Alexander Varchenko

Alexander Varchenko's AcademicInfluence.com Rankings

Alexander Varchenko

Mathematics

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Algebraic Geometry

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#67

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#17

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Measure Theory

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#473

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According to Wikipedia, Alexander Nikolaevich Varchenko is a Soviet and Russian mathematician working in geometry, topology, combinatorics and mathematical physics. Education and career From 1964 to 1966 Varchenko studied at the Moscow Kolmogorov boarding school No. 18 for gifted high school students, where Andrey Kolmogorov and Ya. A. Smorodinsky were lecturing mathematics and physics. Varchenko graduated from Moscow State University in 1971. He was a student of Vladimir Arnold. Varchenko defended his Ph.D. thesis Theorems on Topological Equisingularity of Families of Algebraic Sets and Maps in 1974 and Doctor of Science thesis Asymptotics of Integrals and Algebro-Geometric Invariants of Critical Points of Functions in 1982. From 1974 to 1984 he was a research scientist at the Moscow State University, in 1985–1990 a professor at the Gubkin Institute of Gas and Oil, and since 1991 he has been the Ernest Eliel Professor at the University of North Carolina at Chapel Hill.

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Alexander Varchenko'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 Works

Arrangements of hyperplanes and Lie algebra homology (1991) (412)
The classification of critical points, caustics and wave fronts (1985) (295)
Zeta-function of monodromy and Newton's diagram (1976) (237)
Newton polyhedra and estimation of oscillating integrals (1976) (203)
Multidimensional hypergeometric functions and representation theory of Lie algebras and quantum groups (1995) (190)
Quasiclassical asymptotics of solutions to the KZ equations (1994) (163)
Singularities of Differentiable Maps, Volume 1 (2012) (157)
The Elliptic Gamma Function and SL(3, Z)⋉Z3 (1999) (152)
Why the boundary of a round drop becomes a curve of order four (1992) (144)
Solutions of the Quantum Dynamical Yang–Baxter Equation and Dynamical Quantum Groups (1997) (142)
Schubert calculus and representations of the general linear group (2007) (135)
Geometry and Classificatin of Solutions of the Classical Dynamical Yang–Baxter Equation (1997) (134)
GEOMETRY AND CLASSIFICATION OF SOLUTIONS OF THE CLASSICAL DYNAMICAL YANG-BAXTER EQUATION (1997) (126)
The complex exponent of a singularity does not change along strataµ = const (1982) (125)
Differential Equations Compatible with KZ Equations (2000) (124)
Bethe eigenvectors of higher transfer matrices (2006) (122)
Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors (1994) (121)
Geometry of q-hypergeometric functions, quantum affine algebras and elliptic quantum groups (1997) (120)
Estimate of the number of zeros of an abelian integral depending on a parameter and limit cycles (1984) (120)
The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz (2005) (115)
On representations of the elliptic quantum groupEτ,η(sl2) (1996) (106)
Geometry of q-hypergeometric functions as a bridge between Yangians and quantum affine algebras (1996) (105)
Dynamical Weyl Groups and Applications (2000) (103)
Critical points of master functions and flag varieties (2002) (99)
Integral representation of solutions of the elliptic knizhnik-zamolodchikov-bernard equations (1995) (99)
Algebraic Bethe ansatz for the elliptic quantum group E t, ? ( sl 2) (1996) (98)
Exchange Dynamical Quantum Groups (1998) (98)
Hypergeometric solutions of Knizhnik-Zamolodchikov equations (1990) (96)
