Prof. Dr. Yuri Ivanovich Manin

E-mail: manin(at)
Phone: +49 228 402 229
Location: Max Planck Institute for Mathematics
Institute: Max Planck Institute for Mathematics
Research Areas: Research Area C
Former Research Area L
Date of birth: 16.Feb 1937
Mathscinet-Number: 190766

Academic Career


PhD, Steklov Mathematical Institute, Moscow, Russia


Habilitation, Steklov Mathematical Institute, Moscow, Russia

1960 - 1993

Principal Researcher, Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

1965 - 1992

Professor (Algebra Chair), University of Moscow, Russia

1992 - 1993

Professor, Massachusetts Institute of Technology, Cambridge, MA, USA

1993 - 2005

Scientific Member, Max Planck Institute for Mathematics, Bonn

1995 - 2005

Director, Max Planck Institute for Mathematics, Bonn

2002 - 2011

Board of Trustees Professor, Northwestern University, Evanston, IL, USA

Since 2005

Professor Emeritus, Max Planck Institute for Mathematics, Bonn

Since 2011

Professor Emeritus, Northwestern University, Evanston, IL, USA

Research Profile

Currently I work on several projects, new or continuing former ones. They include:

• development and understanding of recently discovered by me “zeta polynomials”, conjecturally producing Euler factors of Mellin transforms of cusp forms “in characteristic one”.

• developing the theory of non-commutative modular symbols and Dedekind symbols.

• studying the motivic properties of moduli spaces and non-commutative modular symbols.

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.
In [3], new quantum pictures of the Universe near the Big Bang point were developed.
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.
See [4,5,6].

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
[2] Franz Luef, Yuri I. Manin
Quantum theta functions and Gabor frames for modulation spaces
Lett. Math. Phys. , 88: (1-3): 131--161
DOI: 10.1007/s11005-009-0306-7
[3] Yuri Manin, Matilde Marcolli
Symbolic dynamics, modular curves, and Bianchi IX cosmologies
Ann. Fac. Sci. Toulouse Math. (6) , 25: (2-3): 517--542
DOI: 10.5802/afst.1503
[4] Yuri Manin, Matilde Marcolli
Kolmogorov complexity and the asymptotic bound for error-correcting codes
J. Differential Geom. , 97: (1): 91--108
[5] Yu. I. Manin
Zipf's law and Levin probability distributions
Funktsional. Anal. i Prilozhen. , 48: (2): 51--66
[6] Yuri I. Manin
Renormalisation and computation II: time cut-off and the Halting problem
Math. Structures Comput. Sci. , 22: (5): 729--751
DOI: 10.1017/S0960129511000508
[7] Yu. I. Manin
Hypersurfaces cubiques. II. Automorphismes birationnels en dimension deux
Invent. Math. , 6: : 334--352
[8] Jens Franke, Yuri I. Manin, Yuri Tschinkel
Erratum: “Rational points of bounded height on Fano varieties&rdquot; [Invent.\ Math.\ \bf 95 (1989), no.\ 2, 421--435; MR0974910 (89m:11060)]
Invent. Math. , 102: (2): 463
DOI: 10.1007/BF01233436
[9] 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
[10] M. Kontsevich, Yu. Manin
Quantum cohomology of a product
With an appendix by R. Kaufmann
Invent. Math. , 124: (1-3): 313--339
DOI: 10.1007/s002220050055
[11] K. Behrend, Yu. Manin
Stacks of stable maps and Gromov-Witten invariants
Duke Math. J. , 85: (1): 1--60
DOI: 10.1215/S0012-7094-96-08501-4
[12] Sergei I. Gelfand, Yuri I. Manin
Methods of homological algebra
Springer Monographs in Mathematics : xx+372
Publisher: Springer-Verlag, Berlin
ISBN: 3-540-43583-2
DOI: 10.1007/978-3-662-12492-5
[13] Yuri I. Manin
Theta functions, quantum tori and Heisenberg groups
EuroConférence Moshé Flato 2000, Part III (Dijon)
Lett. Math. Phys. , 56: (3): 295--320
DOI: 10.1023/A:1017909525397
[14] Yuri I. Manin, Matilde Marcolli
Continued fractions, modular symbols, and noncommutative geometry
Selecta Math. (N.S.) , 8: (3): 475--521
DOI: 10.1007/s00029-002-8113-3
[15] A. Losev, Yu. Manin
Extended modular operad
Frobenius manifolds
Aspects Math., E36 : 181--211
Publisher: Friedr. Vieweg, Wiesbaden

Publication List


• Mathematical Sbornik (Member, Editorial and Advisory Boards)
• Uspekhi Mat. 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)



Moscow Mathematical Society Award


Highest USSR National Prize (Lenin Prize)


Brouwer Gold Medal


Frederic Esser Nemmers Prize


Rolf Schock Prize


Doctor honoris causa, University of Paris VI (Université Pierre et Marie Curie), Sorbonne, France


King Faisal Prize for Mathematics


Georg Cantor Medal of the German Mathematical Society


Abel Bicentennial Doctor Phil. honoris causa, University of Oslo, Norway


Doctor honoris causa, University of Warwick, England, UK


Order Pour le Mérite, Germany


Great Cross of Merit with Star, Germany


János Bolyai International Mathematical Prize


Honorary Member, London Mathematical Society

Selected Invited Lectures


International Congress of Mathematicians, Moscow, Russia


International Congress of Mathematicians, Nice, France


International Congress of Mathematicians, Helsinki, Finland


International Congress of Mathematicians, Berkeley, CA, USA


International Congress of Mathematicians, Kyoto, Japan


International Congress of Mathematicians, special activity, Madrid, Spain

Selected PhD students

Vasili Iskovskih (1968)

Yuri Zarkhin (1975): “Tate's conjectures for abelian varieties in finite characteristic”

Vladimir Drinfeld (1978),
now Harry Pratt Judson Distinguished Service Professor, University of Chicago, IL, USA

Alexei Panchishkin (1979): “Convolutions of Mdular Forms of Integral and Half Integral Weight”,
now Professor, Institut Fourier, Grenoble University I

Mikhail Vishik (1980),
now Professor, University of Texas, Austin, TX, USA

Ivan Penkov (1987): “Typical Modules over Classical Lie Superalgebras and their Geometric Realizations”,
now Professor, Jacobs University Bremen

Alexander Voronov (1988),
now Professor, University of Minnesota-Minneapolis, MN, USA

Yuri Tschinkel (1992): “Arithmetic of Algebraic Surfaces”,
now Professor, New York University, NY, USA

Arend Bayer (2006): “Semisimple Quantum Cohomology, Deformations of Stability Conditions and the Derived Category”,
now Reader, University of Edinburgh, Scotland, UK

Alexander Beilinson,
now David and Mary Winton Green University Professor, University of Chicago, IL, USA

Ivan Cherednik,
now Austin M. Carr Distinguished Professor, University of North Carolina at Chapel Hill, NC, USA

Mikhail Kapranov

Vladimir Berkovich,
now Professor, Weizmann Institute of Science, Israel

Alexei Skorobogatov,
now Professor, Imperial College London, England, UK

Supervised Theses

  • PhD theses: 51
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