Edit Profile (opens in new tab) Varchenko, Alexander Nikolaevich Co-Author Distance Author ID: varchenko.alexander-n Published as: Varchenko, A. N.; Varchenko, Alexander; Varchenko, A.; Varchenko, Alexander N.; Varchenko, Alexandre; Varchenko, Alexandre N. more...less External Links: MGP · Wikidata · Math-Net.Ru · GND · IdRef Documents Indexed: 272 Publications since 1969, including 11 Books 5 Contributions as Editor Co-Authors: 99 Co-Authors with 187 Joint Publications 3,154 Co-Co-Authors all top 5 Co-Authors 83 single-authored 54 Tarasov, Vitaly Olegovich 42 Mukhin, Evgeny 20 Felder, Giovanni 18 Rimányi, Richárd 18 Schechtman, Vadim 11 Arnol’d, Vladimir Igorevich 10 Etingof, Pavel Il’ich 10 Khovanskiĭ, Askold Georgievich 9 Gusein-Zade, Sabir M. 6 Givental, Alexander Borisovich 6 Vasil’ev, Viktor Anatol’evich 5 Chmutov, Sergei V. 4 Falk, Michael J. 3 Cohen, Daniel C. 3 Feĭgin, Boris L’vovich 3 Khesin, Boris A. 3 Scherbak, Inna 3 Slinkin, Alexey M. 3 Woodruff, Tyler 2 Beilinson, Alexander A. 2 Cotti, Giordano 2 Denham, Graham 2 Gel’fand, Israil’ Moiseevich 2 Goncharov, Alexander Borisovich 2 Karev, Maksim V. 2 Krasil’shchik, Joseph 2 Lando, Sergei K. 2 Lu, Kang 2 Mnëv, Nikolai Evgen’evich 2 Panina, Gaiane Yu. 2 Petersen, Karl E. 2 Smirnov, Andrey V. 2 Sosinskiĭ, Alekseĭ Bronislavovich 2 Tyurina, Svetlana 2 Vershik, Anatoliĭ Moiseevich 2 Viro, Oleg Ya. 2 Young, Charles A. S. 2 Zhou, Zijun 1 Abramov, Aleksandr Mikhailovich 1 Arinkin, Dima 1 Barlet, Daniel 1 Belkale, Prakash 1 Berry, Michael Victor 1 Blok, B. 1 Bolsinov, Alexey V. 1 Brillon, Laura 1 Bukhshtaber, Viktor Matveevich 1 Chekhov, Leonid O. 1 Dobrokhotov, Sergei Yurievich 1 Felder, D. Zh. 1 Felder, T. G. 1 Frenkel, Igor B. 1 Galgani, Luigi 1 Gorbounov, Vassily 1 Grinevich, Pëtr Georgievich 1 Grushevsky, S. M. 1 Hertling, Claus 1 Ilyashenko, Yulij Sergeevich 1 Jensen, Erik J. 1 Kirillov, Alexander A. jun. 1 Kozlov, Valeriĭ Vasil’evich 1 Krichever, Igor’ Moiseevich 1 Levin, Andrey M. 1 Marsden, Jerrold Eldon 1 Marshakov, Andrei V. 1 Mironov, Andreĭ Evgen’evich 1 Molchanov, Stanislav Alekseevich 1 Neĭshtadt, Anatoliĭ Iserovich 1 Nekrasov, Nikita Alexandrovich 1 Novikov, Sergeĭ Petrovich 1 Okun’kov, Andreĭ Yur’evich 1 Olshanetsky, Mikhail A. 1 Piterbarg, Vladimir Il’ich 1 Pogrebkov, Andrei K. 1 Porteous, Hugh L. 1 Prudhom, Andrew 1 Rains, Eric M. 1 Ramazashvili, Revaz 1 Reshekikhin, Nicolai 1 Schiffmann, Olivier G. 1 Sevryuk, Mikhail Borisovich 1 Sheĭnman, Oleg Karlovich 1 Shlosman, Senya B. 1 Skorobogatov, Alexei Nikolaïevitch 1 Smale, Steve 1 Sperber, Steven I. 1 Sun, Yi 1 Tabachnikov, Serge L. 1 Taimanov, Iskander Asanovich 1 Tapia, Joseph 1 Terao, Hiroaki 1 Tsfasman, Michael A. 1 Valisyev, N. 1 Vasil’ev, N. N. 1 Vassilev, Victor A. 1 Veselov, Alexander Petrovich 1 Yashchenko, Valery V. 1 Zabrodin, Anton V. 1 Zakalyukin, Vladimir M. 1 Zhilinskií, Boris I. ...and 1 more Co-Authors all top 5 Serials 16 Functional Analysis and its Applications 11 Communications in Mathematical Physics 10 Letters in Mathematical Physics 10 Advances in Mathematics 10 Moscow Mathematical Journal 9 IMRN. International Mathematics Research Notices 9 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 8 Soviet Mathematics. Doklady 7 Russian Mathematical Surveys 7 Mathematics of the USSR. Izvestiya 6 Funktsional’nyĭ Analiz i ego Prilozheniya 5 Journal of