Yuri Manin Explained

Birth Name:Yuri Ivanovich Manin
Native Name:Юрий Манин
Native Name Lang:ru
Birth Date:16 February 1937
Birth Place:Simferopol, Crimean ASSR, Russian SFSR, Soviet Union
Death Place:Bonn, Germany[1]
Nationality:Russian
Field:Mathematics
Doctoral Advisor:Igor Shafarevich
Known For:Manin conjecture
Manin matrix
Manin obstruction
Manin triple
Manin–Drinfeld theorem
Manin–Mumford conjecture
ADHM construction
Gauss–Manin connection
Cartier–Manin operator
CH-quasigroup
Modular symbol
Quantum simulator

Yuri Ivanovich Manin (Russian: link=no|Ю́рий Ива́нович Ма́нин; 16 February 1937 – 7 January 2023) was a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.

Life and career

Manin was born on 16 February 1937 in Simferopol, Crimean ASSR, Soviet Union.

He received a doctorate in 1960 at the Steklov Mathematics Institute as a student of Igor Shafarevich. He became a professor at the Max-Planck-Institut für Mathematik in Bonn, where he was director from 1992 to 2005 and then director emeritus.[2] He was also a Trustee Chair Professor at Northwestern University from 2002 to 2011.[3]

He had over the years more than 40 doctoral students, including Vladimir Berkovich, Mariusz Wodzicki, Alexander Beilinson, Ivan Cherednik, Alexei Skorobogatov, Vladimir Drinfeld, Mikhail Kapranov, Vyacheslav Shokurov, Ralph Kaufmann, Victor Kolyvagin, Alexander A. Voronov, and Hà Huy Khoái.

Manin died on 7 January 2023.[4]

Research

Manin's early work included papers on the arithmetic and formal groups of abelian varieties, the Mordell conjecture in the function field case, and algebraic differential equations. The Gauss–Manin connection is a basic ingredient of the study of cohomology in families of algebraic varieties.[5]

He developed the Manin obstruction, indicating the role of the Brauer group in accounting for obstructions to the Hasse principle via Grothendieck's theory of global Azumaya algebras, setting off a generation of further work.[6] [7]

Manin pioneered the field of arithmetic topology (along with John Tate, David Mumford, Michael Artin, and Barry Mazur).[8] He also formulated the Manin conjecture, which predicts the asymptotic behaviour of the number of rational points of bounded height on algebraic varieties.[9]

In mathematical physics, Manin wrote on Yang–Mills theory, quantum information, and mirror symmetry.[10] [11] He was one of the first to propose the idea of a quantum computer in 1980 with his book Computable and Uncomputable.[12]

He wrote a book on cubic surfaces and cubic forms, showing how to apply both classical and contemporary methods of algebraic geometry, as well as nonassociative algebra.[13]

Awards

He was awarded the Brouwer Medal in 1987, the first Nemmers Prize in Mathematics in 1994, the Schock Prize of the Royal Swedish Academy of Sciences in 1999, the Cantor Medal of the German Mathematical Society in 2002, the King Faisal International Prize in 2002, and the Bolyai Prize of the Hungarian Academy of Sciences in 2010.[4]

In 1990, he became a foreign member of the Royal Netherlands Academy of Arts and Sciences.[14] He was a member of eight other academies of science and was also an honorary member of the London Mathematical Society.[4]

Selected works

See also

Further reading

External links

Notes and References

  1. Fedor Bogomolov. Yuri Tschinkel. Memorial Article for Yuri Manin. Notices of the American Mathematical Society. December 2023. 70. 11. 1831–1849. 10.1090/noti2814. free.
  2. Web site: Yuri Manin Max Planck Institute for Mathematics. www.mpim-bonn.mpg.de. en. 6 August 2018.
  3. Web site: Yuri Manin – Northwestern University . 20 May 2024 . math.northwestern.edu . en.
  4. Web site: Max Planck Institute for Mathematics in Bonn Mourns Death of Yuri Manin . . 8 January 2023 . 8 January 2023.
  5. English translation in
  6. Book: Serge Lang

    . Serge Lang . Serge Lang . Survey of Diophantine geometry . . 1997 . 3-540-61223-8 . 0869.11051 . 250–258 .

  7. Alexei N. Skorobogatov . Beyond the Manin obstruction . . Appendix A by S. Siksek: 4-descent . 135 . 2 . 399–424 . 1999 . 10.1007/s002220050291 . 0951.14013 . alg-geom/9711006 . 1999InMat.135..399S . 14285244 .
  8. Book: Morishita, Masanori . 2012 . Introduction . Knots and Primes . Universitext . 1–7 . . London . 10.1007/978-1-4471-2158-9_1. 978-1-4471-2157-2 .
  9. Franke . J. . Manin . Y. I. . Yuri I. Manin . Tschinkel . Y. . Rational points of bounded height on Fano varieties . . 95 . 1989 . 2 . 421–435 . 974910 . 0674.14012 . 10.1007/bf01393904. 1989InMat..95..421F . 121044839 .
  10. Michael . Atiyah . Michael Atiyah . Vladimir . Drinfeld . Vladimir Drinfeld . Nigel . Hitchin . Nigel Hitchin . Yuri . Manin . Construction of instantons . . 65 . 1978 . 3 . 185–187. 10.1016/0375-9601(78)90141-X . 1978PhLA...65..185A .
  11. Book: Devchand . Chandrashekar . Ogievetsky . Victor I. . Integrability of N=3 super Yang-Mills equations . Topics in statistical and theoretical physics . 51–58 . Amer. Math. Soc. Transl. Ser. 2 . 177 . . Providence, RI . 1996.
  12. Book: Manin, Yu. I.. Vychislimoe i nevychislimoe. Computable and Noncomputable. 1980. Sov.Radio. 13–15. ru. 4 March 2013. dead. https://web.archive.org/web/20130510173823/http://publ.lib.ru/ARCHIVES/M/MANIN_Yuriy_Ivanovich/Manin_Yu.I._Vychislimoe_i_nevychislimoe.%281980%29.%5Bdjv%5D.zip. 10 May 2013.
  13. Manin: Cubic forms – algebra, geometry, arithmetics, North Holland 1986
  14. Web site: Y.I. Manin . Royal Netherlands Academy of Arts and Sciences . 19 July 2015.
  15. Getzler . Ezra . Review: Frobenius manifolds, quantum cohomology, and moduli spaces by Yuri I. Manin . Bull. Amer. Math. Soc. (N.S.) . 2001 . 38 . 1 . 101–108 . 10.1090/S0273-0979-00-00888-0 . free.
  16. Penkov . Ivan . Review: Topics in non-commutative geometry by Yuri I. Manin . Bull. Amer. Math. Soc. (N.S.) . 1993 . 29 . 1 . 106–111 . 10.1090/S0273-0979-1993-00391-4 . free.
  17. LeBrun . Claude . Claude LeBrun . Review: Gauge field theory and complex geometry by Yuri I. Manin; trans. by N. Koblitz and J. R. King . Bull. Amer. Math. Soc. (N.S.) . 1989 . 21 . 1 . 192–196 . 10.1090/S0273-0979-1989-15816-3 . free.
  18. Shoenfield . J. R. . Review: A course in mathematical logic by Yu. I Manin . Bull. Amer. Math. Soc. (N.S.) . 1979 . 1 . 3 . 539–541 . 10.1090/s0273-0979-1979-14613-5 . free.

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