Critical Points of the Product of Powers of Linear Functions and Families of Bases of Singular Vectors (1993) (90)
Jackson Integral Representations for Solutions to the Quantized Knizhnik-Zamolodchikov Equation (1993) (86)
Singularities of Differentiable Maps, Volume 2: Monodromy and Asymptotics of Integrals (2012) (82)
Singularities of Differentiable Maps, Volume 2 (2012) (82)
Special Functions, Kz Type Equations, and Representation Theory (2002) (82)
Sixth Painlevé Equation, Universal Elliptic Curve, and Mirror of $\bold{P}^2$ (1996) (75)
Critical points of functions, sl_2 representations, and Fuchsian differential equations with only univalued solutions (2001) (72)
Duality for Knizhnik–Zamolodchikov and Dynamical Equations (2001) (71)
Difference equations compatible with trigonometric KZ differential equations (2000) (71)
Bethe Algebra of Homogeneous XXX Heisenberg Model has Simple Spectrum (2007) (70)
Traces of Intertwiners for Quantum Groups and Difference Equations (1999) (69)
Remarks on the vassiliev knot invariants coming from sl2 (1997) (68)
Norm of a Bethe vector and the Hessian of the master function (2004) (63)
Bispectral and (glN, glM) dualities, discrete versus differential (2006) (62)
Elliptic Quantum Groups and Ruijsenaars Models (1997) (61)
TOPOLOGICAL CONFORMAL FIELD THEORIES AND THE FLAT COORDINATES (1992) (60)
Solutions of the elliptic qKZB equations and Bethe ansatz I (1996) (58)
Quantum Groups and Homology of Local Systems (1991) (58)
Three formulas for eigenfunctions of integrable Schrödinger operators (1995) (58)
Monodromy of solutions of the elliptic quantum Knizhnik-Zamolodchikov-Bernard difference equations (1997) (56)
Trigonometric weight functions as K-theoretic stable envelope maps for the cotangent bundle of a flag variety (2014) (56)
Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra (2012) (54)
Aomoto Dilogarithms, Mixed Hodge Structures and Motivic Cohomology of Pairs of Triangles on the Plane (2007) (51)
THE EULER BETA-FUNCTION, THE VANDERMONDE DETERMINANT, LEGENDRE'S EQUATION, AND CRITICAL VALUES OF LINEAR FUNCTIONS ON A CONFIGURATION OF HYPERPLANES. II (1990) (49)
Completeness of Bethe vectors and difference equations with regular singular points (1995) (48)
On algebraic equations satisfied by hypergeometric correlators in WZW models. I (1994) (47)
Gaudin Hamiltonians generate the Bethe algebra of a tensor power of vector representation of gl_N (2009) (45)
Integral representations of N-point conformal correlators in the WZW model (1989) (45)
Combinatorial Formulae for Nested Bethe Vectors (2007) (44)
Remarks on critical points of phase functions and norms of Bethe vectors (1998) (42)
Topics in singularity theory : V.I. Arnold's 60th anniversary collection (1997) (41)
Asymptotic solutions to the quantized Knizhnik-Zamolodchikov equation and Bethe vectors (1994) (40)
On algebraic equations satisfied by hypergeometric correlators in WZW models. II (1994) (39)
KZ Characteristic Variety as the Zero Set of Classical Calogero{Moser Hamiltonians (2012) (38)
Partial flag varieties, stable envelopes and weight functions (2012) (37)
Multiple orthogonal polynomials and a counterexample to the Gaudin Bethe Ansatz Conjecture (2005) (37)
Monodromy and asymptotics of integrals (1988) (36)
Quantized Knizhnik-Zamolodchikov equations, quantum Yang-Baxter equation, and difference equations forq-hypergeometric functions (1994) (36)
Three-Dimensional Mirror Self-Symmetry of the Cotangent Bundle of the Full Flag Variety (2019) (35)
Equivariant Chern-Schwartz-MacPherson classes in partial flag varieties: interpolation and formulae (2015) (35)
Elliptic and K-theoretic stable envelopes and Newton polytopes (2017) (35)
Solutions to the XXX type Bethe ansatz equations and flag varieties (2002) (33)