Geometry and Physics 5 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 5 Arnold Mathematical Journal 4 Mathematical Notes 4 Compositio Mathematica 4 Selecta Mathematica. New Series 4 Journal of Singularities 3 Moscow University Mathematics Bulletin 3 Inventiones Mathematicae 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Central European Journal of Mathematics 3 Pure and Applied Mathematics Quarterly 2 Matematicheskie Zametki 2 Uspekhi Matematicheskikh Nauk [N. S.] 2 Duke Mathematical Journal 2 Glasgow Mathematical Journal 2 Journal of Soviet Mathematics 2 International Journal of Mathematics 2 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 2 Journal of Knot Theory and its Ramifications 2 St. Petersburg Mathematical Journal 2 Transformation Groups 2 The Ramanujan Journal 2 Annals of Combinatorics 2 Communications in Contemporary Mathematics 2 IMRP. International Mathematics Research Papers 2 Monographs in Mathematics 2 Mathematics 2 Modern Birkhäuser Classics 2 Translations. Series 2. American Mathematical Society 1 International Journal of Modern Physics A 1 Houston Journal of Mathematics 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Nuclear Physics. B 1 Soviet Scientific Reviews. Section C 1 Bulletin des Sciences Mathématiques. Deuxième Série 1 Canadian Journal of Mathematics 1 Geometriae Dedicata 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Zeitschrift 1 Proceedings of the American Mathematical Society 1 Tokyo Journal of Mathematics 1 Topology 1 Transactions of the American Mathematical Society 1 Acta Applicandae Mathematicae 1 Journal of the American Mathematical Society 1 Algebra i Analiz 1 Leningrad Mathematical Journal 1 Mathematics of the USSR, Sbornik 1 Notices of the American Mathematical Society 1 Journal of Mathematical Sciences (New York) 1 Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya 1 Mathematical Research Letters 1 European Mathematical Society Newsletter 1 Mathematical Physics, Analysis and Geometry 1 Reviews in Mathematics and Mathematical Physics 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Annals of Mathematics. Second Series 1 Computational Methods and Function Theory 1 Journal of Statistical Mechanics: Theory and Experiment 1 Advanced Series in Mathematical Physics 1 Astérisque 1 Proceedings of the Steklov Institute of Mathematics 1 University Lecture Series 1 Functional Analysis and Other Mathematics 1 Journal of Physics A: Mathematical and Theoretical 1 Confluentes Mathematici 1 Quantum Topology 1 European Journal of Mathematics 1 Journal de l’École Polytechnique – Mathématiques 1 CBMS Regional Conference Series in Mathematics 1 Journal of Integrable Systems all top 5 Fields 119 Nonassociative rings and algebras (17-XX) 90 Several complex variables and analytic spaces (32-XX) 77 Quantum theory (81-XX) 66 Special functions (33-XX) 62 Algebraic geometry (14-XX) 50 Statistical mechanics, structure of matter (82-XX) 36 Global analysis, analysis on manifolds (58-XX) 21 Dynamical systems and ergodic theory (37-XX) 21 Difference and functional equations (39-XX) 17 Partial differential equations (35-XX) 15 Number theory (11-XX) 15 Ordinary differential equations (34-XX) 15 Convex and discrete geometry (52-XX) 15 Differential geometry (53-XX) 15 Manifolds and cell complexes (57-XX) 13 Algebraic topology (55-XX) 11 Combinatorics (05-XX) 11 Commutative algebra (13-XX) 10 History and biography (01-XX) 5 Geometry (51-XX) 4 Group theory and generalizations (20-XX) 3 General and overarching topics; collections (00-XX) 3 \(K\)-theory (19-XX) 3 Fluid mechanics (76-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Associative rings and algebras (16-XX) 2 Topological groups, Lie groups (22-XX) 2 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Optics, electromagnetic theory (78-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Potential theory (31-XX) 1 Integral transforms, operational calculus (44-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Relativity and gravitational theory (83-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 232 Publications have been cited 3,398 times in 1,973 Documents Cited by ▼ Year ▼ Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol’d. Reprint of the 1985 hardback edition. Zbl 1290.58001Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. 199 2012 Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi. Reprint of the 1988 hardback edition. Zbl 1297.32001Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. 153 2012 Arrangements of hyperplanes and Lie algebra homology. Zbl 0754.17024Shekhtman, V. V.; Varchenko, Alexander N. 144 1991 Singularities of differentiable maps. Volume I: The classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, ed. by V. I. Arnol’d. Zbl 0554.58001Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N. 96 1985 The complex exponent of a singularity does not change along strata mu=const. Zbl 0498.32010Varchenko, A. N. 83 1982 Newton polyhedra and estimation of oscillating integrals. Zbl 0351.32011Varchenko, A. N. 79 1977 Zeta-function of monodromy and Newton’s diagram. Zbl 0333.14007Varchenko, A. N. 72 1976 Multidimensional hypergeometric functions and representation theory of Lie algebras and quantum groups. Zbl 0951.33001Varchenko, A. 69 1995 Schubert calculus and representations of the general linear group. Zbl 1205.17026Mukhin, E.; Tarasov, V.; Varchenko, A. 61 2009 The elliptic gamma function and \(\text{SL}(3,\mathbb Z)\ltimes\mathbb Z^3\). Zbl 1038.11029Felder, Giovanni; Varchenko, Alexander 59 2000 Singularities of differentiable maps. Volume II: Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous. Zbl 0659.58002Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N. 58 1988 Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors. Zbl 0849.32025Schechtman, Vadim; Terao, Hiroaki; Varchenko, Alexander 58 1995 Geometry of \(q\)-hypergeometric functions, quantum affine algebras and elliptic quantum groups. Zbl 0938.17012Tarasov, V.; Varchenko, A. 44 1997 Geometry and classification of solutions of the classical dynamical Yang-Baxter equation. Zbl 0915.17018Etingof, Pavel; Varchenko, Alexander 44 1998 Estimate of the number of zeros of an Abelian integral depending on a parameter and limit cycles. Zbl 0578.58035Varchenko, A. N. 43 1984 Bethe eigenvectors of higher transfer matrices. Zbl 1456.82301Mukhin, E.; Tarasov, V.; Varchenko, A. 43 2006 Asymptotic Hodge structure in the vanishing cohomology. Zbl 0489.14003Varchenko, A. N. 42 1982 Why the boundary of a round drop becomes a curve of order four. Zbl 0768.76073Varchenko, A. N.; Etingof, P. I. 41 1992 Solutions of the quantum dynamical Yang-Baxter equation and dynamical quantum