

1960  PhD, Steklov Mathematical Institute, Moscow, Russia  1963  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 


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 noncommutative modular symbols and Dedekind symbols.
• studying the motivic properties of moduli spaces and noncommutative modular symbols.


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 wallcrossing phromena are studied in the space of stability conditions. In [2], signal analysis and noncommutative 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 errorcorrecting 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]. 


[ 1] Arend Bayer, Yu. I. Manin
Stability conditions, wallcrossing and weighted GromovWitten invariants Mosc. Math. J. , 9: (1): 332, backmatter 2009[ 2] Franz Luef, Yuri I. Manin
Quantum theta functions and Gabor frames for modulation spaces Lett. Math. Phys. , 88: (13): 131161 2009 DOI: 10.1007/s1100500903067[ 3] Yuri Manin, Matilde Marcolli
Symbolic dynamics, modular curves, and Bianchi IX cosmologies Ann. Fac. Sci. Toulouse Math. (6) , 25: (23): 517542 2016 DOI: 10.5802/afst.1503[ 4] Yuri Manin, Matilde Marcolli
Kolmogorov complexity and the asymptotic bound for errorcorrecting codes J. Differential Geom. , 97: (1): 91108 2014[ 5] Yu. I. Manin
Zipf's law and Levin probability distributions Funktsional. Anal. i Prilozhen. , 48: (2): 5166 2014[ 6] Yuri I. Manin
Renormalisation and computation II: time cutoff and the Halting problem Math. Structures Comput. Sci. , 22: (5): 729751 2012 DOI: 10.1017/S0960129511000508[ 7] Yu. I. Manin
Hypersurfaces cubiques. II. Automorphismes birationnels en dimension deux Invent. Math. , 6: : 334352 1969 DOI: 10.1007/BF01425424[ 8] Jens Franke, Yuri I. Manin, Yuri Tschinkel
Erratum: “Rational points of bounded height on Fano varieties” [Invent.\ Math.\ 95(1989), no.\ 2, 421435; MR0974910 (89m:11060)] Invent. Math. , 102: (2): 463 1990 DOI: 10.1007/BF01233436[ 9] M. Kontsevich, Yu. Manin
GromovWitten classes, quantum cohomology, and enumerative geometry [ MR1291244 (95i:14049)] Mirror symmetry, II of AMS/IP Stud. Adv. Math. : 607653 Publisher: Amer. Math. Soc., Providence, RI 1997[ 10] M. Kontsevich, Yu. Manin
Quantum cohomology of a product With an appendix by R. Kaufmann Invent. Math. , 124: (13): 313339 1996 DOI: 10.1007/s002220050055[ 11] K. Behrend, Yu. Manin
Stacks of stable maps and GromovWitten invariants Duke Math. J. , 85: (1): 160 1996 DOI: 10.1215/S0012709496085014[ 12] Sergei I. Gelfand, Yuri I. Manin
Methods of homological algebra Springer Monographs in Mathematics : xx+372 Publisher: SpringerVerlag, Berlin 2003 ISBN: 3540435832 DOI: 10.1007/9783662124925[ 13] Yuri I. Manin
Theta functions, quantum tori and Heisenberg groups EuroConférence Moshé Flato 2000, Part III (Dijon) Lett. Math. Phys. , 56: (3): 295320 2001 DOI: 10.1023/A:1017909525397[ 14] Yuri I. Manin, Matilde Marcolli
Continued fractions, modular symbols, and noncommutative geometry Selecta Math. (N.S.) , 8: (3): 475521 2002 DOI: 10.1007/s0002900281133[ 15] A. Losev, Yu. Manin
Extended modular operad Frobenius manifolds Aspects Math., E36 : 181211 Publisher: Friedr. Vieweg, Wiesbaden 2004



• 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)


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  1999  Doctor honoris causa, University of Paris VI (Université Pierre et Marie Curie), Sorbonne, France  2002  King Faisal Prize for Mathematics  2002  Georg Cantor Medal of the German Mathematical Society  2002  Abel Bicentennial Doctor Phil. honoris causa, University of Oslo, Norway  2006  Doctor honoris causa, University of Warwick, England, UK  2007  Order Pour le Mérite, Germany  2008  Great Cross of Merit with Star, Germany  2010  János Bolyai International Mathematical Prize  2011  Honorary Member, London Mathematical Society 


1966  International Congress of Mathematicians, Moscow, Russia  1970  International Congress of Mathematicians, Nice, France  1978  International Congress of Mathematicians, Helsinki, Finland  1986  International Congress of Mathematicians, Berkeley, CA, USA  1990  International Congress of Mathematicians, Kyoto, Japan  2006  International Congress of Mathematicians, special activity, Madrid, Spain 


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 MinnesotaMinneapolis, 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



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