Solutions of Trigonometric KZ Equations satisfy Dynamical Difference Equations (2001) (33)
ON THE LOCAL RESIDUE AND THE INTERSECTION FORM ON THE VANISHING COHOMOLOGY (1986) (33)
On reality property of Wronski maps (2007) (31)
Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel ? (2007) (30)
A Generalization of the Capelli Identity (2006) (30)
Quantum Integrable Model of an Arrangement of Hyperplanes (2010) (29)
3d Mirror Symmetry and Elliptic Stable Envelopes (2019) (29)
Selberg-Type Integrals Associated with SL3 (2003) (28)
Bethe Ansatz for Arrangements of Hyperplanes and the Gaudin Model (2004) (27)
Critical Points and Resonance of Hyperplane Arrangements (2009) (26)
Miura opers and critical points of master functions (2003) (26)
Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology (2017) (26)
Quasi-polynomials and the Bethe Ansatz (2006) (26)
Bethe Algebra of Gaudin Model, Calogero–Moser Space, and Cherednik Algebra (2009) (26)
THE DETERMINANT OF A HYPERGEOMETRIC PERIOD MATRIX (1997) (24)
Solutions of KZ differential equations modulo p (2017) (24)
Spaces of quasi-exponentials and representations of the Yangian Y(gl_N) (2013) (24)
q-deformed KZB heat equation: completeness, modular properties and SL(3,Z) (2001) (23)
Bases of Bethe Vectors and Difference Equations with Regular Singular Points (1995) (21)
Discrete Miura Opers and Solutions of the Bethe Ansatz Equations (2004) (20)
Local classification of volume forms in the presence of a hypersurface (1985) (20)
Populations of solutions of the XXX Bethe equations associated to Kac-Moody algebras (2002) (19)
Combinatorics of Rational Functions and Poincaré- Birchoff-Witt Expansions of the Canonical U $({\frak n}\_)$ -Valued Differential Form (2004) (19)
The Determinant Formula for a Matroid Bilinear Form (1997) (18)
Determinant formula for Selberg-type integrals (1991) (17)
Multidimensional hypergeometric functions and their appearance in conformal field theory, algebraic k-theory, algebraic geometry, etc. : plenary address, International Congress of Mathematicians, Kyoto, Japan, August, 1990 (1990) (17)
Extended Joseph polynomials, quantized conformal blocks, and a q-Selberg type integral (2011) (17)
Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety (2013) (17)
The q-Deformed Knizhnik–Zamolodchikov–Bernard Heat Equation (1998) (17)
The Euler adic dynamical system and path counts in the Euler graph (2008) (17)
Dynamical Differential Equations Compatible with Rational qKZ Equations (2005) (17)
Spaces of quasi-exponentials and representations of (2008) (16)
Hypergeometric theta functions and elliptic Macdonald polynomials (2003) (16)
Evolutions of convex hulls and phase transitions in thermodynamics (1990) (16)
Verlinde algebras and the intersection form on vanishing cycles (1996) (16)
On algebraic equations satisfied by correlators in Wess-Zumino-Witten models (1990) (15)
Obstructions to local equivalence of distributions (1981) (15)
Bispectral and $(\glN,\glM)$ Dualities (2005) (15)
SPACES OF QUASI-EXPONENTIALS AND REPRESENTATIONS OF THE YANGIAN $$ Y\left( {\mathfrak{g}{{\mathfrak{l}}_N}} \right) $$ (2014) (15)
Quiver D-modules and homology of local systems over an arrangement of hyperplanes (2005) (15)
Unitarity of SL(2)-conformal blocks in genus zero (2008) (14)
A Selberg Integral Type Formula for an sl_2 One-Dimensional Space of Conformal Blocks (2008) (14)
Selberg Integrals (2004) (14)
On the representation of functions of several variables as a superposition of functions of a smaller number of variables (2009) (14)
Solutions Modulo p of Gauss–Manin Differential Equations for Multidimensional Hypergeometric Integrals and Associated Bethe Ansatz (2017) (14)
RESONANCE RELATIONS FOR SOLUTIONS OF THE ELLIPTIC QKZB EQUATIONS, FUSION RULES, AND EIGENVECTORS OF TRANSFER MATRICES OF RESTRICTED INTERACTION-ROUND-A-FACE MODELS (1999) (14)
