delivered many invited series of lectures around the world. In 1995 Eliashberg was a recipient of the Guggenheim Fellowship.

In 2001 he was awarded the Oswald Veblen Prize in Geometry from the AMS for his work in symplectic and contact topology. In particular for his proof of the symplectic rigidity and the development of 3-dimensional contact topology. In 2009 he received the Doctorat Honoris Causa from the ENS Lyon and in 2017 the Doctorat Honoris Causa from the University of Uppsala. In 2013 Eliashberg shared with Helmut Hofer the Heinz Hopf Prize from the ETH, Zurich, for their pioneering research in symplectic topology. In 2002 Eliashberg was elected to the National Academy of Sciences of the USA. In 2012 he became a fellow of the American Mathematical Society.[6] He also was a member of the Selection Committee in mathematical sciences Shaw Prize.

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. In 2020 he received the Wolf Prize in Mathematics (jointly with Simon K. Donaldson).[7]

Major publications
  • Eliashberg, Y. Classification of overtwisted contact structures on 3-manifolds. Invent. Math. 98 (1989), no. 3, 623–637.
  • Eliashberg, Yakov. Filling by holomorphic discs and its applications. Geometry of low-dimensional manifolds, 2 (Durham, 1989), 45–67, London Math. Soc. Lecture Note Ser., 151, Cambridge Univ. Press, Cambridge, 1990.
  • Eliashberg, Yakov. Topological characterization of Stein manifolds of dimension >2. Internat. J. Math. 1 (1990), no. 1, 29–46.
  • Eliashberg, Yakov; Gromov, Mikhael. Convex symplectic manifolds. Several complex variables and complex geometry, Part 2 (Santa Cruz, CA, 1989), 135–162, Proc. Sympos. Pure Math., 52, Part 2, Amer. Math. Soc., Providence, RI, 1991.
  • Eliashberg, Yakov. Contact 3-manifolds twenty years since J. Martinet's work. Ann. Inst. Fourier (Grenoble) 42 (1992), no. 1-2, 165–192.
  • Eliashberg, Y.; Givental, A.; Hofer, H. Introduction to symplectic field theory. GAFA 2000 (Tel Aviv, 1999). Geom. Funct. Anal. 2000, Special Volume, Part II, 560–673.
  • Bourgeois, F.; Eliashberg, Y.; Hofer, H.; Wysocki, K.; Zehnder, E. Compactness results in symplectic field theory. Geom. Topol. 7 (2003), 799–888.

Books
  • Eliashberg, Yakov M.; Thurston, William P. Confoliations. University Lecture Series, 13. American Mathematical Society, Providence, RI, 1998. x+66 pp. ISBN 0-8218-0776-5
  • Eliashberg, Y.; Mishachev, N. Introduction to the h-principle. Graduate Studies in Mathematics, 48. American Mathematical Society, Providence, RI, 2002. xviii+206 pp. ISBN 0-8218-3227-1
  • Cieliebak, Kai; Eliashberg, Yakov. From Stein to Weinstein and back. Symplectic geometry of affine complex manifolds. American Mathematical Society Colloquium Publications, 59. American Mathematical Society, Providence, RI, 2012. xii+364 pp. ISBN 978-0-8218-8533-8
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References
  1. Yakov Eliashberg at the Mathematics Genealogy Project
  2. Yakov Eliashberg at the Mathematics Genealogy Project
  3. Eliashberg, Ya M. (1986). "Combinatorial methods in symplectic geometry". Proc. of the International Congress of Mathematicians, 1986. pp. 531–539.
  4. Eliashberg, Yakov (1998). "Invariants in contact topology". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. II. pp. 327–338.
  5. Eliashberg, Yakov (2007). "Symplectic field theory and its applications". International Congress of Mathematicians, 2006. vol. 1. pp. 217–246.
  6. List of Fellows of the American Mathematical Society, retrieved 2012-12-02.
  7. Wolf Prize 2020
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