A. Varchenko

发表

Singularities of Differentiable Maps, Volume 1

V. Arnold, S. Gusein-Zade, A. Varchenko, 2012 .

Newton polyhedra and estimation of oscillating integrals

Alexander Varchenko, A. Varchenko, 1976 .

New Prize " Ems Monograph Award " by the Ems Publishing House European Mathematical Society Editor-in-chief Copy Editor

J. Nesetril, J. Buescu, M. Röckner, 2013 .

Arrangements of hyperplanes and Lie algebra homology

Vadim Schechtman, Alexander Varchenko, A. Varchenko, 1991 .

On the number of $p$-hypergeometric solutions of KZ equations

A. Varchenko, 2022, 2201.11820.

Notes on solutions of KZ equations modulo $p^s$ and $p$-adic limit $s\to\infty$

A. Varchenko, 2021, 2103.01725.

An Invariant Subbundle of the KZ Connection mod $$p$$ and Reducibility of $$\widehat{{\mathfrak{sl}_2}}$$ Verma Modules mod $$p$$

A. Varchenko, 2021 .

Dynamical Bethe algebra and functions on pairs of quasi-polynomials

A. Varchenko, A. Slinkin, D. Thompson, 2021 .

Determinant of $\mathbb F_p$-hypergeometric solutions under ample reduction

A. Varchenko, 2020, 2010.11275.

Hypergeometric Integrals Modulo p and Hasse–Witt Matrices

A. Varchenko, A. Slinkin, 2020, Arnold Mathematical Journal.

An invariant subbundle of the KZ connection mod $p$ and reducibility of $\hat{sl}_2$ Verma modules mod $p$

A. Varchenko, 2020, 2002.05834.

Elliptic and K-theoretic stable envelopes and Newton polytopes

A. Varchenko, V. Tarasov, Richárd Rimányi, 2017, Selecta Mathematica.

Potentials of a Family of Arrangements of Hyperplanes and Elementary Subarrangements

A. Varchenko, Andrew Prudhom, 2016, Moscow Mathematical Journal.

Twisted de Rham Complex on Line and Singular Vectors in sl2 Verma Modules

A. Varchenko, A. Slinkin, 2019, Symmetry, Integrability and Geometry: Methods and Applications.

Hyperelliptic integrals modulo $p$ and Cartier–Manin matrices

A. Varchenko, 2018, Pure and Applied Mathematics Quarterly.

Solutions of KZ differential equations modulo p

A. Varchenko, V. Schechtman, 2017, The Ramanujan Journal.

Twisted De Rham complex on line and $\widehat{\frak{sl}_2}$ singular vectors

A. Varchenko, A. Slinkin, 2018, 1812.09791.

Rational differential forms on the line and singular vectors in Verma modules over sl

A. Varchenko, V. Schechtman, 2017 .

Remarks on the Gaudin model modulo $p$

A. Varchenko, 2017, 1708.06264.

Solutions Modulo p of Gauss–Manin Differential Equations for Multidimensional Hypergeometric Integrals and Associated Bethe Ansatz

A. Varchenko, 2017, 1709.06189.

Rational differential forms on line and singular vectors in Verma modules over $\widehat {sl}_2$

A. Varchenko, V. Schechtman, 2015, 1511.09014.

bundle of a partial flag variety

A. Varchenko, V. Tarasov, 2014 .

Characteristic variety of the Gauss-Manin differential equations of a generic parallelly translated arrangement

A. Varchenko, 2014, 1402.0924.

On the number of populations of critical points of master functions

A. Varchenko, E. Mukhin, 2013, 1306.4429.

Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety

A. Varchenko, V. Tarasov, Alexander Varchenko, 2013, 1301.2705.

Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra

A. Varchenko, V. Tarasov, Richárd Rimányi, 2012, 1204.5138.

Combinatorial Formulae for Nested Bethe Vectors

A. Varchenko, V. Tarasov, 2007, math/0702277.

Critical points of master functions and integrable hierarchies

A. Varchenko, D. Wright, 2012, 1207.2274.

KZ Characteristic Variety as the Zero Set of Classical Calogero{Moser Hamiltonians

