Yuri Manin

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Yuri Manin at the ICM 2006 in Madrid , with his wife Ksenia Semenova

Yuri Manin ( Russian Юрий Иванович Манин / Juri Iwanowitsch Manin ; born February 16, 1937 in Simferopol , Soviet Union , today Ukraine ) is a mathematician and emeritus scientific member and director at the Max Planck Institute for Mathematics in Bonn . His main areas of work are number theory , Diophantine geometry , mathematical physics and algebraic geometry .

life and work

Manin studied physics and mathematics at Moscow's Lomonosov University , where he graduated summa cum laude in 1958 , but had previously published his first work. He then went to the Steklov Institute for Mathematics in Moscow, where he received his doctorate (candidate title) under Igor Schafarewitsch in 1960 . Then he was a Principal Researcher there. In 1963 he completed his habilitation (Russian doctorate). From 1965 to 1992 he was also professor of algebra at Moscow University. In 1966 he gave a lecture at the ICM in Moscow on rational surfaces and Galois cohomology . In 1991/92 he was at Columbia University (Eilenberg Chair) and from 1992 to 1993 at MIT, but remained ( in absentia ) a member of the Steklow Institute, which he also visits regularly. Since 1992 he has been a scientific member of the Max Planck Institute for Mathematics in Bonn, where he was director from 1993 to 2005 (he has been an emeritus since 2005). Since 2002 he has been a Board of Trustees Professor at Northwestern University in Evanston . In addition to Russian, he also has German citizenship.

He was visiting professor at the University of Pisa (1964), the University of Montreal (1984), the IHES (1967, 1989), the Collège 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 functional bodies . He wrote a book about cubic surfaces and forms ("Cubic Forms"), examined algebraic surfaces over the rational numbers (e.g. Fano varieties ) and showed the role of the brewing group in connection with deviations from Helmut Hasse's local-global principle on. He also worked on modular forms in number theory ( p-adic modular forms ) and on the torsion points of elliptical curves . With Wassili Alexejewitsch Iskowskich in 1971, using the example of smooth quartic 3 varieties (examples of Fano varieties), he proved that unirational varieties need not be rational in three dimensions (a counter-example to Jacob Lüroth's Lüroth problem ).

He coined the term motif in algebraic geometry after he knew the concept from a visit to Alexander Grothendieck (IHES seminar May 1967). His essay Correspondences, Mofifs and monoidal transformations (in Russian) from 1968 was the first publication on motifs.

The Gauss-Manin connection is named after him. He describes a vector bundle based on families of algebraic varieties with the parameter space that indexes these families. 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 relation becomes a differential equation of the second order ( Picard-Fuchs differential equation ) for the periods.

The Manin-Mumford conjecture (first demonstrated by Michel Raynaud ) makes a statement about the finite section of a curve with sex over a number field with the torsion subgroup its jacobian variety (wherein in is embedded). It was inspired by the Mordell conjecture .

From the 1980s he became increasingly concerned with mathematical physics and its connections to algebraic geometry ( gauge theories , 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), Vyacheslav Vladimirovich Schokurow , Mikhail Kapranow , Yuri Tschinkel , Mikhail Zfasman , Ivan Tscherednik (Cherednik), Vladimir Ivanovich Danilov (Danilov), Alexander L. Rosenberg , Boris Tsygan , Mariusz Wodzicki and Vladimir Berkovich .

He is married to Xenia Glebovna Semenova.

