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Deformation Quantization of Poisson Manifolds

- M. Kontsevich
- Mathematics, Physics
- 29 September 1997

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the… Expand

Intersection theory on the moduli space of curves and the matrix airy function

- M. Kontsevich
- Mathematics
- 1 June 1992

We show that two natural approaches to quantum gravity coincide. This identity is nontrivial and relies on the equivalence of each approach to KdV equations. We also investigate related mathematical… Expand

Stability structures, motivic Donaldson-Thomas invariants and cluster transformations

- M. Kontsevich, Y. Soibelman
- Mathematics, Physics
- 16 November 2008

We define new invariants of 3d Calabi-Yau categories endowed with a stability structure. Intuitively, they count the number of semistable objects with fixed class in the K-theory of the category… Expand

The Geometry of the Master Equation and Topological Quantum Field Theory

- M. Alexandrov, M. Kontsevich, A. Schwarz, O. Zaboronsky
- Physics
- 2 February 1995

In Batalin–Vilkovisky formalism, a classical mechanical system is specified by means of a solution to the classical master equation. Geometrically, such a solution can be considered as a QP-manifold,… Expand

Homological Algebra of Mirror Symmetry

- M. Kontsevich
- Mathematics, Physics
- 30 November 1994

Mirror symmetry (MS) was discovered several years ago in string theory as a duality between families of 3-dimensional Calabi-Yau manifolds (more precisely, complex algebraic manifolds possessing… Expand

FORMAL (NON)-COMMUTATIVE SYMPLECTIC GEOMETRY

- M. Kontsevich
- Mathematics
- 1993

Some time ago B. Feigin, V. Retakh and I had tried to understand a remark of J. Stasheff [S1] on open string theory and higher associative algebras [S2]. Then I found a strange construction of… Expand

Canonical bases for cluster algebras

- M. Gross, P. Hacking, S. Keel, M. Kontsevich
- Mathematics
- 5 November 2014

In [GHK11], Conjecture 0.6, the first three authors conjectured that the ring of regular functions on a natural class of affine log Calabi-Yau varieties (those with maximal boundary) has a canonical… Expand

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

Enumeration of Rational Curves Via Torus Actions

- M. Kontsevich
- Physics, Mathematics
- 5 May 1994

This paper contains an attempt to formulate rigorously and to check predictions in enumerative geometry of curves following from Mirror Symmetry.

Feynman Diagrams and Low-Dimensional Topology

- M. Kontsevich
- Mathematics
- 1994

We shall describe a program here relating Feynman diagrams, topology of manifolds, homotopical algebra, non-commutative geometry and several kinds of “topological physics.”

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