A. Varchenko, V. Tarasov, E. Mukhin, 2012, 1201.3990.

Arrangements and Frobenius like structures

A. Varchenko, 2012, 1210.3802.

Cohomology of a flag variety as a Yangian Bethe algebra

A. Varchenko, V. Tarasov, Richárd Rimányi, 2012 .

Conformal blocks and equivariant cohomology

A. Varchenko, Richárd Rimányi, V. Schechtman, 2010 .

Unitarity of SL(2)-conformal blocks in genus zero

E. Looijenga, A. Varchenko, 2008, 0810.4310.

Three sides of the geometric Langlands correspondence for gl_N Gaudin model and Bethe vector averaging maps

A. Varchenko, V. Tarasov, E. Mukhin, 2009, 0907.3266.

ON SEPARATION OF VARIABLES AND COMPLETENESS OF THE BETHE ANSATZ FOR QUANTUM N GAUDIN MODEL

A. Varchenko, V. Tarasov, E. Mukhin, 2007, Glasgow Mathematical Journal.

Conformal blocks in the tensor product of vector representations and localization formulas

A. Varchenko, Richárd Rimányi, 2009, 0911.3253.

A Selberg Integral Type Formula for an sl_2 One-Dimensional Space of Conformal Blocks

A. Varchenko, 2008, 0810.3355.

Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel ?

A. Varchenko, V. Tarasov, E. Mukhin, 2007, math/0703893.

On the new form of Bethe ansatz equations and separation of variables in the $sl_3$ Gaudin model

A. Varchenko, V. Tarasov, E. Mukhin, 2006 .

Bethe eigenvectors of higher transfer matrices

Alexander Varchenko, Evgeny Mukhin, A. Varchenko, 2006 .

Higher Lame Equations and Critical Points of Master Functions

E. Mukhin, A. Varchenko, A. Varchenko, 2006 .

Dynamical Differential Equations Compatible with Rational qKZ Equations

A. Varchenko, V. Tarasov, 2005 .

Norm of a Bethe vector and the Hessian of the master function

Alexander Varchenko, Evgeny Mukhin, A. Varchenko, 2005, Compositio Mathematica.

The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz

E. Mukhin, A. Varchenko, A. Varchenko, 2005 .

Poincare-Birkhoff-Witt expansions of the canonical elliptic differential form

G. Felder, A. Varchenko, Richárd Rimányi, 2005, math/0502296.

Discrete Miura Opers and Solutions of the Bethe Ansatz Equations

A. Varchenko, E. Mukhin, 2004, math/0401137.

Selberg-Type Integrals Associated with SL3

A. Varchenko, V. Tarasov, A. Varchenko, 2003 .

Miura opers and critical points of master functions

A. Varchenko, E. Mukhin, 2003, math/0312406.

Critical points of master functions and flag varieties

E. Mukhin, A. Varchenko, A. Varchenko, 2002, math/0209017.

Critical points of functions, sl_2 representations, and Fuchsian differential equations with only univalued solutions

A. Varchenko, A. Varchenko, I. Scherbak, 2001 .

Solutions of Trigonometric KZ Equations satisfy Dynamical Difference Equations

A. Varchenko, Y. Markov, 2001, math/0103226.

Difference equations compatible with trigonometric KZ differential equations

A. Varchenko, V. Tarasov, 2000, math/0002132.

Remarks on critical points of phase functions and norms of Bethe vectors

A. Varchenko, E. Mukhin, 1998, math/9810087.

Geometry and Classificatin of Solutions of the Classical Dynamical Yang–Baxter Equation

A. Varchenko, P. Etingof, 1997, q-alg/9703040.

Canonical Basis and Homology of Local Systems

A. Kirillov, A. Varchenko, I. Frenkel, 1997, q-alg/9703007.

On algebraic equations satisfied by hypergeometric solutions of the qKZ equation

A. Varchenko, E. Mukhin, 1997, q-alg/9710040.

GEOMETRY AND CLASSIFICATION OF SOLUTIONS OF THE CLASSICAL DYNAMICAL YANG-BAXTER EQUATION

A. Varchenko, P. Etingof, 1997 .

Quantization of geometry associated to the quantized Knizhnik-Zamolodchikov equations