ON SEPARATION OF VARIABLES AND COMPLETENESS OF THE BETHE ANSATZ FOR QUANTUM N GAUDIN MODEL (2007) (14)
Bifurcations of caustics and wave fronts (2012) (14)
Cohomology of a flag variety as a Bethe algebra (2011) (13)
Conformal blocks in the tensor product of vector representations and localization formulas (2009) (13)
Algebraic integrability of the two-body Ruijsenaars operator (1996) (13)
Bispectral and $(\mathfrak{gl}_{N},\mathfrak{gl}_{M})$ dualities (2007) (13)
Resonant Local Systems on Complements of Discriminantal Arrangements and Sl2Representations (2002) (13)
Asymptotic solutions to the Knizhnik-Zamolodchikov equation and crystal base (1995) (12)
Finite irreducible groups, generated by reflections, are monodromy groups of suitable singularities (1984) (12)
How to regularize singular vectors and kill the dynamical Weyl group (2002) (12)
Cohomology of the complement to an elliptic arrangement (2011) (11)
Small elliptic quantum group eτ,γ (SLN). (2001) (11)
The relation between topological and algebro-geometric equisingularities according to zariski (1973) (11)
Conformal blocks and equivariant cohomology (2010) (11)
Multiplicity of critical points of master functions and Schubert calculus (2005) (11)
Hyperelliptic integrals modulo $p$ and Cartier–Manin matrices (2018) (11)
Three sides of the geometric Langlands correspondence for gl_N Gaudin model and Bethe vector averaging maps (2009) (10)
An invariant subbundle of the KZ connection mod $p$ and reducibility of $\hat{sl}_2$ Verma modules mod $p$ (2020) (10)
Remarks on the Gaudin model modulo $p$ (2017) (10)
Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator (2002) (10)
Critical points of master functions and integrable hierarchies (2012) (10)
The Quantized Knizhnik-Zamolodchikov Equation in Tensor Products of Irreducible sl(2)-Modules (1997) (10)
Orthogonality and the qKZB-heat equation for traces of $U_q(\mathfrak{g})$-intertwiners (2005) (9)
Multiplication Formulas for the Elliptic Gamma Function (2002) (9)
Canonical Basis and Homology of Local Systems (1997) (9)
On the Gaudin model associated to Lie algebras of classical types (2015) (8)
Solutions of the Qkzb Equation in Tensor Products of Finite Dimensional Modules over the Elliptic Quantum Group E Τ,η Sl 2 (1997) (8)
Vladimir I. Arnold - Collected Works (2009) (8)
Semicontinuity of the complex singularity index (1983) (8)
Cohomology classes of conormal bundles of Schubert varieties and Yangian weight functions (2012) (8)
Hypergeometric Integrals Modulo p and Hasse–Witt Matrices (2020) (8)
Bethe subalgebras of the group algebra of the symmetric group (2010) (8)
A.Varchenko, Algebraic Bethe ansatz for the elliptic quantum group (1996) (7)
Higher Lame Equations and Critical Points of Master Functions (2006) (7)
ON NORMAL FORMS OF NONSMOOTHNESS OF SOLUTIONS OF HYPERBOLIC EQUATIONS (1988) (7)
Special functions, conformal blocks, Bethe ansatz and SL(3, Z) (2001) (7)
Dynamical Gelfand-Zetlin algebra and equivariant cohomology of Grassmannians (2015) (7)
Representations of functions, celestial mechanics and KAM theory, 1957-1965 (2009) (6)
The simplest examples (2012) (6)
Singularities of functions, wave fronts, caustics and multidimensional integrals (2012) (6)
COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: Critical values and the determinant of the periods (1989) (6)
Poincare-Birkhoff-Witt expansions of the canonical elliptic differential form (2005) (6)
Spaces of quasi-polynomials and the Bethe Ansatz (2006) (6)
Notes on solutions of KZ equations modulo $p^s$ and $p$-adic limit $s\to\infty$ (2021) (6)
Quantization of the Space of Conformal Blocks (1997) (6)
The orthogonality and qKZB-heat equation for traces of U_q(g)-intertwiners (2003) (6)
