Yuri Ivanovitch Manin

Yuri Ivanovitch Manin (born 1937) is a Russian-born mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.

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1937 - Algebraic geometry - Diophantine geometry - Mathematical logic - Theoretical physics

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He was born in Simferopol. He gained a doctorate in 1960 at the Steklov Mathematics Institute as a student of Igor Shafarevich.

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Simferopol - Steklov Mathematics Institute - Igor Shafarevich

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He is now a Professor and Directior of the Max-Planck-Institut für Mathematik in Bonn, and a professor at Northwestern University.

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Max-Planck-Institut für Mathematik - Bonn - Northwestern University

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His early work included papers on the arithmetic and formal groups of abelian varieties, the Mordell conjecture in the function field case, and algebraic differential equations. The Gauss-Manin connection is a basic ingredient of the study of cohomology in families of algebraic varieties. He wrote an influential book on cubic surfaces and cubic forms, showing how to apply both classical and contemporary methods of algebraic geometry, as well as nonassociative algebra. He also indicated the role of the Brauer group, via Grothendieck's theory of global Azumaya algebras, in accounting for obstructions to the Hasse principle, setting off a generation of further work.

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Formal group - Abelian varieties - Mordell conjecture - Function field - Algebraic differential equation - Gauss-Manin connection - Cohomology - Algebraic varieties - Cubic surface - Cubic form - Nonassociative algebra - Brauer group - Grothendieck - Azumaya algebra - Hasse principle

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He has also written on Yang-Mills theory and mirror symmetry.

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Yang-Mills theory - Mirror symmetry

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He was awarded the Schock Prize in 1999 and the Cantor Medal in 2002.

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Schock Prize - Cantor Medal

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See also: Manin-Mumford conjecture.

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