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:
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:
Introducing quantum linear groups as universal co-acting bialgebras (and their quotient Hopf algebras):
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
On homological algebra and homotopical algebra (via triangulated categories and including the model structure on dgc-algebras for rational homotopy theory):
On Frobenius manifolds and quantum cohomology:
and generalized to Frobenius supermanifolds in supergeometry:
On relations of AdS3/CFT2 to hyperbolic geometry and Arakelov geometry of algebraic curves:
On doubly monoidal categories and quadratic operads:
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 September 12, 2024 at 10:15:37. See the history of this page for a list of all contributions to it.