Maxim Kontsevich | Academic Influence

Why Is Maxim Kontsevich Influential?

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By Erik J. Larson, PhD

Kontsevich is Professor of Mathematics at the prestigious Institut des Hautes Études Scientifiques in France, as well as a distinguished professor at the University of Miami. Having dual Russian and French citizenship, Kontsevich studied at Moscow University before leaving before degree completion to take a position as a researcher at the Institute for Information Transmission Problems in Moscow. His research there attracted the attention of the University of Bonn, where he was invited to attend. While there he sketched a proof of the famous Witten Conjecture, and was recognized as a true mathematical genius. He received his Ph.D. in Mathematics from the University of Bonn in 1992.

Kontsevich’s work focuses on difficult problems in the geometry of mathematical physics, such as knot theory (literally: the study of mathematical knots), as well as quantization and mirror symmetry. One of the best mathematicians of his generation, Kontsevich won the Fields Medal in 1998. He was awarded the Breakthrough Prize in Mathematics in 2014.

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According to Wikipedia, Maxim Lvovich Kontsevich is a Russian and French mathematician and mathematical physicist. He is a professor at the Institut des Hautes Études Scientifiques and a distinguished professor at the University of Miami. He received the Henri Poincaré Prize in 1997, the Fields Medal in 1998, the Crafoord Prize in 2008, the Shaw Prize and Fundamental Physics Prize in 2012, and the Breakthrough Prize in Mathematics in 2014.

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Maxim Kontsevich's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Papers