groups. Zbl 0957.17019Etingof, Pavel; Varchenko, Alexander 40 1998 Differential equations compatible with KZ equations. Zbl 0984.35134Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A. 39 2000 Critical points of master functions and flag varieties. Zbl 1050.17022Mukhin, E.; Varchenko, A. 38 2004 Quasiclassical asymptotics of solutions to the KZ equations. Zbl 0867.58065Reshekikhin, Nicolai; Varchenko, Alexander 36 1995 On representations of the elliptic quantum group \(E_ \tau,\eta(sl_ 2)\). Zbl 0870.17012Felder, Giovanni; Varchenko, Alexander 34 1996 Geometric \(q\)-hypergeometric functions as a bridge between Yangians and quantum affine algebras. Zbl 0877.33013Tarasov, V.; Varchenko, A. 33 1997 Exchange dynamical quantum groups. Zbl 0943.17010Etingof, P.; Varchenko, A. 33 1999 Bispectral and \((\mathfrak{gl}_N,\mathfrak{gl}_M)\) dualities, discrete versus differential. Zbl 1142.82005Mukhin, E.; Tarasov, V.; Varchenko, A. 32 2008 The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz. Zbl 1213.14101Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander 32 2009 Dynamical Weyl groups and applications. Zbl 1033.17010Etingof, P.; Varchenko, A. 32 2002 Special functions, KZ type equations, and representation theory. Zbl 1053.33001Varchenko, Alexander 32 2003 Duality for Knizhnik-Zamolodchikov and dynamical equations. Zbl 1013.17006Tarasov, V.; Varchenko, A. 31 2002 Asymptotic Hodge structure in vanishing cohomologies. Zbl 0476.14002Varchenko, A. N. 30 1981 Algebraic Bethe ansatz for the elliptic quantum group \(E_{\tau,\eta} (sl_2\)). Zbl 0925.17020Felder, Giovanni; Varchenko, Alexander 29 1996 Bethe algebra of homogeneous \(XXX\) Heisenberg model has simple spectrum. Zbl 1173.82006Mukhin, E.; Tarasov, V.; Varchenko, A. 28 2009 Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra. Zbl 1287.81063Gorbounov, V.; Rimányi, R.; Tarasov, V.; Varchenko, A. 28 2013 Trigonometric weight functions as \(K\)-theoretic stable envelope maps for the cotangent bundle of a flag variety. Zbl 1349.19002Rimányi, R.; Tarasov, V.; Varchenko, A. 27 2015 Difference equations compatible with trigonometric KZ differential equations. Zbl 0971.39009Tarasov, V.; Varchenko, A. 26 2000 Remarks on the Vassiliev knot invariants coming from \(sl_ 2\). Zbl 0876.57013Chmutov, S. V.; Varchenko, A. N. 26 1997 Hypergeometric solutions of Knizhnik-Zamolodchikov equations. Zbl 0719.35079Shekhtman, V. V.; Varchenko, A. N. 25 1990 Norm of a Bethe vector and the Hessian of the master function. Zbl 1072.82012Mukhin, Evgeny; Varchenko, Alexander 24 2005 On semicontinuity of the spectrum and an upper estimate for the number of singular points of a projective hypersurface. Zbl 0537.14003Varchenko, A. N. 24 1983 Critical points of the product of powers of linear functions and families of bases of singular vectors. Zbl 0842.17044Varchenko, A. 24 1995 Aomoto dilogarithms, mixed Hodge structures and motivic cohomology of pairs of triangles on the plane. Zbl 0737.14003Beilinson, A. A.; Goncharov, A. B.; Schechtman, V. V.; Varchenko, A. N. 23 1990 Bilinear form of real configuration of hyperplanes. Zbl 0777.52006Varchenko, Alexandre 23 1993 Integral representation of solutions of the elliptic Knizhnik-Zamolodchikov-Bernard equations. Zbl 0840.17020Felder, Giovanni; Varchenko, Alexander 22 1995 Number of lattice points in families