Yuri Ivanovich Manin (russian: Ю́рий Ива́нович Ма́нин; born 16 February 1937) is a Russian mathematician, known for work in algebraic geometry and

diophantine geometry In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became clear for some mathematicians that methods of algebraic geometry are ideal tools to study ...

, and many expository works ranging from

mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

. Moreover, Manin was one of the first to propose the idea of a quantum computer in 1980 with his book ''Computable and Uncomputable''.

Life and career

Manin gained a doctorate in 1960 at the Steklov Mathematics Institute as a student of Igor Shafarevich. He is now a Professor at the

Max-Planck-Institut für Mathematik The Max Planck Institute for Mathematics (german: Max-Planck-Institut für Mathematik, MPIM) is a prestigious research institute located in Bonn, Germany. It is named in honor of the German physicist Max Planck and forms part of the Max Planck ...

Bonn The federal city of Bonn ( lat, Bonna) is a city on the banks of the Rhine in the German state of North Rhine-Westphalia, with a population of over 300,000. About south-southeast of Cologne, Bonn is in the southernmost part of the Rhine-Ru ...

, and a professor emeritus at

Northwestern University Northwestern University is a private research university in Evanston, Illinois. Founded in 1851, Northwestern is the oldest chartered university in Illinois and is ranked among the most prestigious academic institutions in the world. Charte ...

. Manin's early work included papers on the arithmetic and

formal group In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were introduced by . The term formal group sometimes means the same as formal group law, and sometimes means one ...

s of

abelian varieties In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a Algebraic variety#Projective variety, projective algebraic variety that is also an algebraic group, i.e., has a group law th ...

, the

Mordell conjecture Louis Joel Mordell (28 January 1888 – 12 March 1972) was an American-born British mathematician, known for pioneering research in number theory. He was born in Philadelphia, United States, in a Jewish family of Lithuanian extraction. Educati ...

in the function field case, and

algebraic differential equation In mathematics, an algebraic differential equation is a differential equation that can be expressed by means of differential algebra. There are several such notions, according to the concept of differential algebra used. The intention is to i ...

s. The

Gauss–Manin connection In mathematics, the Gauss–Manin connection is a connection on a certain vector bundle over a base space ''S'' of a family of algebraic varieties V_s. The fibers of the vector bundle are the de Rham cohomology groups H^k_(V_s) of the fibers V_s o ...

is a basic ingredient of the study of

cohomology In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewe ...

in families of

algebraic varieties Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. ...

. He wrote a book on

cubic surface In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather th ...

s and

cubic form In mathematics, a cubic form is a homogeneous polynomial of degree 3, and a cubic hypersurface is the zero set of a cubic form. In the case of a cubic form in three variables, the zero set is a cubic plane curve. In , Boris Delone and Dmitry Fa ...

s, showing how to apply both classical and contemporary methods of algebraic geometry, as well as

nonassociative algebra A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative. That is, an algebraic structure ''A'' is a non-associative algebra over a field ''K'' if ...

. He also indicated the role of the

Brauer group Brauer or Bräuer is a surname of German origin, meaning "brewer". Notable people with the name include:- * Alfred Brauer (1894–1985), German-American mathematician, brother of Richard * Andreas Brauer (born 1973), German film producer * Arik ...

, via Grothendieck's theory of global

Azumaya algebra In mathematics, an Azumaya algebra is a generalization of central simple algebras to ''R''-algebras where ''R'' need not be a field. Such a notion was introduced in a 1951 paper of Goro Azumaya, for the case where ''R'' is a commutative local rin ...

s, in accounting for obstructions to the

Hasse principle In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of eac ...

, setting off a generation of further work. He pioneered the field of

arithmetic topology Arithmetic topology is an area of mathematics that is a combination of algebraic number theory and topology. It establishes an analogy between number fields and closed, orientable 3-manifolds. Analogies The following are some of the analogies used ...