Identities between q -hypergeometric and hypergeometric integrals of different dimensions (2003) (6)
Critical points of master functions and the mKdV hierarchy of type A^2_2 (2013) (5)
On the number of populations of critical points of master functions (2013) (5)
Quantum KZB heat equation, modular transformations and GL(3,Z), I (1998) (5)
On algebraic equations satisfied by hypergeometric solutions of the qKZ equation (1997) (5)
On the new form of Bethe ansatz equations and separation of variables in the $sl_3$ Gaudin model (2006) (5)
Asymptotic integrals and Hodge structures (1984) (5)
Solutions to the Quantized Knizhnik-Zamolodchikov Equation and the Bethe Ansatz (1994) (5)
Cyclotomic discriminantal arrangements and diagram automorphisms of Lie algebras (2016) (5)
Reality Property of Discrete Wronski Map with Imaginary Step (2011) (5)
q-hypergeometric solutions of quantum differential equations, quantum Pieri rules, and Gamma theorem (2017) (5)
Rational differential forms on the line and singular vectors in Verma modules over sl (2017) (4)
Even powers of divisors and elliptic zeta values (2002) (4)
Critical Set of the Master Function and Characteristic Variety of the Associated Gauss–Manin Differential Equations (2014) (4)
Hodge properties of Gauss - Manin connectivities (1980) (4)
Landau–Ginzburg mirror, quantum differential equations and qKZ difference equations for a partial flag variety (2022) (4)
Vanishing products of one-forms and critical points of master functions (2010) (4)
Arrangements and Frobenius like structures (2012) (4)
On axioms of Frobenius like structure in the theory of arrangements (2015) (4)
Equivariant quantum differential equation, Stokes bases, and K-theory for a projective space (2019) (4)
On the bifurcation of multiple integrals depending on a parameter (1969) (4)
Equivariant quantum differential equation and $qKZ$ equations for a projective space: Stokes bases as exceptional collections, Stokes matrices as Gram matrices, and B-Theorem. (2019) (3)
Differential Equations for Jacobi-Pineiro Polynomials (2005) (3)
COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: The topology of caustics, wave fronts, and degeneracies of critical points (1984) (3)
Self-dual Grassmannian, Wronski map, and representations of $\mathfrak{gl}_N$, ${\mathfrak{sp}}_{2r}$, ${\mathfrak{so}}_{2r+1}$ (2017) (3)
The ∗-Markov Equation for Laurent Polynomials (2020) (3)
Norms of eigenfunctions to trigonometric KZB operators (2010) (3)
Rational differential forms on line and singular vectors in Verma modules over $\widehat {sl}_2$ (2015) (3)
Hodge filtration of hypergeometric integrals associated with an affine configuration of general position and a local Torelli theorem (1993) (3)
Three-Dimensional Mirror Symmetry and Elliptic Stable Envelopes (2021) (3)
Cohomology of a flag variety as a Yangian Bethe algebra (2012) (3)
Multidemensional hypergeometric functions and their appearance in conformal field theory, algebraic K-theory, algebraic geometry, etc. (1990) (3)
Nikolai Nikolaevich Nekhoroshev (obituary) (2009) (2)
Potentials of a Frobenius like structure and $m$ bases of a vector space (2016) (2)
The $${\mathbb {F}}_p$$-Selberg integral of type $$A_n$$ (2020) (2)
Quasihomogeneous and semiquasihomogeneous singularities (2012) (2)
Populations of solutions to cyclotomic Bethe equations (2015) (2)
Affine Macdonald conjectures and special values of Felder–Varchenko functions (2016) (2)
Remarks on the structure constants of the Verlinde algebra associated to sl3 (1995) (2)
Positive Populations (2019) (2)
Small Elliptic Quantum Group $e_{tau,\gamma}(sl_N)$ (2000) (2)
Newton polygons and estimates of oscillatory integrals (1978) (2)
Potentials of a Family of Arrangements of Hyperplanes and Elementary Subarrangements (2016) (2)