A. Varchenko, 1996, q-alg/9606006.

Integral representation of solutions of the elliptic knizhnik-zamolodchikov-bernard equations

G. Felder, A. Varchenko, 1995, hep-th/9502165.

Quantized Knizhnik-Zamolodchikov equations, quantum Yang-Baxter equation, and difference equations forq-hypergeometric functions

A. Varchenko, 1994 .

On algebraic equations satisfied by hypergeometric correlators in WZW models. II

A. Varchenko, B. Feigin, V. Schechtman, 1994, hep-th/9407010.

Solutions to the Quantized Knizhnik-Zamolodchikov Equation and the Bethe Ansatz

A. Varchenko, V. Tarasov, 1994 .

Critical Points of the Product of Powers of Linear Functions and Families of Bases of Singular Vectors

Alexander Varchenko, A. Varchenko, 1993, hep-th/9312119.

Quantum Groups and Homology of Local Systems

Vadim Schechtman, Alexander Varchenko, A. Varchenko, 1991 .

Ju l 2 01 0 CONFORMAL BLOCKS AND EQUIVARIANT COHOMOLOGY

A. Varchenko, Richárd Rimányi, V. Schechtman, 2022 .

Integral representations of N-point conformal correlators in the WZW model

A. Varchenko, Schechtman, 1989 .

Exchange Dynamical Quantum Groups

A. Varchenko, P. Etingof, 1998, math/9801135.

Cohomology of a flag variety as a Bethe algebra

A. Varchenko, V. Tarasov, Richárd Rimányi, 2011 .

Когомологии многообразия флагов как алгебра Бете@@@Cohomology of a flag variety as a Bethe algebra

A. Varchenko, V. Tarasov, Richárd Rimányi, 2011 .

Resonance relations, holomorphic trace functions and hypergeometric solutions to qKZB equations

A. Varchenko, K. Styrkas, 2006 .

POTENTIALS OF A FROBENIUS-LIKE STRUCTURE

A. Varchenko, C. Hertling, 2017, Glasgow Mathematical Journal.

Difference equations compatible with trigonometric KZ differential equations

A. Varchenko, V. Tarasov, 2000, math/0002132.

Critical points of functions, sl_2 representations, and Fuchsian differential equations with only univalued solutions

A. Varchenko, I. Scherbak, 2001, math/0112269.

Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology

G. Felder, A. Varchenko, Richárd Rimányi, 2017, Symmetry, Integrability and Geometry: Methods and Applications.

Exchange Dynamical Quantum Groups

A. Varchenko, P. Etingof, 1998, math/9801135.

Determinants of the Hypergeometric Period Matrices of an Arrangement and Its Dual

A. Varchenko, D. Mukherjee, 2006, math/0603005.

Special Functions, Kz Type Equations, and Representation Theory

A. Varchenko, 2002, math/0205313.

Remarks on critical points of phase functions and norms of Bethe vectors

A. Varchenko, E. Mukhin, 1998, math/9810087.

THE EULER BETA-FUNCTION, THE VANDERMONDE DETERMINANT, LEGENDRE'S EQUATION, AND CRITICAL VALUES OF LINEAR FUNCTIONS ON A CONFIGURATION OF HYPERPLANES. II

A. Varchenko, 1990 .

Local classification of volume forms in the presence of a hypersurface

A. Varchenko, 1985 .

Equivariant quantum differential equation, Stokes bases, and K-theory for a projective space

A. Varchenko, V. Tarasov, 2019, European Journal of Mathematics.

q-hypergeometric solutions of quantum differential equations, quantum Pieri rules, and Gamma theorem

A. Varchenko, V. Tarasov, 2017, Journal of Geometry and Physics.

Even powers of divisors and elliptic zeta values

G. Felder, A. Varchenko, 2002, math/0205116.

The $${{\mathbb {F}}}_p$$ F p -Selberg Integral

A. Varchenko, Richárd Rimányi, 2022, Arnold Mathematical Journal.

Jackson Integral Representations for Solutions to the Quantized Knizhnik-Zamolodchikov Equation