Prizes and awards

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

Memberships:

Fonts

  • Manin: Selected works with commentary . World Scientific 1996 (Commentary by Manin)
  • Manin: Mathematics as metaphor - selected essays . American Mathematical Society 2009
  • Manin: Mathematics as a metaphor. Selected Essays, Vol. 1 . e-enterprise 2016
  • Manin: Mathematics and Physics, Selected Essays, Vol. 2 . e-enterprise 2017
  • Manin: Mathematics and Language, Selected Essays, Vol. 3 . e-enterprise 2019
  • Manin: Rational points of algebraic curves over function fields . AMS translations 1966 (Mordell assumption 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, Center de Recherches Mathématiques, 1988, 2nd edition Springer 2018 (with contributions by Theo Raedschelders and Michel Van den Bergh)
  • Manin: Topics in non commutative geometry . Princeton University Press 1991
  • Manin: Gauge field theory and complex geometry . Springer 1988 (basic mathematical science)
  • Manin: Cubic forms - algebra, geometry, arithmetics . North Holland 1986
  • Manin: A course in mathematical logic . Springer 1977
  • Manin: The provable and the unprovable (Russian), Moscow 1979
  • Manin: Mathematics and Physics (Russian), Moscow 1979
  • Manin: The predictable and the unpredictable (Russian), Moscow 1980
  • Manin: Mathematics and physics . Birkhäuser 1981
  • Manin: New dimensions in geometry . In: Arbeitstagung Bonn 1984, Lectures Notes in Mathematics, Volume 1111, Springer Verlag
  • Manin, Alexei Iwanowitsch 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: Lectures on Zeta functions and motives , Astérisque, Volume 228, 1995, pp. 121-163, numdam
  • Manin, Igor Kobzarev : Elementary Particles: mathematics, physics and philosophy . Kluwer, Dordrecht 1989 (the book is introductory)
  • Manin, Panchishkin: Introduction to Number Theory . Springer Verlag 1995, 2nd edition 2005
  • Manin: Interrelations between mathematics and physics , in: Michele Audin (ed.), Matériaux pour l'histoire des mathématiques au XXe siècle Actes du colloque à la mémoire de Jean Dieudonné (Nice 1996), SMF 1998, p. 157
  • Manin: Moduli, Motives, Mirrors . 3rd European Congress Math. Barcelona 2000, plenary lecture, arxiv : math.AG/0005144
  • Manin: Classical computing, quantum computing and Shor's factoring algorithm . Bourbaki Seminar 1999, arxiv : quant-ph / 9903008
  • Manin: Of numbers and figures . 2002, arxiv : math.AG/0201005
  • Manin, Mathilde Marcolli: Holography principle and arithmetic of algebraic curves . 2002, arxiv : hep-th / 0201036
  • Manin: Three-dimensional hyperbolic geometry as infinite-adic Arakelov geometry . Inventiones Mathematicae, 1991
  • Manin: Math, Art, and Civilization . e-enterprise, 2014

literature

  • Yuri Zarhin , Yuri Tschinkel (Editor) Arithmetic, Algebra and Geometry. In Honor of Yu. I. Manin . 2 volumes. Birkhäuser, Progress in Mathematics, 2009 (Manin's curriculum vitae with list of publications and directory of his doctoral students in volume 1).
  • Good proofs are proofs that make us wiser: Interview with Yuri I. Manin . In: Mitteilungen der Deutschen Mathematiker-Vereinigung , 1998, pp. 40–44 (interview with M. Aigner, VA Schmidt).
  • VG Drinfeld, VA Iskovskikh, AI Kostrikin, AN Tyurin, IR Shafarevich: Yurii Ivanovich Manin (on the occasion of his sixtieth birthday) . In: Russian Mathematical Surveys , Volume 52, 1997, pp. 863-873.
  • Manin receives Nemmers prize . In: Notices Amer. Math. Soc. , Vol. 41, 1994, pp. 796-797.
  • Late Style - Yuri I. Manin looking back on a life in mathematics . Springer VideoMath, 2012.

Web links

Individual evidence

  1. Manin, Correspondences, motifs and monoidal transformations, Math. USSR-Sb., Volume 6, 1968, pp. 439-470, Russian at mathnet.ru
  2. Manin, Forgotten motives: the varieties of scientific experience, in: Leila Schneps, Alexandre Grothendieck, a mathematical portrait, International Press, Boston 2014, Arxiv