Vladimir igorevich arnold in the eyes of his students (2007) (2)
The contravariant form on singular vectors of a projective arrangement (2011) (2)
On the germs of analytic mappings whose topological type is determined by a finite jet (1972) (2)
POTENTIALS OF A FROBENIUS-LIKE STRUCTURE (2017) (2)
On a new form of Bethe ansatz equations and separation of variables in the $$\mathfrak{s}\mathfrak{l}_3 $$ Gaudin model (2007) (2)
Twisted de Rham Complex on Line and Singular Vectors in sl2 Verma Modules (2019) (2)
Dynamical elliptic Bethe algebra, KZB eigenfunctions, and theta-polynomials (2018) (2)
BGG resolutions via configuration spaces (2013) (2)
Path count asymptotics and Stirling numbers (2009) (2)
Geometry of Differential Equations (1998) (1)
Intersection cohomology of a rank one local system on the complement of a hyperplane-like divisor (2011) (1)
Bethe algebra and the algebra of functions on the space of differential operators of order two with polynomial kernel (2008) (1)
Congruences for Hasse--Witt matrices and solutions of $p$-adic KZ equations (2021) (1)
Elements of the theory of Picard-Lefschetz (2012) (1)
The proof of the stability theorem (1985) (1)
A ] 2 0 N ov 2 00 0 Small Elliptic Quantum Group e τ , γ ( sl N ) (1)
Quantization of geometry associated to the quantized Knizhnik-Zamolodchikov equations (1996) (1)
Around the intersection form of an isolated singularity of hypersurface (1988) (1)
The gl_2 Bethe algebra associated with a nilpotent element (2008) (1)
The $\mathbb F$-Selberg Integral (2020) (1)
Dwork-type congruences and $p$-adic KZ connection (2022) (1)
A start to the classification of critical points (2012) (1)
Derived KZ Equations (2020) (1)
Jackson Integral Representations for solutions of quantized KZ equations(GEOMETRIC ASPECTS OF INFINITE ANALYSIS) (1994) (1)
ARE MONODROMY GROUPS OF SUITABLE SINGULARITIES (1985) (1)
Collected works || uniform distribution of points on a sphere and some ergodic properties of solutions of linear ordinary differential equations in a complex region (2009) (1)
Knizhnik–Zamolodchikov-Type Equations, Selberg Integrals and Related Special Functions (2020) (1)
Communications of the Moscow Mathematical Society: the Integrality of the Limit of the Curvature Integral Along the Boundary of AN Isolated Singularity of a Surface in C3 (1978) (1)
Characteristic variety of the Gauss-Manin differential equations of a generic parallelly translated arrangement (2014) (1)
The classes Σ I (1985) (1)
THE FUNDAMENTAL GROUP OF THE COMPLEMENT OF A PLANE ALGEBRAIC CURVE (2017) (1)
Solutions of KZ differential equations modulo p (2018) (1)
Determinant of $\mathbb F_p$-hypergeometric solutions under ample reduction (2020) (1)
Dynamical and qKZ Equations Modulo $$p^s$$ : an Example (2022) (1)
Solutions of the qKZB Equation in Tensor Products of finite dimensional modules over the elliptic quantum group $E_{\tau,\eta}sl_2$ (1997) (1)
A Remark on the sl2 Approximation of the Kontsevich Integral of the Unknot (2005) (1)
COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: On the number of integral points in a domain (1982) (1)
The p-adic approximations of vertex functions via 3D-mirror symmetry (2023) (1)
Spectral sequences for the reduction to normal forms (2012) (1)
Resonance relations, holomorphic trace functions and hypergeometric solutions to qKZB and Macdonald-Ruijsenaars equations (2006) (1)
Critical points of master functions and mKdV hierarchy of type ⁽²⁾_{2} (2018) (1)
Arnold’s seminar, first years (2014) (1)
Николай Николаевич Нехорошев (некролог)@@@Nikolai Nikolaevich Nekhoroshev (obituary) (2009) (1)
The classification of stable germs by genotype (2012) (0)
Ju l 2 01 0 CONFORMAL BLOCKS AND EQUIVARIANT COHOMOLOGY (0)
Bethe subalgebras of the group algebra of the symmetric group (2013) (0)