A. Varchenko, V. Tarasov, 1993, hep-th/9311040.

Multiplication Formulas for the Elliptic Gamma Function

G. Felder, A. Varchenko, 2002, math/0212155.

The Elliptic Gamma Function and SL(3, Z)⋉Z3

G. Felder, A. Varchenko, 1999, math/9907061.

Asymptotic integrals and Hodge structures

A. Varchenko, 1984 .

The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz

A. Varchenko, V. Tarasov, E. Mukhin, 2005, math/0512299.

Monodromy and asymptotics of integrals

V. I. Arnolʹd, S. Gusein-Zade, A. Varchenko, 1988 .

Newton polygons and estimates of oscillatory integrals

A. Varchenko, A. N. Varchenko, 1978 .

RESONANCE RELATIONS FOR SOLUTIONS OF THE ELLIPTIC QKZB EQUATIONS, FUSION RULES, AND EIGENVECTORS OF TRANSFER MATRICES OF RESTRICTED INTERACTION-ROUND-A-FACE MODELS

G. Felder, A. Varchenko, 1999, math/9901111.

Algebraic Bethe ansatz for the elliptic quantum group E t, ? ( sl 2)

G. Felder, A. Varchenko, 1996, q-alg/9605024.

A.Varchenko, Algebraic Bethe ansatz for the elliptic quantum group

G. Felder, A. Varchenko, 1996 .

Higher Lame Equations and Critical Points of Master Functions

A. Varchenko, V. Tarasov, E. Mukhin, 2006, math/0601703.

The Quantized Knizhnik-Zamolodchikov Equation in Tensor Products of Irreducible sl(2)-Modules

A. Varchenko, E. Mukhin, 1997, q-alg/9709026.

Dynamical Weyl Groups and Applications

A. Varchenko, P. Etingof, 2000, math/0011001.

ARE MONODROMY GROUPS OF SUITABLE SINGULARITIES

S. Chmutov, A. Varchenko, 1985 .

Finite irreducible groups, generated by reflections, are monodromy groups of suitable singularities

S. Chmutov, A. Varchenko, 1984 .

Incarnations of XXX $\widehat{\frak{sl}_N}$ Bethe ansatz equations and integrable hierarchies

I. Krichever, A. Varchenko, 2019, 1907.12198.

The ∗-Markov Equation for Laurent Polynomials

A. Varchenko, G. Cotti, 2020, Moscow Mathematical Journal.

Geometry and Classificatin of Solutions of the Classical Dynamical Yang–Baxter Equation

A. Varchenko, P. Etingof, 1997, q-alg/9703040.

The complex exponent of a singularity does not change along strataµ = const

A. Varchenko, 1982 .

Multidimensional hypergeometric functions and representation theory of Lie algebras and quantum groups

A. Varchenko, 1995 .

Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors

H. Terao, A. Varchenko, V. Schechtman, 1994 .

On algebraic equations satisfied by hypergeometric correlators in WZW models. I

A. Varchenko, B. Feigin, V. Schechtman, 1994 .

On algebraic equations satisfied by correlators in Wess-Zumino-Witten models

A. Varchenko, B. Feigin, V. Schechtman, 1990 .

Hypergeometric solutions of Knizhnik-Zamolodchikov equations

A. Varchenko, V. Schechtman, 1990 .

Gaudin Hamiltonians generate the Bethe algebra of a tensor power of vector representation of gl_N

A. Varchenko, V. Tarasov, E. Mukhin, 2009, 0904.2131.

Bethe Algebra of Homogeneous XXX Heisenberg Model has Simple Spectrum

A. Varchenko, V. Tarasov, E. Mukhin, 2007, 0706.0688.

Sixth Painlevé Equation, Universal Elliptic Curve, and Mirror of $\bold{P}^2$

V. Vassiliev, A. Varchenko, A. Khovanskii, 1996 .

Equivariant quantum differential equation and $qKZ$ equations for a projective space: Stokes bases as exceptional collections, Stokes matrices as Gram matrices, and B-Theorem.