(along with John Tate,

David Mumford David Bryant Mumford (born 11 June 1937) is an American mathematician known for his work in algebraic geometry and then for research into vision and pattern theory. He won the Fields Medal and was a MacArthur Fellow. In 2010 he was awarded t ...

, Michael Artin and Barry Mazur). He also formulated the Manin conjecture, which predicts the asymptotic behaviour of the number of rational points of bounded height on algebraic varieties. He has further written on Yang–Mills theory, quantum information, and mirror symmetry (string theory), mirror symmetry. Manin had over 40 doctoral students, including Vladimir Berkovich, Mariusz Wodzicki, Alexander Beilinson, Ivan Cherednik, Alexei Skorobogatov, Vladimir Drinfeld, Mikhail Kapranov, Vyacheslav Shokurov, Arend Bayer and Victor Kolyvagin, as well as foreign students including Hà Huy Khoái.

Awards

He was awarded the Brouwer Medal in 1987, the first Nemmers Prize in Mathematics in 1994, the Schock Prize of the Royal Swedish Academy of Sciences in 1999, the Cantor Medal of the German Mathematical Society in 2002, the King Faisal International Prize in 2002 and the Bolyai Prize of the Hungarian Academy of Sciences in 2010. In 1990 he became a foreign member of the Royal Netherlands Academy of Arts and Sciences.

Works

* Manin: ''Selected works with commentary'', World Scientific 1996 * Manin:
Mathematics as metaphor - selected essays
', American Mathematical Society 2009 * Manin:
Rational points of algebraic curves over function fields
'. AMS translations 1966 (Mordell conjecture for function fields) * 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 (Grundlehren der mathematischen Wissenschaften) * Manin:
Cubic forms - algebra, geometry, arithmetics
', North Holland 1986 * Manin:
A course in mathematical logic
', Springer 1977, second expanded edition with new chapters by the author and Boris Zilber, Springer 2010. * Manin: ''The provable and the unprovable'' (Russ.), Moscow 1979 * Manin: ''Computable and Uncomputable'' (Russ.), Moscow 1980 * Manin:
Mathematics and physics
', Birkhäuser 1981 * Manin:
New dimensions in geometry
'. in Arbeitstagung Bonn 1984, Lectures Notes in Mathematics Vol. 1111, Springer Verlag * Manin, Alexei Ivanovich Kostrikin: ''doi:10.1201/9781466593480, 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 * Manin, Igor Kobzarev:
Elementary Particles: mathematics, physics and philosophy
', Dordrecht, Kluwer, 1989 (This book is introductory.) * Manin, Alexei A. Panchishkin:
Introduction to Number theory
', Springer Verlag 1995, 2nd edn. 2005 * Manin
Moduli, Motives, Mirrors
', 3. European Congress Math. Barcelona 2000, Plenary talk * Manin
Classical computing, quantum computing and Shor´s factoring algorithm
', Bourbaki Seminar 1999 * Manin
Von Zahlen und Figuren
' 2002 * Manin, Matilde Marcolli
Holography principle and arithmetic of algebraic curves
', 2002 * Manin
3-dimensional hyperbolic geometry as infinite-adic Arakelov geometry
', Inventiones Mathematicae 1991 * Manin:

', e-enterprise, 2014

References

External links

*
Manin's page at Max-Planck-Institut für Mathematik website
*

', interview by Martin Aigner and Vasco A. Schmidt
Biography
{{DEFAULTSORT:Manin, Yuri 1937 births Living people Scientists from Simferopol Algebraic geometers Algebraists Moscow State University alumni Northwestern University faculty Members of the Pontifical Academy of Sciences Members of the French Academy of Sciences Members of the Royal Netherlands Academy of Arts and Sciences Corresponding Members of the Russian Academy of Sciences Rolf Schock Prize laureates Brouwer Medalists Soviet mathematicians 21st-century Russian mathematicians 20th-century Russian mathematicians Knights Commander of the Order of Merit of the Federal Republic of Germany Recipients of the Pour le Mérite (civil class) Quantum information scientists Max Planck Institute directors

Life and career

Awards

Works

See also

References

Further reading

External links