Yuri I. Manin

Yuri Manin (Russian Юрий Иванович Манин / Yuri Ivanovich Manin, born February 16, 1937 in Simferopol, Soviet Union, now Ukraine) is a mathematician and Emeritus Scientific Member and Director at the Max Planck Institute for Mathematics in Bonn. His main areas of interest are number theory, Diophantine geometry, mathematical physics and algebraic geometry.

Life and work

Manin studied at the University of Moscow ( Lomonosov University) physics and mathematics and graduated in 1958 summa cum laude, but his first work had previously been published. Then he was at the Steklov Institute of Mathematics in Moscow, where in 1960 he received his doctorate with Igor Shafarevich ( candidate items). He subsequently senior scientist ( Principal Researcher ). In 1963 he completed his habilitation (Russian doctorate ). 1965 to 1992 he was also Professor of Algebra at the University of Moscow. In 1966 he gave a lecture on the ICM in Moscow on rational surfaces and Galoiskohomologie. 1991/92 he was at Columbia University ( Eilenberg Chair ) and from 1992 to 1993 at MIT, but remained ( in absentia ) Member of the Steklov Institute, which he attended regularly. Since 1992 he has been a scientific member at the Max Planck Institute for Mathematics in Bonn, where he was from 1993 to 2005 also director ( he is there since 2005 emeritus). Since 2002 he is Board of Trustees Professor at Northwestern University in Evanston. In addition to Russian, he also has the German nationality.

He has been a visiting professor at the University of Pisa (1964 ), the University of Montreal (1984 ), at the IHES (1967, 1989), at the College de France (1989, 2006), the University of California, Berkeley ( Miller Professor 1989 Chern Lecturer 1999), Harvard University ( 1991) and the University of Antwerp (International Franqui Chair 1996/97).

In the 1960s, he proved the Mordell conjecture for function fields. He wrote a book on cubic surfaces and shapes ( " Cubic Forms " ), examined algebraic surfaces over the rational numbers (eg Fano varieties ) and showed the role of the Brauer group associated with deviations from Helmut Hasse local-global principle. He also worked on modular forms in number theory (p- adic modular forms ) and the Torsionspunkte elliptic curves.

From him the concept of motive in algebraic geometry was coined, which arose from conversations with Alexander Grothendieck.

The Gauss - Manin connection ( Gauss - Manin connection) is named after him. He describes a vector bundle on families of algebraic varieties with the parameter space, which indicated these families, as a base. In the case of elliptic curves the base space is a straight line; the cohomology groups are given by the periods of the elliptic function and the Gauss - Manin connection is to a second order differential equation ( Picard -Fuchs differential equation) for the periods.

From the 1980s he worked increasingly with mathematical physics and its connections to algebraic geometry ( gauge theory, instantons, mirror symmetry, supersymmetry, non-commutative geometry, string theory, etc.). He also worked on quantum information theory.

Among his students Vladimir Drinfeld, Victor Kolyvagin, Alexander Beilinson, Yuri Sarchin ( Zarhin ), Mikhail Kapranow, Yuri Tschinkel, Mikhail Zfasman, Ivan Tscherednik ( Cherednik ) and Vladimir Berkovich.

He is married to Xenia Semenova Glebowna.

Prizes and awards

  • Price of the Moscow Mathematical Society 1963
  • Lenin Prize (1967 )
  • Brouwer Medal ( 1987)
  • Nemmers Prize for Mathematics ( 1994)
  • Rolf Schock Prize in Mathematics ( 1999)
  • Georg Cantor Medal ( 2002)
  • King Faisal Prize (2002 )
  • Pour le Mérite for Sciences and Arts (2007)
  • Great Cross of Merit of the Federal Republic of Germany with Star (2008)
  • Honorary Doctor of the University of Paris VI (1999 ), University of Oslo ( 2002), University of Warwick (2006)

In 1966 he was invited speaker on the ICM in Moscow ( Rational surfaces and Galois cohomology ), 1970 in Nice ( Groupe de Brauer - Grothendieck s geometry diophantienne ), 1978 in Helsinki ( plenary lecture, Modular forms and number theory ), 1986 in Berkeley (Quantum strings and algebraic curves ) and 1990 in Kyoto (Mathematics as metaphor ).

Memberships:

  • Corresponding Member of the Russian Academy of Sciences ( 1990)
  • Member of the Royal Dutch Academy of Sciences ( 1990)
  • Academia Europaea (1993 )
  • Corresponding member of the Göttingen Academy of Sciences ( 1996)
  • Member of the Leopoldina (2000)
  • Member of the Pontifical Academy of Sciences ( 1996)
  • American Academy of Arts and Sciences (2004)
  • Foreign Member of the Academie des Sciences de l'Institut de France ( 2005)

Writings

  • Manin: Selected works with commentary, World Scientific 1996 ( comment by Manin )
  • Manin: Mathematics as metaphor - selected essays, American Mathematical Society 2009
  • Manin: Rational points of algebraic curves over function fields. AMS translations 1966 ( Mordell conjecture function body )
  • 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
  • Manin: Quantum groups and non commutative geometry, Montreal, Centre de Recherches Mathématiques, 1988
  • Manin: Topics in non commutative geometry, Princeton University Press 1991
  • Manin: Gauge field theory and complex geometry. Springer 1988 ( basic teachings of the mathematical sciences )
  • Manin: Cubic forms - algebra, geometry, arithmetics, North Holland 1986
  • Manin: A course in mathematical logic, Springer 1977
  • Manin: The provable and not provable ( in Russian), Moscow 1979
  • Manin: The Computable and non computable ( in Russian), Moscow 1980
  • Manin: Mathematics and physics, Birkhauser 1981
  • Manin: New dimensions in geometry. in Workshop Bonn 1984, Lectures Notes in Mathematics Bd.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, doi: 10.1007/978-3-662-03220-6
  • Manin, Igor Kobzarev: Elementary Particles: Mathematics, physics and philosophy, Dordrecht, Kluwer, 1989 ( the book has an introductory nature )
  • Manin, Panchishkin: Introduction to Number Theory, Springer Verlag 1995, 2nd edition 2005
  • Manin moduli, Motives, Mirrors, 3rd European Congress Math Barcelona 2000, plenary lecture
  • Manin Classical computing, quantum computing and Shor 's factoring algorithm, Bourbaki Seminar 1999
  • Manin From numbers and figures 2002
  • Manin, Mathilde Marcolli Holography principle and arithmetic of algebraic curves, 2002
  • Manin Three-dimensional hyperbolic geometry as infinite - adic Arakelov geometry, Inventiones Mathematicae 1991
Abstract algebra Evanston (Illinois) Institut des Hautes Études Scientifiques Collège de France Faltings' theorem Quantum information science Rolf Schock Prizes Order of Merit of the Federal Republic of Germany Berkeley, California Alexei Kostrikin Digital Object Identifier Mathematics Genealogy Project Integrated Authority File
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