A. Varchenko, G. Cotti, 2019, 1909.06582.

Spaces of quasi-exponentials and representations of the Yangian Y(gl_N)

A. Varchenko, V. Tarasov, E. Mukhin, 2013, 1303.1578.

Three formulas for eigenfunctions of integrable Schrödinger operators

G. Felder, A. Varchenko, 1995, Compositio Mathematica.

Trigonometric weight functions as K-theoretic stable envelope maps for the cotangent bundle of a flag variety

A. Varchenko, V. Tarasov, Richárd Rimányi, 2014, 1411.0478.

Q A / 0 21 00 40 v 1 3 O ct 2 00 2 ELLIPTIC SELBERG INTEGRALS AND CONFORMAL BLOCKS

G. Felder, A. Varchenko, L. Stevens, 2002 .

Q A ] 1 2 Fe b 20 03 Selberg Type Integrals Associated with sl 3

A. Varchenko, V. Tarasov, 2022 .

Critical points of master functions and mKdV hierarchy of type $C^{(1)}_{n}$

A. Varchenko, T. Woodruff, 2017, 1702.06169.

Q A ] 2 2 A pr 2 01 1 NORMS OF EIGENFUNCTIONS TO TRIGONOMETRIC KZB OPERATORS

A. Varchenko, E. Jensen, 2018 .

Cyclotomic discriminantal arrangements and diagram automorphisms of Lie algebras

A. Varchenko, C. Young, 2016, 1603.07125.

Populations of solutions to cyclotomic Bethe equations

A. Varchenko, C. Young, 2015, 1505.07582.

Critical points of master functions and the mKdV hierarchy of type A^2_2

A. Varchenko, D. Wright, T. Woodruff, 2013, 1305.5603.

Quantum Integrable Model of an Arrangement of Hyperplanes

A. Varchenko, 2010, 1001.4553.

Norms of eigenfunctions to trigonometric KZB operators

A. Varchenko, E. Jensen, 2010, 1010.0447.

Multiple orthogonal polynomials and a counterexample to the Gaudin Bethe Ansatz Conjecture

A. Varchenko, E. Mukhin, E. Mukhin, 2005, math/0501144.

Norm of a Bethe vector and the Hessian of the master function

A. Varchenko, E. Mukhin, 2004, Compositio Mathematica.

Bethe Ansatz for Arrangements of Hyperplanes and the Gaudin Model

A. Varchenko, 2004, math/0408001.

Asymptotic solutions to the Knizhnik-Zamolodchikov equation and crystal base

A. Varchenko, 1995 .

Combinatorial Formulae for Nested Bethe Vectors

A. Varchenko, V. Tarasov, 2007, math/0702277.

Dynamical elliptic Bethe algebra, KZB eigenfunctions, and theta-polynomials

D. Thompson, A. Varchenko, 2018, 1810.09001.

Q A ] 2 1 Ja n 20 08 SPACES OF QUASI-EXPONENTIALS AND REPRESENTATIONS OF gl

A. Varchenko, V. Tarasov, E. Mukhin, 2018 .

Partial flag varieties, stable envelopes and weight functions

A. Varchenko, V. Tarasov, Richárd Rimányi, 2012, 1212.6240.

Extended Joseph polynomials, quantized conformal blocks, and a q-Selberg type integral

P. Zinn-Justin, A. Varchenko, V. Tarasov, 2011, 1110.2187.

The gl_2 Bethe algebra associated with a nilpotent element

A. Varchenko, V. Tarasov, E. Mukhin, 2008, 0810.2257.

Spaces of quasi-exponentials and representations of

A. Varchenko, V. Tarasov, E. Mukhin, 2008, 0801.3120.

Schubert calculus and representations of the general linear group

E. Mukhin, A. Varchenko, A. Varchenko, 2007, 0711.4079.

Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel ?

