nLab Yuri Manin

Yuri Ivanovich Manin (1937-2023, Russian: Юрий Иванович Манин) was a Russian-born mathematician of polymath broadness, with main works in number theory and arithmetic geometry, noncommutative geometry, algebraic geometry and mathematical physics.

His diverse work includes a classification theorem in the theory of commutative formal group, early study of monoidal transformations and exposition on motives in 1960-s, a fundamental starting work in quantum information theory, proposals on quantum logics, an approach to quantum groups, ADHM construction in soliton theory, work with Maxim Kontsevich on Gromov-Witten invariants, work on Frobenius manifolds (and introduced more general “F-manifolds” with Claus Hertling). He published a number of influential monographs including on noncommutative geometry, quantum groups, complex geometry and gauge theories, introduction to schemes, Frobenius manifolds, mathematical logics…

Manin’s students include:

Selected writings

Introducing what came to be called the Gauss-Manin connection:

  • Yuri Manin, Algebraic curves over fields with differentiation, Izv. Akad. Nauk SSSR Ser. Mat. 22 6 (1958) 737-756 [[mathnet:izv3998, pdf]] (in Russian)

Introducing the ADHM construction for Yang-Mills instantons:

Introducing the notion of quantum computation:

  • Yuri I. Manin, Introduction to: Computable and Uncomputable, Sov. Radio (1980) [Russian original: pdf], English translation on p. 69-77 of Mathematics as Metaphor: Selected essays of Yuri I. Manin, Collected Works 20, AMS (2007) [ISBN:978-0-8218-4331-4]

    Perhaps, for a better understanding of [molecular biology], we need a mathematical theory of quantum automata.

and review of Shor's algorithm:

Early discussion of mathematical supergeometry:

On the Penrose-Ward transform relating twistor space to Minkowski spacetime, on its generalization to superalgebra and supergeometry, and on applications to super Yang-Mills theory and supergravity:

On homological algebra and homotopical algebra (via triangulated categories and including the model structure on dgc-algebras for rational homotopy theory):

Introduced quantum linear groups as universal coacting bialgebras (and their quotient Hopf algebras) in

  • Yu. I. Manin, Quantum groups and non-commutative geometry, CRM, Montreal 1988.

Some of these structures have repercussion on the study of quadratic operads, as in

On relations of AdS3/CFT2 to hyperbolic geometry and Arakelov geometry of algebraic curves:

On quantum cohomology and Gromov-Witten invariants


What binds us to space-time is our rest mass, which prevents us from flying at the speed of light, when time stops and space loses meaning. In a world of light there are neither points nor moments of time; beings woven from light would live “nowhere” and “nowhen”; only poetry and mathematics are capable of speaking meaningfully about such things

Mathematics as Metaphor: Selected Essays of Yuri I. Manin (ed. 2007) (libquotes)

category: people

Last revised on March 10, 2024 at 05:53:56. See the history of this page for a list of all contributions to it.