Profile
Profile

Prof. Dr. Yuri Ivanovich Manin

E-mail: manin(at)mpim-bonn.mpg.de
Phone: +49 228 402 229
Homepage: http://www.mpim-bonn.mpg.de/node/99
Location: Max-Planck-Institute for Mathematics
Institute: Max-Planck-Institute for Mathematics
Research Areas: Research Area C
Former Research Area L
Birthdate: 16.Feb 1937
Mathscinet-Number: 190766

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, USA

1993--2005

Director of the Max Planck Institute, Bonn

2005--

Professor emeritus, Max Planck Institute, Bonn

2002--2011

Board of Trustees Professor, Northwestern University, Evanston, USA

2011--

Professor Emeritus

Research Profile

The main themes of the mathematical research of Yu. Manin can be summarized as follows: Geometry, especially Algebraic Geometry, and geometric thinking, as the unifying and creative principle in Number Theory, Physics and Computer Science.

Contribution to Research Areas

Research Area C
The foundations of quantum cohomology of algebraic varieties have been developed by Kontsevich, Manin, Pandharipande, and many others some 15 years ago. Variants and the finer structure are currently investigated. In [1] weighted stable curves are generalized to weighted stable maps and wall crossing phromena are studied in the space of stability conditions. In [2] signal analysis and non-commutative geometry are brought together.
Former Research Area L
In joint work with Marcolli error-correcting codes have been related to the asymptotic bound to phase diagrams of quantum statistical mechanical systems. In a series of papers it is argued that infinities in classical computation theory can be addressed in the same way as Feynman divergences, and that meaningful versions of renormalization in this context can be devised.

Selected Publications

[1] Arend Bayer, Yu. I. Manin
Stability conditions, wall-crossing and weighted Gromov-Witten invariants
Mosc. Math. J. , 9: (1): 3--32, backmatter
2009
ISSN: 1609-3321
[2] Franz Luef, Yuri I. Manin
Quantum theta functions and Gabor frames for modulation spaces
Lett. Math. Phys. , 88: (1-3): 131--161
2009
ISSN: 0377-9017
DOI: 10.1007/s11005-009-0306-7
[3] Yu. I. Manin
Hypersurfaces cubiques. II. Automorphismes birationnels en dimension deux
Invent. Math. , 6: : 334--352
1969
ISSN: 0020-9910
[4] Jens Franke, Yuri I. Manin, Yuri Tschinkel
Erratum: ``Rational points of bounded height on Fano varieties" [Invent.\ Math.\ \bf 95 (1989), no.\ 2, 421--435; MR0974910 (89m:11060)]
Invent. Math. , 102: (2): 463
1990
ISSN: 0020-9910
DOI: 10.1007/BF01233436
[5] M. Kontsevich, Yu. Manin
Gromov-Witten classes, quantum cohomology, and enumerative geometry [ MR1291244 (95i:14049)]
Mirror symmetry, II
of AMS/IP Stud. Adv. Math. : 607--653
Publisher: Amer. Math. Soc., Providence, RI
1997
[6] M. Kontsevich, Yu. Manin
Quantum cohomology of a product
With an appendix by R. Kaufmann
Invent. Math. , 124: (1-3): 313--339
1996
ISSN: 0020-9910
DOI: 10.1007/s002220050055
[7] K. Behrend, Yu. Manin
Stacks of stable maps and Gromov-Witten invariants
Duke Math. J. , 85: (1): 1--60
1996
ISSN: 0012-7094
DOI: 10.1215/S0012-7094-96-08501-4
[8] Sergei I. Gelfand, Yuri I. Manin
Methods of homological algebra
Springer Monographs in Mathematics : xx+372
Publisher: Springer-Verlag, Berlin
2003
ISBN: 3-540-43583-2
[9] Yuri I. Manin
Theta functions, quantum tori and Heisenberg groups
EuroConférence Moshé Flato 2000, Part III (Dijon)
Lett. Math. Phys. , 56: (3): 295--320
2001
ISSN: 0377-9017
DOI: 10.1023/A:1017909525397
[10] Yuri I. Manin, Matilde Marcolli
Continued fractions, modular symbols, and noncommutative geometry
Selecta Math. (N.S.) , 8: (3): 475--521
2002
ISSN: 1022-1824
DOI: 10.1007/s00029-002-8113-3
[11] A. Losev, Yu. Manin
Extended modular operad
Frobenius manifolds
Aspects Math., E36 : 181--211
Publisher: Vieweg, Wiesbaden
2004

Publication List

Editorships

Member, Editorial and Advisory Boards of Mathematical Sbornik, Uspekhi Math. Nauk, Inventiones Math., Duke Mathematical Journal, Functional Analysis and its
Applications, Crelle's Journal, Journal of Number Theory, Journal of Geometry and Physics, Advances of Math., International Journal of Mathematics, American Journal of Mathematics, Algebra and Number Theory et al. (various years).

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

2007

Order Pour le m'erite, Germany

2008

Great Cross of Merit with Star, Germany

2010

Janos Bolyai International Mathematical Prize

Selected PhD students

V. Iskovskikh, Yu. Zarkhin, V. Berkovich, V. Drinfeld, A. Panchishkin, A. Beilinson,
V. Cherednik, Yu. Tschinkel, M. Kapranov, A. Bayer, M. Vishik, A. Skorobogatov, A. Voronov, I. Penkov.

Supervised Theses

  • PhD theses: 51
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