A. Varchenko, V. Tarasov, E. Mukhin, 2007, math/0703893.

Duality for Knizhnik–Zamolodchikov and Dynamical Equations

A. Varchenko, V. Tarasov, A. Varchenko, 2001, math/0112005.

On representations of the elliptic quantum groupEτ,η(sl2)

G. Felder, A. Varchenko, 1996, q-alg/9601003.

Traces of Intertwiners for Quantum Groups and Difference Equations

P. Etingof, O. Schiffmann, A. Varchenko, 1999, math/0207157.

Reality Property of Discrete Wronski Map with Imaginary Step

A. Varchenko, V. Tarasov, E. Mukhin, 2011, 1102.5368.

On reality property of Wronski maps

Alexander Varchenko, Evgeny Mukhin, A. Varchenko, 2007, 0710.5856.

Quasi-polynomials and the Bethe Ansatz

A. Varchenko, E. Mukhin, 2006, math/0604048.

Solutions to the XXX type Bethe ansatz equations and flag varieties

A. Varchenko, E. Mukhin, 2002, math/0211321.

Asymptotic solutions to the quantized Knizhnik-Zamolodchikov equation and Bethe vectors

A. Varchenko, V. Tarasov, 1994, hep-th/9406060.

The classification of critical points, caustics and wave fronts

Alexander Varchenko, V. I. Arnolʹd, S. Gusein-Zade, 1985 .

Solutions of the Quantum Dynamical Yang–Baxter Equation and Dynamical Quantum Groups

A. Varchenko, P. Etingof, 1997, q-alg/9708015.

Differential Equations Compatible with KZ Equations

G. Felder, A. Varchenko, V. Tarasov, 2000, math/0001184.

Self-dual Grassmannian, Wronski map, and representations of $\mathfrak{gl}_N$, ${\mathfrak{sp}}_{2r}$, ${\mathfrak{so}}_{2r+1}$

A. Varchenko, E. Mukhin, Kang Lu, 2017, 1705.02048.

Bispectral and (glN, glM) dualities, discrete versus differential

A. Varchenko, V. Tarasov, E. Mukhin, 2008 .

Populations of solutions of the XXX Bethe equations associated to Kac-Moody algebras

A. Varchenko, E. Mukhin, 2002, math/0212092.

Aomoto Dilogarithms, Mixed Hodge Structures and Motivic Cohomology of Pairs of Triangles on the Plane

Alexander Varchenko, A. Goncharov, A. Varchenko, 2007 .

How to regularize singular vectors and kill the dynamical Weyl group

A. Varchenko, V. Tarasov, K. Styrkas, 2002, math/0206294.

Solutions of Trigonometric KZ Equations satisfy Dynamical Difference Equations

A. Varchenko, Y. Markov, A. Varchenko, 2001, math/0103226.

A ] 2 7 Ju l 1 99 9 TRACES OF INTERTWINERS FOR QUANTUM GROUPS AND DIFFERENCE EQUATIONS ,

A. Varchenko, I. Etingof, 2022 .

SPACES OF QUASI-EXPONENTIALS AND REPRESENTATIONS OF THE YANGIAN $$ Y\left( {\mathfrak{g}{{\mathfrak{l}}_N}} \right) $$

A. Varchenko, V. Tarasov, E. Mukhin, 2014 .

Multiplicity of critical points of master functions and Schubert calculus

A. Varchenko, E. Mukhin, P. Belkale, 2005, math/0503132.

Quasiclassical asymptotics of solutions to the KZ equations

Nicolai Reshetikhin, Alexander Varchenko, N. Reshetikhin, 1994, hep-th/9402126.

Elliptic Quantum Groups and Ruijsenaars Models

G. Felder, A. Varchenko, 1997, q-alg/9704005.

The orthogonality and qKZB-heat equation for traces of U_q(g)-intertwiners

A. Varchenko, P. Etingof, 2003, math/0302071.

Q A ] 6 F eb 2 00 3 THE ORTHOGONALITY AND q KZB-HEAT EQUATION FOR TRACES

A. Varchenko, P. Etingof, 2022 .

Bethe Algebra of Gaudin Model, Calogero–Moser Space, and Cherednik Algebra

A. Varchenko, V. Tarasov, E. Mukhin, 2009, 0906.5185.

3 1 Ja n 20 00 Differential Equations Compatible with KZ Equations

G. Felder, A. Varchenko, V. Tarasov, 2008 .

Singularities of Differentiable Maps, Volume 2: Monodromy and Asymptotics of Integrals

Vladimir I. Arnold, Sabir M. Gusein-Zade, Alexander Varchenko, 2012 .

