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* February 16, 1937

Yuri Ivanovich Manin

Max Planck Institute for Mathematics

Academic career

1960	PhD, Steklov Mathematical Institut, Moscow
1963	Habilitation, Steklov Mathematical Institut, Moscow
1960	Principal researcher, Steklov Mathematical Institut,
	Moscow
1965-1992	Professor, algebra, Moscow University
1992-1993	Professor, MIT
1993-2005	Director of the Max Planck Institute, Bonn
2002-	Professor, Northwestern University, Evanston, US
2005-	Professor emeritus, Max Planck Institute, Bonn

Awards

1963	Moscow Mathematical Society Award
1967	Highest USSR National Prize (Lenin Prize)
1987	Brouwer Gold Medal
1994	Frederic Esser Nemmers Prize
1999	Rolf Schock Prize
2002	King Faisal Prize for Mathematics
2002	Georg Cantor Medal of the German Mathematical Society

Member of: Academy of Sciences Russia, Academy of Natural Science Russia, Royal Academy of Sciences the Netherlands, Academia Europaea, Göttingen Academy of Sciences, Pontifical Academy of Sciences, Academia Leopoldina, American Academy of Arts and Sciences, Académie des sciences de l'Institut de France.
Honorary doctoral degrees : Sorbonne, Oslo (Abel Bicentennial), Warwick.

Editorship

Int. Math. Research Notes, Duke Math. J., Theoretical and Math. Phys., Invent. Math. (1966-1978), Amer. J. Math., Crelle J. für die reine u. angew. Math..

Research profile

Algebra and algebraic geometry, non-commutative geometry, mathematical physics.

Contribution to research area "Geometric structures in quantum physics"

Algebraic geometric description of instantons (in collaboration with Atiyah, Drinfeld, Hitchin). Calculation of Polyakov measure in quantum string theory. Laying down foundations of quantum cohomology of algebraic manifolds (in collaboration with M. Kontsevich, K. Behrend). Development of an approach to quantum groups as symmetry objects of quantum spaces.

Contribution to research area "Structural and algorithmic complexity"

Definition and study of Kolmogorov's complexity of partially recursive functions. Development of the notion of algebraic geometric error-correcting codes generalizing Goppa codes which led to the construction by Drinfeld, Tsfasman and Vladut of codes ameliorationg the Gilbert-Varshamov bound. An early (preceding Feynman) suggestion to develop a theory of quantum computation.

General research topics for PhD theses

Algebraic geometry, number theory, mathematical physics

Supervised theses

PhD theses: 45, currently 1

Selected PhD Students

Alexander Beilinson
Vladimir Drinfeld
Yuri Zarhin
Mikhail Kapranov
Yuri Tschinkel
Ralph Kaufmann

Publications

[1]	FRANKE, J., MANIN, Y., AND TSCHINKEL, Y. Rational points of bounded height on Fano varieties. Invent. Math. 95, 2 (1989), 421-435.
[2]	GELFAND, S., AND MANIN, Y. Methods of homological algebra. Springer-Verlag, 1996.
[3]	KONTSEVICH, M., AND MANIN, Y. Gromov-Witten classes, quantum cohomology, and enumerative geometry. Comm. Math. Phys. 164, 3 (1994), 525-562.
[4]	KONTSEVICH, M., AND MANIN, Y. Quantum cohomology of a product. Invent. Math. 124, 1-3 (1996), 313-339.
[5]	MANIN, Y. Hypersurfaces cubiques. II. Automorphismes birationnels en dimension deux. Invent. Math. 6 (1969), 334-352.
[6]	MANIN, Y. Three-dimensional hyperbolic geometry as $\infty$ -adic Arakelov geometry. Invent. Math. 104, 2 (1991), 223-243.
[7]	MANIN, Y. Topics in noncommutative geometry. Princeton University Press, 1991.
[8]	MANIN, Y. Gauge field theory and complex geometry. Springer-Verlag, 1997.
[9]	MANIN, Y. Frobenius manifolds, quantum cohomology, and moduli spaces. American Mathematical Society, 1999.
[10]	MANIN, Y. Classical computing, quantum computing, and Shor's factoring algorithm. Astérisque 266 (2000), 375-404.
[11]	MANIN, Y. Theta functions, quantum tori and Heisenberg groups. Letters Math. Phys. 56:3 (2001), 295-320.
[12]	MANIN, Y. Real multiplication and non-commutative geometry. The Legacy of Niels Henrik Abel (2004), 685-727.
[13]	MANIN, Y., AND LOSEV, A. Extended modular operad. in : Frobenius Manifods, ed. by C.Hertling and M.Marcolli (2004), 181-211.
[14]	MANIN, Y., AND MARCOLLI, M. Continued fractions, modular symbols, and non-commutative geometry. Selecta math. 8 (new series) (2002), 475-521.

seminars

phd students

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