of homothetic domains in \(R^ n\). Zbl 0522.10031Varchenko, A. N. 21 1983 Traces of intertwiners for quantum groups and difference equations. I. Zbl 1004.17006Etingof, Pavel; Varchenko, Alexander 20 2000 Combinatorial formulae for nested Bethe vectors. Zbl 1288.82024Tarasov, Vitaly; Varchenko, Alexander 19 2013 Solutions of the elliptic qKZB equations and Bethe ansatz. I. Zbl 0884.65127Felder, T. G.; Tarasov, V.; Varchenko, A. 19 1997 Partial flag varieties, stable envelopes, and weight functions. Zbl 1361.14030Rimányi, Richárd; Tarasov, Vitaly; Varchenko, Alexander 19 2015 The asymptotics of holomorphic forms determine a mixed Hodge structure. Zbl 0516.14007Varchenko, A. N. 18 1980 An estimate of the number of zeros of an Abelian integral depending on a parameter and limiting cycles. Zbl 0545.58038Varchenko, A. N. 18 1984 Elliptic and \(K\)-theoretic stable envelopes and Newton polytopes. Zbl 1452.55009Rimányi, R.; Tarasov, V.; Varchenko, A. 18 2019 Equivariant Chern-Schwartz-MacPherson classes in partial flag varieties: interpolation and formulae. Zbl 1391.14108Rimányi, Richárd; Varchenko, Alexander 18 2018 The Euler beta-function, the Vandermonde determinant, Legendre’s equation, and critical values of linear functions on a configuration of hyperplanes. I. Zbl 0709.33001Varchenko, A. N. 17 1990 Jackson integral representations for solutions of the quantized Knizhnik- Zamolodchikov equation. Zbl 0818.33012Varchenko, A. N.; Tarasov, V. O. 17 1994 Topological conformal field theories and the flat coordinates. Zbl 0802.53034Blok, B.; Varchenko, A. 17 1992 Multiple orthogonal polynomials and a counterexample to the Gaudin Bethe ansatz conjecture. Zbl 1127.82019Mukhin, E.; Varchenko, A. 17 2007 Three-dimensional mirror self-symmetry of the cotangent bundle of the full flag variety. Zbl 1451.53116Rimányi, Richárd; Smirnov, Andrey; Varchenko, Alexander; Zhou, Zijun 17 2019 KZ characteristic variety as the zero set of classical Calogero-Moser Hamiltonians. Zbl 1269.82018Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander 17 2012 A generalization of the Capelli identity. Zbl 1287.17026Mukhin, E.; Tarasov, V.; Varchenko, A. 16 2009 Quantum integrable model of an arrangement of hyperplanes. Zbl 1217.82026Varchenko, Alexander 16 2011 On algebraic equations satisfied by hypergeometric correlators in WZW models. I. Zbl 0835.17019Feigin, Boris; Schechtman, Vadim; Varchenko, Alexander 16 1994 Critical points of functions, \({\mathfrak {sl}}_2\) representations, and Fuchsian differential equations with only univalued solutions. Zbl 1039.34077Scherbak, I.; Varchenko, A. 16 2003 Gauss-Manin connection of isolated singular point and Bernstein polynomial. Zbl 0434.32008Varchenko, Alexandre N. 16 1980 Selberg-type integrals associated with \(\mathfrak{sl}_3\). Zbl 1055.33016Tarasov, V.; Varchenko, A. 15 2003 Quantized Knizhnik-Zamolodchikov equations, quantum Yang-Baxter equation, and difference equations for \(q\)-hypergeometric functions. Zbl 0807.17014Varchenko, Alexander 15 1994 Solutions to the \(XXX\) type Bethe ansatz equations and flag varieties. Zbl 1029.82008Mukhin, E.; Varchenko, A. 15 2003 Spaces of quasi-exponentials and representations of the Yangian \(Y(\mathfrak{gl}_N)\). Zbl 1365.17006Mukhin, E.; Tarasov, V.; Varchenko, A. 14 2014 Bispectral and \((\mathfrak{gl}_{N},\mathfrak{gl}_{M})\) dualities. Zbl 