Remarks on Homology Groups of a Configuration with Coefficients in Local Systems More General than Complex One-Dimensional (1995) (0)
The determinator of singularities (2012) (0)
The bifurcation sets and the monodromy group of a singularity (2012) (0)
Igorevich Arnold in the Eyes of His Students On the occasion of his 70 th birthday (2008) (0)
De Rham - Witt KZ equations (2022) (0)
Dynamical Bethe algebra and functions on pairs of quasi-polynomials (2021) (0)
Q A ] 2 1 Ja n 20 08 SPACES OF QUASI-EXPONENTIALS AND REPRESENTATIONS OF gl (2018) (0)
The period map and the intersection form (2012) (0)
The local algebra of a map and the Weierstrass preparation theorem (2012) (0)
Quasiisomorphism of Two-sided Hochschild Complexes to Suitable One-sided Hochschild Complexes (1995) (0)
Identities for Hypergeometric Integrals of Different Dimensions (2003) (0)
Errata to V.I. Arnol’d’s paper: “Small denominators. I.” (2009) (0)
Ju l 2 00 2 Duality for Knizhnik-Zamolodchikov and Dynamical Equations (0)
Q A ] 1 2 Fe b 20 03 Selberg Type Integrals Associated with sl 3 (0)
Twisted De Rham complex on line and $\widehat{\frak{sl}_2}$ singular vectors (2018) (0)
New Prize " Ems Monograph Award " by the Ems Publishing House European Mathematical Society Editor-in-chief Copy Editor (2013) (0)
Complex oscillatory integrals (2012) (0)
Small Elliptic Quantum Group eτ,γ(slN) V.Tarasov ⋆ (2000) (0)
Q A / 0 21 00 40 v 1 3 O ct 2 00 2 ELLIPTIC SELBERG INTEGRALS AND CONFORMAL BLOCKS (2002) (0)
Functional equations for a volume map (1988) (0)
The coefficients of series expansions of integrals, the weight and Hodge filtrations and the spectrum of a critical point (2012) (0)
An Invariant Subbundle of the KZ Connection mod $$p$$ and Reducibility of $$\widehat{{\mathfrak{sl}_2}}$$ Verma Modules mod $$p$$ (2021) (0)
q-hypergeometric solutions of qKZ equations (2003) (0)
The topology of the non-singular level set and the variation operator of a singularity (2012) (0)
Resonance relations, holomorphic trace functions and hypergeometric solutions to qKZB equations (2006) (0)
Frobenius-Like Structure in Gaudin Model (2022) (0)
R-matrix Operator as the Canonical Element, Quantum Doubles (1995) (0)
Sergei Duzhin (June 17, 1956–February 1, 2015) (2015) (0)
Selberg integral, determinant formulas, and dynamical equations (2003) (0)
A formula for the ranks of the homology groups of the boundary of an isolated singularity of a surface in C3 and the Newton diagram (1979) (0)
The quadratic differential of a map (2012) (0)
The survey is devoted to the asymptotics of integrals of the method of descent and to the Hodge structures of critical points of phases of integrals. The problem of how asymptotics change under deformation of phases is discussed. (1984) (0)
Incarnations of XXX $\widehat{\frak{sl}_N}$ Bethe ansatz equations and integrable hierarchies (2019) (0)
Stability and instability in classical mechanics (2009) (0)
The mathematics workshop for schools at Moscow State University (2009) (0)
Cycles of integrals and the monodromy of the KZ equation (2003) (0)
Elliptic hypergeometric functions (2003) (0)
2 3 A ug 2 00 4 SELBERG INTEGRALS (2004) (0)
COHOMOLOGY OF A FLAG AS A BETHE ALGEBRA (2018) (0)
Q A ] 2 2 A pr 2 01 1 NORMS OF EIGENFUNCTIONS TO TRIGONOMETRIC KZB OPERATORS (2018) (0)
R-Matrix for the Two-sided Hochschild Complexes (1995) (0)
The school mathematics circle at Moscow State University: harmonic functions (2009) (0)
Finite-order Invariants for (n, 2)-Torus Knots and the Curve ${Y^2}={X^3}+{X^2}$ (2004) (0)
bundle of a partial flag variety (2014) (0)
Kac–Moody Lie Algebras without Serre's Relations and Their Doubles (1995) (0)
The mixed Hodge structure of an isolated critical point of a holomorphic function (2012) (0)
