Yuri Manin

Yuri Ivanovich Manin (Russian: Юрий Иванович Манин) 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…

His students include

- A. Beilinson,
- V. Drinfel'd
- Vera Serganova
- Ivan Penkov
- M. Kapranov
- Yu. Tschinkel
- …

On homological algebra and homotopical algebra (via a model structure on dgc-algebras for rational homotopy theory):

- Sergei Gelfand, Yuri Manin,
*Methods of homological algebra*, transl. from the 1988 Russian (Nauka Publ.) original, Springer 1996. xviii+372 pp. 2nd corrected ed. 2002 (doi:10.1007/978-3-662-12492-5)

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

- Yuri Manin, Matilde Marcolli,
*Holography principle and arithmetic of algebraic curves*, Adv. Theor. Math. Phys. 5 (2002) 617-650 (arXiv:hep-th/0201036

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