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Gromov-Witten classes, quantum cohomology, and enumerative geometry

- M. Kontsevich, Y. Manin
- Physics, Mathematics
- 26 February 1994

The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic… Expand

Construction of Instantons

- M. Atiyah, N. Hitchin, V. Drinfeld, Y. Manin
- Physics
- 6 March 1978

A complete construction, involving only linear algebra, is given for all self-dual euclidean Yang-Mills fields.

AUTOMORPHIC PSEUDODIFFERENTIAL OPERATORS

- Paula B. Cohen, Y. Manin, D. Zagier
- Mathematics
- 1997

The theme of this paper is the correspondence between classical modular forms and pseudodifferential operators (ΨDO’s) which have some kind of automorphic behaviour. In the simplest case, this… Expand

Multiparametric quantum deformation of the general linear supergroup

- Y. Manin
- Mathematics
- 1 March 1989

In the work L. D. Faddeev and his collaborators, and subsequently V. G. Drinfeld, M. Jimbo, S. L. Woronowicz, a new class of Hopf algebras was constructed. They can be considered as one-parametric… Expand

Relations Between the Correlators of the Topological Sigma-Model Coupled to Gravity

- M. Kontsevich, Y. Manin
- Mathematics, Physics
- 28 August 1997

Abstract:We prove a new recursive relation between the correlators ¶, which together with known relations allows one to express all of them through the full system of Gromov–Witten invariants in the… Expand

A supersymmetric extension of the Kadomtsev-Petviashvili hierarchy

An extension of the Kadomtsev-Petviashvili hierarchy by odd variables is given. Conservation laws and formal integrability are proved.

Real multiplication and noncommutative geometry (ein Alterstraum)

- Y. Manin
- Mathematics
- 2004

Preface. Abel’s name is associated with a number of key notions of modern mathematics, such as abelian varieties, Abel’s integrals, etc. Moreover, it became almost synonymous with the idea of… Expand

Semi)simple exercises in quantum cohomology

The paper is dedicated to the study of algebraic manifolds whose quantum cohomology or a part of it is a semisimple Frobenius manifold. Theorem 1.8.1 says, roughly speaking, that the sum of… Expand

Continued fractions, modular symbols, and noncommutative geometry

- Y. Manin, M. Marcolli
- Mathematics, Physics
- 1 February 2001

Abstract. Using techniques introduced by D. Mayer, we prove an extension of the classical Gauss-Kuzmin theorem about the distribution of continued fractions, which in particular allows one to take… Expand

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