The classes $ \sum^{I} $ (2012) (0)
The Fp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}_p$$\end{document}-Selberg integral of type An\docu (2021) (0)
Critical points of master functions and mKdV hierarchy of type $C^{(1)}_{n}$ (2017) (0)
Elliptic and K-theoretic stable envelopes and Newton polytopes (2019) (0)
Hypergeometric Integrals Modulo p and Hasse–Witt Matrices (2020) (0)
Functorial properties of the hypergeometric map (1998) (0)
Review of further results (2012) (0)
The classification of Lagrangian and Legendrian singularities (2012) (0)
Real, symmetric and boundary singularities (2012) (0)
ON THE REAL PREIMAGES OF A REAL POINT UNDER THE LYASHKO-LOOIJENGA COVERING FOR SIMPLE SINGULARITIES (2017) (0)
Solutions modulo $p^s$ of the differential KZ and dynamical equations (2023) (0)
Determinants of the Hypergeometric Period Matrices of an Arrangement and Its Dual (2006) (0)
A remark on sl_2 approximation of the Kontsevich integral of the unknot (2001) (0)
Reality Property of Discrete Wronski Map with Imaginary Step (2011) (0)
The singular index, examples (2012) (0)
The simplest properties of the integrals (2012) (0)
Critical Set of the Master Function and Characteristic Variety of the Associated Gauss–Manin Differential Equations (2015) (0)
Critical points and mKdV hierarchy of type $C^{(1)}_n$ (2020) (0)
Asymptotics and Newton polyhedra (2012) (0)
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Vladimir Igorevich Arnol'd (on his sixtieth birthday) (1987) (0)
Elementary integrals and the resolution of singularities of the phase (2012) (0)
Vanishing Cycles and Cartan Eigenvectors (2017) (0)
Integrals and differential equations (2012) (0)
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INVARIANT ESTIMATES OF TWO-DIMENSIONAL TRIGONOMETRIC INTEGRALS (2017) (0)
Monodromy of the equivariant quantum differential equation of the cotangent bundle of a Grassmannian (2022) (0)
The Fp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {F}}}_p$$\end{document}-Selberg Integral (2022) (0)
Stability and infinitesimal stability (2012) (0)
Cohomology classes of conormal bundles of Schubert varieties and Yangian weight functions (2014) (0)
Динамическая алгебра Бете над $\mathfrak{sl}_2$ и функции на парах квазимногочленов (2021) (0)
Hypergeometric solutions of KZ equations (2003) (0)
Vladimir Arnold (12 June 1937–3 June 2010) (2010) (0)
The intersection forms of boundary singularities and the topology of complete intersections (2012) (0)
Lists of singularities (2012) (0)
Discussion of results (2012) (0)
The classification of quasihomogeneous functions (2012) (0)
Q A ] 1 5 M ay 2 00 3 IDENTITIES FOR HYPERGEOMETRIC INTEGRALS OF DIFFERENT DIMENSIONS (2003) (0)
Игорь Моисеевич Кричевер (к семидесятилетию со дня рождения) (2021) (0)
The local multiplicity of a holomorphic map (2012) (0)
Bethe algebra and algebra of functions on the space of differential operators of order two with poly (2007) (0)
$q$-Hypergeometric solutions of quantum differential equations and quantum Pieri rules (2017) (0)
The $${{\mathbb {F}}}_p$$ F p -Selberg Integral (2022) (0)
3 1 Ja n 20 00 Differential Equations Compatible with KZ Equations (2008) (0)
The intersection matrices of singularities of functions of two variables (2012) (0)
Vanishing Cycles and Cartan Eigenvectors (2015) (0)
Critical points of master functions and the Bethe ansatz (2003) (0)
Solutions of the $sl_2$ qKZ equations modulo an integer (2022) (0)
On the number of p-hypergeometric solutions of KZ equations (2022) (0)
A ] 2 7 Ju l 1 99 9 TRACES OF INTERTWINERS FOR QUANTUM GROUPS AND DIFFERENCE EQUATIONS , (0)
THE PERIOD MAP AND THE DISCRIMINANT (1989) (0)
Affine Macdonald conjectures and special values of Felder–Varchenko functions (2017) (0)

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