Kontsevich, Maxim
Overview
Works:  34 works in 56 publications in 3 languages and 597 library holdings 

Genres:  Documentary films 
Roles:  Editor, Author, Thesis advisor, Interviewee 
Classifications:  QA3, 515.253 
Publication Timeline
.
Most widely held works by
Maxim Kontsevich
Pseudoperiodic topology(
Book
)
7 editions published between 1999 and 2000 in English and held by 213 WorldCat member libraries worldwide
7 editions published between 1999 and 2000 in English and held by 213 WorldCat member libraries worldwide
Colors of math by
Ekaterina Eremenko(
Visual
)
3 editions published in 2012 in English and French and held by 8 WorldCat member libraries worldwide
"To most people math appears abstract, mysterious. Complicated. Inaccessible. But math is nothing but a different language to express the world. Math can be sensual. Math can be tasted, it smells, it creates sound and color. One can touch it and be touched by it...."  Container
3 editions published in 2012 in English and French and held by 8 WorldCat member libraries worldwide
"To most people math appears abstract, mysterious. Complicated. Inaccessible. But math is nothing but a different language to express the world. Math can be sensual. Math can be tasted, it smells, it creates sound and color. One can touch it and be touched by it...."  Container
Intersection theory on the moduli space of curves and the matrix Airy function by
Maxim Kontsevich(
Book
)
3 editions published in 1991 in English and German and held by 5 WorldCat member libraries worldwide
3 editions published in 1991 in English and German and held by 5 WorldCat member libraries worldwide
Homological mirror symmetry and tropical geometry by
Ricardo CastañoBernard(
Book
)
6 editions published in 2014 in English and held by 3 WorldCat member libraries worldwide
The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of nonarchimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the {esc}(3z{esc}(Btropical{esc}(3y{esc}(B approach to GromovWitten theory, and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of CalabiYau manifolds (the socalled StromingerYauZaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Geometry studies piecewiselinear objects which appear as {esc}(3z{esc}(Bdegenerations{esc}(3y{esc}(B of the corresponding algebrogeometric objects
6 editions published in 2014 in English and held by 3 WorldCat member libraries worldwide
The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of nonarchimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the {esc}(3z{esc}(Btropical{esc}(3y{esc}(B approach to GromovWitten theory, and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of CalabiYau manifolds (the socalled StromingerYauZaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Geometry studies piecewiselinear objects which appear as {esc}(3z{esc}(Bdegenerations{esc}(3y{esc}(B of the corresponding algebrogeometric objects
A category of kernels for equivariant factorizations and its implications for Hodge theory. Affine MirkovićVilonen polytopes
/ by Pierre Baumann, Joel Kamnitzer, and Peter Tingley. Sum of Lyapunov exponents of the Hodge bundle with respect to te Teichmüller
geodesic flow / by Alex Eskin, Maxim Kontsevich, Anton Zorich. The space of metrics of positive scalar curvature / by Bernhard
Hanke, Thomas Schick, and Wolfgang Steimle. by
Matthew Robert Ballard(
Book
)
2 editions published in 2014 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 2014 in English and held by 3 WorldCat member libraries worldwide
Lyapunov exponents and hodge theory by
Maxim Kontsevich(
Book
)
2 editions published in 1997 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1997 in English and held by 2 WorldCat member libraries worldwide
Sur le groupe de Cremona et ses sousgroupes by
Alexandr Usnich(
Book
)
1 edition published in 2008 in English and held by 2 WorldCat member libraries worldwide
Ce travail peut être divisé en trois partie: 1. Théorie des groupes. Il s'agit ici d'une étude de la structure du groupe T de Thompson. On explique la notion de la mutation linéaire par morceaux et on obtient la nouvelle présentation de ce groupe en termes des génerateurs et relations. 2. Géometrie birationnelle. On étudie en détail le groupe de Cremona qui est un groupe des automorphismes birationnels du plan projectif. En particulier on s'interesse à son sousgroupe Symp des elements qui préserve le crochet de Poisson dit logarithmique, aussi bien qu'à un sousgroupe H engendré par SL(2,Z) et par les mutations. On construit des limites projectives des surfaces sur lesquelles ces groupes agissent régulièrement, et on en déduit les répresentations linéaires de ces groupes dans les limites inductives des groupes de Picard des surfaces. 3. Algèbre homologique. A partir d'une variété algébrique on construit une catégorie triangulée qui ne dépend que de sa classe birationnelle. En utilisant la technique de quotient de dgcatégories, on calcule explicitement cette catégorie pour les surfaces rationnelles. Comme consequence on obtient l'action du groupe de Cremona sur une algébre noncommutative par les automorphismes extérieures. On donne les applications de ces résultats aux formules des mutations des variables noncommutatives
1 edition published in 2008 in English and held by 2 WorldCat member libraries worldwide
Ce travail peut être divisé en trois partie: 1. Théorie des groupes. Il s'agit ici d'une étude de la structure du groupe T de Thompson. On explique la notion de la mutation linéaire par morceaux et on obtient la nouvelle présentation de ce groupe en termes des génerateurs et relations. 2. Géometrie birationnelle. On étudie en détail le groupe de Cremona qui est un groupe des automorphismes birationnels du plan projectif. En particulier on s'interesse à son sousgroupe Symp des elements qui préserve le crochet de Poisson dit logarithmique, aussi bien qu'à un sousgroupe H engendré par SL(2,Z) et par les mutations. On construit des limites projectives des surfaces sur lesquelles ces groupes agissent régulièrement, et on en déduit les répresentations linéaires de ces groupes dans les limites inductives des groupes de Picard des surfaces. 3. Algèbre homologique. A partir d'une variété algébrique on construit une catégorie triangulée qui ne dépend que de sa classe birationnelle. En utilisant la technique de quotient de dgcatégories, on calcule explicitement cette catégorie pour les surfaces rationnelles. Comme consequence on obtient l'action du groupe de Cremona sur une algébre noncommutative par les automorphismes extérieures. On donne les applications de ces résultats aux formules des mutations des variables noncommutatives
