Yuri I. Manin

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Yuri I. Manin

Yuri Manin with his wife Ksenia Semenova at the ICM 2006 in Madrid
Born Yuri Ivanovitch Manin
(1937-02-16) February 16, 1937
Simferopol, Soviet Union
Residence Germany
Nationality Russia
Fields Mathematician
Institutions Max-Planck-Institut für Mathematik
Northwestern University
Alma mater Moscow State University
Steklov Mathematics Institute (PhD)
Doctoral advisor Igor Shafarevich
Doctoral students Alexander Beilinson, Vladimir Drinfeld, Vasily Iskovskih, Victor Kolyvagin, Vyacheslav Shokurov, Alexei Skorobogatov, et al.
Known for algebraic geometry, diophantine geometry
Notable awards Schock Prize (1999)
Cantor Medal (2002)
Nemmers Prize in Mathematics (1994)
Bolyai Prize (2010)

Yuri Ivanovitch Manin (Russian: Ю́рий Ива́нович Ма́нин; born 1937) is a Soviet/Russian/German[1] 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 gained a doctorate in 1960 at the Steklov Mathematics Institute as a student of Igor Shafarevich. He is now a Professor at the Max-Planck-Institut für Mathematik in Bonn, and a professor at Northwestern University.

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. He wrote an influential book on cubic surfaces and cubic forms, showing how to apply both classical and contemporary methods of algebraic geometry, as well as nonassociative algebra. He also indicated the role of the Brauer group, via Grothendieck's theory of global Azumaya algebras, in accounting for obstructions to the Hasse principle, setting off a generation of further work. He also formulated a series of conjectures on the behaviour of rational points of bounded height on algebraic varieties. He has further written on Yang-Mills theory, quantum information, and mirror symmetry.

Manin had over 40 doctoral students, including Vladimir Berkovich, Mariusz Wodzicki, Alexander Beilinson, Ivan Cherednik, Alexei Skorobogatov, Vladimir Drinfeld, Vyacheslav Shokurov, Arend Bayer and Victor Kolyvagin, as well as foreign students including Hà Huy Khoái, now the most senior mathematician in Vietnam. He was awarded the Schock Prize in 1999 and the Cantor Medal in 2002. In 1994, he was awarded the Nemmers Prize in Mathematics. In 2010, he received the Bolyai Prize of the Hungarian Academy of Sciences.

Works

  • Manin: Selected works with commentary, World Scientific 1996
  • Manin: Mathematics as metaphor - selected essays, American Mathematical Society 2009
  • Manin: Rational points of algebraic curves over function fields. AMS translations 1966 (Mordell conjecture for function fields)
  • Manin: Algebraic topology of algebraic varieties. Russian Mathematical Surveys 1965
  • Manin: Modular forms and Number Theory. International Congress of Mathematicians, Helsinki 1978
  • Manin: Frobenius manifolds, quantum cohomology, and moduli spaces, American Mathematical Society 1999[2]
  • Manin: Quantum groups and non commutative geometry, Montreal, Centre de Recherches Mathématiques, 1988
  • Manin: Topics in non-commutative geometry, Princeton University Press 1991[3]
  • Manin: Gauge field theory and complex geometry. Springer 1988 (Grundlehren der mathematischen Wissenschaften)[4]
  • Manin: Cubic forms - algebra, geometry, arithmetics, North Holland 1986
  • Manin: A course in mathematical logic, Springer 1977[5]
  • Manin: The provable and the unprovable (Russ.), Moscow 1979
  • Manin: The decidable and the undecidable (Russ.), Moscow 1980
  • Manin: Mathematics and physics, Birkhäuser 1981
  • Manin: New dimensions in geometry. in Arbeitstagung Bonn 1984, Lectures Notes in Mathematics Vol. 1111, Springer Verlag
  • Manin, Alexei Ivanovich Kostrikin: Linear algebra and geometry, Gordon and Breach 1989
  • Manin, Sergei Gelfand: Homological algebra, Springer 1994 (Encyclopedia of mathematical sciences).
  • Manin, Sergei Gelfand: Methods of Homological algebra, Springer 1996
  • Manin, Igor Kobzarev: Elementary Particles: mathematics, physics and philosophy, Dordrecht, Kluwer, 1989 (This book is introductory.)
  • Manin, Alexei A. Panchishkin: Introduction to Number theory, Springer Verlag 1995, 2nd edn. 2005
  • Manin Moduli, Motives, Mirrors, 3. European Congress Math. Barcelona 2000, Plenary talk
  • Manin Classical computing, quantum computing and Shor´s factoring algorithm, Bourbaki Seminar 1999
  • Manin Von Zahlen und Figuren 2002
  • Manin, Mathilde Marcolli Holography principle and arithmetic of algebraic curves, 2002
  • Manin 3-dimensional hyperbolic geometry as infinite-adic Arakelov geometry, Inventiones Mathematicae 1991

See also

References

  1. ↑ CURRICULUM VITAE at Max-Planck-Institut für Mathematik website
  2. ↑ Getzler, Ezra (2001). "Review: Frobenius manifolds, quantum cohomology, and moduli spaces by Yuri I. Manin". Bull. Amer. Math. Soc. (N.S.) 38 (1): 101–108. doi:10.1090/S0273-0979-00-00888-0. 
  3. ↑ Penkov, Ivan (1993). "Review: Topics in non-commutative geometry by Yuri I. Manin". Bull. Amer. Math. Soc. (N.S.) 29 (1): 106–111. doi:10.1090/S0273-0979-1993-00391-4. 
  4. ↑ LeBrun, Claude (1989). "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.) 21 (1): 192–196. doi:10.1090/S0273-0979-1989-15816-3. 
  5. ↑ Shoenfield, J. R. (1979). "Review: A course in mathematical logic by Yu. I Manin". Bull. Amer. Math. Soc. (N.S.) 1 (3): 539–541. 

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