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Yuri I. Manin
Yuri I. Manin  

File:Juri Manin, Ksenia Semenova.jpeg  
Born 
Yuri Ivanovitch Manin February 16, 1937 Simferopol, Soviet Union 
Residence  Germany 
Nationality  Russia 
Fields  Mathematician 
Institutions 
MaxPlanckInstitut für Mathematik Northwestern University 
Alma mater 
Moscow State University Steklov Mathematics Institute (PhD) 
Doctoral advisor  Template:If empty 
Doctoral students  Alexander Beilinson, Vladimir Drinfeld, Vasily Iskovskih, Mikhail Kapranov, Victor Kolyvagin, Vyacheslav Shokurov, Alexei Skorobogatov, et al. 
Known for  algebraic geometry, diophantine geometry 
Notable awards 
Nemmers Prize in Mathematics (1994) Schock Prize (1999) Cantor Medal (2002) Bolyai Prize (2010) 
Yuri Ivanovitch Manin (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 MaxPlanckInstitut 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 the Manin conjecture, which predicts the asymptotic behaviour of the number 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, Mikhail Kapranov, 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 Brouwer Medal in 1987, 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 noncommutative 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 3dimensional hyperbolic geometry as infiniteadic Arakelov geometry, Inventiones Mathematicae 1991
 Manin: Mathematik, Kunst und Zivilisation, eenterprise, 2014
See also
 ADHM
 Arithmetic topology
 Manin–Drinfeld theorem
 Manin matrices
 ManinMumford conjecture
 Manin obstruction
 Manin triple
References
 ↑ [1] CURRICULUM VITAE at MaxPlanckInstitut für Mathematik website
 ↑ 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/S0273097900008880.
 ↑ Penkov, Ivan (1993). "Review: Topics in noncommutative geometry by Yuri I. Manin". Bull. Amer. Math. Soc. (N.S.) 29 (1): 106–111. doi:10.1090/S027309791993003914.
 ↑ 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/S027309791989158163.
 ↑ Shoenfield, J. R. (1979). "Review: A course in mathematical logic by Yu. I Manin" (PDF). Bull. Amer. Math. Soc. (N.S.) 1 (3): 539–541. doi:10.1090/s027309791979146135.
Further reading
 Némethi, A. . "Yuri Ivanovich Manin", Acta Mathematica Hungarica, April 2011, Volume 133 (1–2), pp. 1–13.
 JeanPaul Pier (1 January 2000). Development of Mathematics 1950–2000. Springer Science & Business Media. p. 1116. ISBN 9783764362805.
External links
40x40px  Wikiquote has quotations related to: Yuri I. Manin 
 Yuri I. Manin at the Mathematics Genealogy Project
 Manin's page at MaxPlanckInstitut für Mathematik website
 Good Proofs are Proofs that Make us Wiser, interview by Martin Aigner and Vasco A. Schmidt
 Biography

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