On the representation of functions of several variables as a superposition of functions of a smaller number of variables

V. Arnold, J. Marsden, B. Khesin, 2009 .

Quiver D-modules and homology of local systems over an arrangement of hyperplanes

A. Varchenko, S. Khoroshkin, 2005, math/0510451.

Potentials of a Frobenius like structure and $m$ bases of a vector space

A. Varchenko, C. Hertling, 2016, 1608.08423.

On axioms of Frobenius like structure in the theory of arrangements

A. Varchenko, 2015, 1601.02208.

Characteristic variety of the Gauss-Manin differential equations of a generic parallelly translated arrangement

A. Varchenko, 2014, 1402.0924.

Vanishing products of one-forms and critical points of master functions

A. Varchenko, M. Falk, D. Cohen, 2010, 1010.3743.

De Rham - Witt KZ equations

A. Varchenko, V. Schechtman, 2022, 2212.03628.

The p-adic approximations of vertex functions via 3D-mirror symmetry

A. Varchenko, A. Smirnov, 2023, 2302.03092.

Zeta-function of monodromy and Newton's diagram

A. Varchenko, 1976 .

Singularities of Differentiable Maps, Volume 2

Vladimir I. Arnold, Sabir M. Gusein-Zade, V. Arnold, 2012 .

Verlinde algebras and the intersection form on vanishing cycles

S. Gusein-Zade, A. Varchenko, 1996, hep-th/9610058.

Three-Dimensional Mirror Self-Symmetry of the Cotangent Bundle of the Full Flag Variety

A. Varchenko, Richárd Rimányi, A. Smirnov, 2019, Symmetry, Integrability and Geometry: Methods and Applications.

3d Mirror Symmetry and Elliptic Stable Envelopes

A. Varchenko, Richárd Rimányi, A. Smirnov, 2019, 1902.03677.

COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: The topology of caustics, wave fronts, and degeneracies of critical points

A. Varchenko, S. M. Husein-Zadeh, 1984 .

Critical Points and Resonance of Hyperplane Arrangements

Daniel C. Cohen, A. Varchenko, M. Falk, 2009, Canadian Journal of Mathematics.

Monodromy of solutions of the elliptic quantum Knizhnik-Zamolodchikov-Bernard difference equations

G. Felder, A. Varchenko, V. Tarasov, 1997, q-alg/9705017.

Three-Dimensional Mirror Symmetry and Elliptic Stable Envelopes

Andrey Smirnov, Zijun Zhou, Alexander Varchenko, 2021 .

Estimate of the number of zeros of an abelian integral depending on a parameter and limit cycles

Alexander Varchenko, A. Varchenko, 1984 .

A Generalization of the Capelli Identity

A. Varchenko, V. Tarasov, E. Mukhin, 2006, math/0610799.

Why the boundary of a round drop becomes a curve of order four

Alexander Varchenko, Pavel Etingof, A. Varchenko, 1992 .

ON THE LOCAL RESIDUE AND THE INTERSECTION FORM ON THE VANISHING COHOMOLOGY

A. Varchenko, 1986 .

Remarks on the vassiliev knot invariants coming from sl2

S. Chmutov, A. Varchenko, 1997 .

A Remark on the sl2 Approximation of the Kontsevich Integral of the Unknot

A. Varchenko, S. Tyurina, 2005 .

Hodge filtration of hypergeometric integrals associated with an affine configuration of general position and a local Torelli theorem

A. Varchenko, 1993 .

Equivariant Chern-Schwartz-MacPherson classes in partial flag varieties: interpolation and formulae

A. Varchenko, Richárd Rimányi, 2015, 1509.09315.

Resonance relations, holomorphic trace functions and hypergeometric solutions to qKZB and Macdonald-Ruijsenaars equations

A. Varchenko, K. Styrkas, 2006, math/0612330.

Geometry of q-hypergeometric functions, quantum affine algebras and elliptic quantum groups

