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


Selected writing

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

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


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