Deformation Quantization of Poisson Manifolds (1997) (2352)
Intersection theory on the moduli space of curves and the matrix airy function (1992) (1472)
Homological Algebra of Mirror Symmetry (1994) (1314)
Gromov-Witten classes, quantum cohomology, and enumerative geometry (1994) (1153)
Stability structures, motivic Donaldson-Thomas invariants and cluster transformations (2008) (783)
Enumeration of Rational Curves Via Torus Actions (1994) (701)
The Geometry of the Master Equation and Topological Quantum Field Theory (1995) (623)
Operads and Motives in Deformation Quantization (1999) (589)
Homological mirror symmetry and torus fibrations (2000) (582)
Feynman Diagrams and Low-Dimensional Topology (1994) (508)
Connected components of the moduli spaces of Abelian differentials with prescribed singularities (2002) (499)
Vassiliev’s knot invariants (1993) (486)
FORMAL (NON)-COMMUTATIVE SYMPLECTIC GEOMETRY (1993) (451)
Canonical bases for cluster algebras (2014) (385)
Affine Structures and Non-Archimedean Analytic Spaces (2004) (378)
Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants (2010) (337)
Frobenius manifolds and formality of Lie algebras of polyvector fields (1997) (280)
Notes on A∞-Algebras, A∞-Categories and Non-Commutative Geometry (2008) (256)
LYAPUNOV EXPONENTS AND HODGE THEORY (1997) (179)
Geometry of determinants of elliptic operators (1994) (175)
Noncommutative smooth spaces (1998) (163)
Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow (2011) (162)
Flat surfaces and stability structures (2014) (160)
Deformations of algebras over operads and Deligne's conjecture (2000) (160)
Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I (2006) (142)
Hodge theoretic aspects of mirror symmetry (2008) (130)
Wall-crossing structures in Donaldson-Thomas invariants, integrable systems and Mirror Symmetry (2013) (118)
Motivic Donaldson-Thomas invariants: Summary of results (2009) (115)
Notes on Motives in Finite Characteristic (2007) (113)
Intersection theory on the moduli space of curves (1991) (105)
Determinants of elliptic pseudo-differential operators (1994) (103)
Automorphisms of the Weyl Algebra (2005) (102)
Relations Between the Correlators of the Topological Sigma-Model Coupled to Gravity (1997) (100)
The Jacobian Conjecture is stably equivalent to the Dixmier Conjecture (2005) (98)
Dynamical systems and categories (2013) (87)
Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models (2014) (82)
Deformation Quantization of Algebraic Varieties (2001) (75)
Virasoro algebra and Teichmüller spaces (1987) (67)
Rozansky-Witten invariants via formal geometry (1997) (64)
Lyapunov spectrum of square-tiled cyclic covers (2010) (60)
Specialization of birational types (2017) (56)
Quantum cohomology of a product (with Appendix by R. Kaufmann2) (1995) (56)
Symplectic geometry of homological algebra (2009) (54)
Holonomic -modules and positive characteristic (2009) (48)
Airy structures and symplectic geometry of topological recursion (2017) (44)
Wick Rotation and the Positivity of Energy in Quantum Field Theory (2021) (44)
Integrality of instanton numbers and p-adic B-model (2006) (38)
On Malliavin measures, SLE, and CFT (2006) (34)
Homological mirror symmetry and tropical geometry (2014) (33)
XI Solomon Lefschetz Memorial Lecture Series: Hodge structures in non-commutative geometry. (Notes by Ernesto Lupercio) (2008) (31)
Product formulas for modular forms on O(2,n) (after R.Borcherds) (1997) (26)
In response to the article by Maxim Kontsevich: Rozansky–Witten Invariants Via Formal Geometry (1999) (25)
Quantization on Curves (2005) (24)
Lower bounds for Lyapunov exponents of flat bundles on curves (2016) (22)
Symmetries of WDVV equations (2005) (21)
Derived Grothendieck-Teichmüller group and graph complexes, (after T. Willwacher) (2019) (19)
Algebra of the infrared and secondary polytopes (2014) (19)
Pre-Calabi-Yau algebras as noncommutative Poisson structures (2021) (19)
Noncommutative identities (2011) (18)
STATISTICS OF KLEIN POLYHEDRA AND MULTI-DIMENSIONAL CONTINUED FRACTIONS (2009) (18)
Equivariant birational geometry and modular symbols (2019) (16)
On Jackson Networks on Denumerable Graphs (1989) (14)
Stability in Fukaya categories of surfaces (2014) (14)
Computational Vision Based on Neurobiology (1993) (13)
Analyticity and resurgence in wall-crossing formulas (2020) (11)
Semistability, modular lattices, and iterated logarithms (2017) (10)
Pre-Calabi-Yau algebras and topological quantum field theories (2021) (9)
Generalized Tian-Todorov theorems (2008) (9)
Mirror symmetry in dimension 3 (1995) (8)
Iterated logarithms and gradient flows (2018) (6)
Quantum Minimal Surfaces (2019) (5)
Pre-Calabi-Yau algebras and double Poisson brackets (2019) (3)
Pre-Calabi-Yau algebras and ξ∂-calculus on higher cyclic Hochschild cohomology (2019) (2)
Spectral description of non-commutative local systems on surfaces and non-commutative cluster varieties (2021) (2)
Pre-Calabi-Yau algebras and noncommutative calculus on higher cyclic Hochschild cohomology (2020) (2)
Multiplication kernels (2021) (1)
Tian-Todorov theorems for Landau-Ginzburg models (2014) (1)
Geometry in dg-Categories (2021) (1)
Automorphisms of Weil algebras (2005) (1)
Coffee Break REPRESENTATION THEORY AT THE CROSSROADS OF MODERN MATHEMATICS IN HONOR OF ALEXANDRE KIRILLOV (0)
Reconstruction of 3D structure from two central projections by a fully linear algorithm (1994) (0)
0 50 70 21 v 1 7 J ul 2 00 5 Quantization on Curves (2008) (0)
Additional bibliography and comments (2002) (0)
The Work of The Fields Medallists : 1998 (2013) (0)
FORMALITY CONJECTURE by Maxim Kontsevich (2009) (0)
p-Determinants and monodromy of differential operators (2020) (0)
Flat surfaces and stability structures (2017) (0)
Intersecting curves ( variation on an observation of (2012) (0)
Vladimir Antonovich Zorich (2018) (0)
J un 2 01 7 Semistability , modular lattices , and iterated logarithms (2018) (0)
Specialization of birational types (2019) (0)
Surgery formulae for 3-manifold invariants defined via configuration space (2005) (0)
Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow (2013) (0)
1 Associative algebras and moduli spaces of algebraic curves : Two constructions (2009) (0)
Noncommutative spaces.dvi (2011) (0)
Vladimir Igorevich Arnol'd (on his sixtieth birthday) (1987) (0)
Preface to the tenth Takagi Lectures (2012) (0)
Fe b 20 18 Iterated logarithms and gradient flows (0)
A generalization of King’s equation via noncommutative geometry (2018) (0)
Analyticity and resurgence in wall-crossing formulas (2022) (0)
Limits of complex structures (2000) (0)
Donaldson-Thomas invariants (2007) (0)

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