A. Varchenko, V. Tarasov, 1997, q-alg/9703044.

Geometry of q-hypergeometric functions as a bridge between Yangians and quantum affine algebras

A. Varchenko, V. Tarasov, 1996, q-alg/9604011.

Differential Equations for Jacobi-Pineiro Polynomials

A. Varchenko, E. Mukhin, 2005 .

The $${\mathbb {F}}_p$$-Selberg integral of type $$A_n$$

A. Varchenko, Richárd Rimányi, 2020, Letters in Mathematical Physics.

Solutions of KZ differential equations modulo p

A. Varchenko, V. Schechtman, 2018, The Ramanujan Journal.

Vladimir Igorevich Arnol'd (on his sixtieth birthday)

Y. Osipov, B. Khesin, Y. Sinai, 1987 .

THE PERIOD MAP AND THE DISCRIMINANT

A. Varchenko, 1989 .

ON NORMAL FORMS OF NONSMOOTHNESS OF SOLUTIONS OF HYPERBOLIC EQUATIONS

A. Varchenko, 1988 .

Semicontinuity of the complex singularity index

A. Varchenko, 1983 .

Hodge properties of Gauss - Manin connectivities

A. Varchenko, 1980 .

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.

A. Varchenko, Asymptotic Integrals, Hodge Structures, 1984 .

INVARIANT ESTIMATES OF TWO-DIMENSIONAL TRIGONOMETRIC INTEGRALS

V. S. Belonosov, V. Kostov, A. Varchenko, 2017 .

Derived KZ Equations

A. Varchenko, V. Schechtman, 2020, Journal of Singularities.

Vanishing Cycles and Cartan Eigenvectors

A. Varchenko, V. Schechtman, Laura Brillon, 2017, Arnold Mathematical Journal.

Vanishing Cycles and Cartan Eigenvectors

A. Varchenko, V. Schechtman, Laura Brillon, 2015, 1509.05591.

On the germs of analytic mappings whose topological type is determined by a finite jet

A. Varchenko, 1972 .

On the bifurcation of multiple integrals depending on a parameter

A. Varchenko, 1969 .

COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: On the number of integral points in a domain

A. Varchenko, 1982 .

Singularities of functions, wave fronts, caustics and multidimensional integrals

V. Arnold, A. Givental, A. Varchenko, 2012 .

Bethe eigenvectors of higher transfer matrices

A. Varchenko, V. Tarasov, E. Mukhin, 2006, math/0605015.

Bispectral and (gl_N, gl_M) Dualities, Discrete Versus Differential

A. Varchenko, V. Tarasov, E. Mukhin, 2006, math/0605172.

Identities between q -hypergeometric and hypergeometric integrals of different dimensions

A. Varchenko, V. Tarasov, 2003, math/0309372.

Small Elliptic Quantum Group $e_{tau,\gamma}(sl_N)$

A. Varchenko, V. Tarasov, 2000 .

2 3 A ug 2 00 4 SELBERG INTEGRALS

A. Varchenko, 2004 .

Q A ] 4 A pr 2 00 4 IDENTITIES BETWEEN q-HYPERGEOMETRIC AND HYPERGEOMETRIC INTEGRALS OF DIFFERENT

A. Varchenko, V. Tarasov, 2003 .

Small Elliptic Quantum Group eτ,γ(slN) V.Tarasov ⋆

A. Varchenko, 2000 .

A ] 2 0 N ov 2 00 0 Small Elliptic Quantum Group e τ , γ ( sl N )

A. Varchenko, V. Tarasov, 2022 .

Duality for Knizhnik-zamolodchikov and Dynamical Equations

A. Varchenko, V. Tarasov, 2022 .

Quasihomogeneous and semiquasihomogeneous singularities

V. Arnold, S. Gusein-Zade, A. Varchenko, 2012 .

Functional equations for a volume map

A. Varchenko, 1988 .

Solutions of the elliptic qKZB equations and Bethe ansatz I

G. Felder, A. Varchenko, V. Tarasov, 1996, q-alg/9606005.