GromovWitten classes, quantum cohomology and enumerative geometry by
Maxim Kontsevich(
Book
)
2 editions published in 1994 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 2 WorldCat member libraries worldwide
Nonocmmutative spaces by
Maxim Kontsevich(
Book
)
2 editions published in 2004 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2004 in English and held by 2 WorldCat member libraries worldwide
La géométrie et la théorie conforme des champs by
Alexandre Engoulatov(
Book
)
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
This thesis deals with a Riemannian geometric question which is motivated by the problem of compactifying the moduli space of Conformal Field Theories (CFT). M. Kontsevich associates to a degenerating sequence of CFT's a limiting object which contains a Riemannian manifold M with nonnegative Ricci curvature, and its graph field theory. This amounts to a family of operators on tensor powers of the Hilbert space L^2(M), indexed by metric graphs. For instance, the operator attached to the graph with two vertices and one edge of length t is the heat semigroup P_t. The main result in the thesis is an a priori estimate of the norm of the gradient of the logarithm of the heat kernel on a compact Riemannian manifold, for short times, depending on the lower bound on Ricci curvature and on diameter only. The proof, which uses stochastic calculus, extends to certain semigroups satisfying curvaturedimension inequalities, in the sense of D. Bakry and M. Emery. Using J. Cheeger and T. H. Colding's structure results on limit spaces of such Riemannian manifolds, it is shown that the a priori estimate extends to these singular limit spaces. A compactness theorem for graph field theories associated with compact Riemannian manifolds satisfying a uniform lower bound on Ricci curvature follows
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
This thesis deals with a Riemannian geometric question which is motivated by the problem of compactifying the moduli space of Conformal Field Theories (CFT). M. Kontsevich associates to a degenerating sequence of CFT's a limiting object which contains a Riemannian manifold M with nonnegative Ricci curvature, and its graph field theory. This amounts to a family of operators on tensor powers of the Hilbert space L^2(M), indexed by metric graphs. For instance, the operator attached to the graph with two vertices and one edge of length t is the heat semigroup P_t. The main result in the thesis is an a priori estimate of the norm of the gradient of the logarithm of the heat kernel on a compact Riemannian manifold, for short times, depending on the lower bound on Ricci curvature and on diameter only. The proof, which uses stochastic calculus, extends to certain semigroups satisfying curvaturedimension inequalities, in the sense of D. Bakry and M. Emery. Using J. Cheeger and T. H. Colding's structure results on limit spaces of such Riemannian manifolds, it is shown that the a priori estimate extends to these singular limit spaces. A compactness theorem for graph field theories associated with compact Riemannian manifolds satisfying a uniform lower bound on Ricci curvature follows
Determinants of elliptic pseudodifferential operators by
Maxim Kontsevich(
Book
)
2 editions published in 1994 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 2 WorldCat member libraries worldwide
Enumeration of rational curves via torus actions by
Maxim Kontsevich(
Book
)
2 editions published in 1994 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 2 WorldCat member libraries worldwide
RozanskyWitten invariants via formal geometry by
Maxim Kontsevich(
Book
)
2 editions published in 1997 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1997 in English and held by 2 WorldCat member libraries worldwide
Frobenius manifolds and formality of Lie algebras of polyvector fields by
Sergeĭ Barannikov(
Book
)
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
A Special volume dedicated to the memory of F.A. Berezin(
Book
)
1 edition published in 2005 in English and held by 1 WorldCat member library worldwide
1 edition published in 2005 in English and held by 1 WorldCat member library worldwide
Noncummutative stacks by
Maxim Kontsevich(
Book
)
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
Noncommutative smooth spaces by
Maxim Kontsevich(
Book
)
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
Deformation quantization of Poisson manifolds by
Maxim Kontsevich(
Book
)
in English and held by 1 WorldCat member library worldwide
in English and held by 1 WorldCat member library worldwide
Noncummutative spaces and flat descent by
Maxim Kontsevich(
Book
)
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
Noncummutative spaces and flat descent(
)
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Soibelman, Yan S. Editor
 Catanese, F. (Fabrizio) Editor
 CastañoBernard, Ricardo 1972 Author Editor
 Zharkov, Ilia 1971 Editor
 Pantev, Tony 1963 Editor
 Zorich, Anton Editor
 Arnolʹd, V. I. (Vladimir Igorevich) 19372010 Editor
 Rangan, Aaditya V. Interviewee
 Ziegler, Günter Interviewee
 Bismut, JeanMichel Interviewee
Useful Links
Alternative Names
Kontsevich, M. L.
Kontsevich, Maxim.
Kontzevitch, Maxim
Konzewitsch, Maxim Lwowitsch 1964
Maksim Koncevič matematico russo
Maksim Koncewicz
Maksim Kontsévich
Maksim Kontsevitš
Maksim Lvovič Koncevič
Maxim Kontsevich Russianborn French mathematician and Fields Medallist
Maxim Kontsevitsj
Maxim Kontsevitsj Russisch wiskundige
Màxim Kontsevitx
Maxim Lvovič Koncevič
Maxim Lwowitsch Konzewitsch russischer Mathematiker
Maxime Kontsevitch mathématicien russe
Концевич Максим Львович
Максим Концевич российский и французский математик
Максим Львович Концевич
מקסים קונטסביץ'
مكسيم كونتسفيتش
میکسم کونٹسیوچ
막심 콘체비치
マキシム・コンツェビッチ
马克西姆·孔采维奇
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