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:
Vera Serganova
Ivan Penkov
…
Introducing what came to be called the Gauss-Manin connection:
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
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
Maxim Kontsevich, Yuri Manin, Gromov-Witten classes, quantum cohomology, and enumerative geometry, Commun. Math. Physics 164 (1994) 525-562 doi arXiv:hep-th/9402147
Yuri Manin, Frobenius manifolds, quantum cohomology, and moduli spaces, Amer. Math. Soc. Colloqium Publications 47, 1999
Maxim Kontsevich, Yuri Manin, Ralph Kaufmann, Quantum cohomology of a product, Invent. Math. 124 (1996) 313-339 doi arXiv:q-alg/9502009
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)
Last revised on March 10, 2024 at 05:53:56. See the history of this page for a list of all contributions to it.