1156.82005Mukhin, Evgenii E.; Tarasov, Vitaly O.; Varchenko, Alexander N. 14 2006 Elliptic quantum groups and Ruijsenaars models. Zbl 0924.17011Felder, Giovanni; Varchenko, Alexander 14 1997 Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of \(\mathfrak{gl}_{N}\). Zbl 1219.82121Mukhin, E.; Tarasov, V.; Varchenko, A. 13 2011 Spaces of quasi-exponentials and representations of \(\mathfrak{gl}_N\). Zbl 1142.81011Mukhin, E.; Tarasov, V.; Varchenko, A. 13 2008 Remarks on critical points of phase functions and norms of Bethe vectors. Zbl 1040.17001Mukhin, Evgeny; Varchenko, Alexander 13 2000 Asymptotics of integrals over vanishing cycles and the Newton polyhedron. Zbl 0595.32012Varchenko, A. N.; Khovanskij, A. G. 13 1985 A lower bound for the codimension of the strata mu=const in terms of the mixed Hodge structure. Zbl 0511.32004Varchenko, A. N. 13 1982 Quasi-polynomials and the Bethe ansatz. Zbl 1138.82010Mukhin, E.; Varchenko, A. 12 2008 Miura opers and critical points of master functions. Zbl 1108.82011Mukhin, Evgeny; Varchenko, Alexander 12 2005 Monodromy of solutions of the elliptic quantum Knizhnik-Zamolodchikov-Bernard difference equations. Zbl 1038.32500Felder, G.; Tarasov, V.; Varchenko, A. 12 1999 Bethe algebra of Gaudin model, Calogero-Moser space, and Cherednik algebra. Zbl 1304.82021Mukhin, E.; Tarasov, V.; Varchenko, A. 12 2014 Three formulae for eigenfunctions of integrable Schrödinger operators. Zbl 0907.17004Felder, Giovanni; Varchenko, Alexander 12 1997 On algebraic equations satisfied by hypergeometric correlators in WZW models. II. Zbl 0842.17043Feigin, Boris; Schechtman, Vadim; Varchenko, Alexander 12 1995 On reality property of Wronski maps. Zbl 1181.81065Mukhin, E.; Tarasov, V.; Varchenko, A. 12 2009 Generating operator of \(XXX\) or Gaudin transfer matrices has quasi-exponential kernel. Zbl 1140.82015Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander 12 2007 Critical points and resonance of hyperplane arrangements. Zbl 1228.32028Cohen, D.; Denham, G.; Falk, M.; Varchenko, A. 12 2011 Traces of intertwiners for quantum groups and difference equations. Zbl 1018.17013Etingof, P.; Schiffmann, O.; Varchenko, A. 12 2002 Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety. Zbl 1294.82016Tarasov, Vitaly; Varchenko, Alexander 12 2014 Combinatorics and topology of the situation of affine hyperplanes in real space. Zbl 0615.52005Varchenko, A. N. 11 1987 The determinant formula for a matroid bilinear form. Zbl 0918.05038Brylawski, T.; Varchenko, A. 11 1997 The Euler beta-function, the Vandermonde determinant, the Legendre equation, and critical values of linear functions on a configuration of hyperplanes. I. Zbl 0695.33004Varchenko, A. N. 11 1989 On Heaviside functions of a hyperplane configuration. Zbl 0647.32013Varchenko, A. N.; Gel’fand, I. M. 11 1987 Extended Joseph polynomials, quantized conformal blocks, and a \(q\)-Selberg type integral. Zbl 1254.22013Rimányi, Richard; Tarasov, Vitaly O.; Varchenko, A.; Zinn-Justin, Paul 11 2012 Multidimensional hypergeometric functions in conformal field theory, algebraic \(K\)-theory, algebraic geometry. Zbl 0747.33002Varchenko, Alexandre 10 1991 Dynamical differential equations compatible with rational qKZ equations. Zbl 1064.32012Tarasov, V.; Varchenko, A. 10 2005 A lower bound for the codimension of the stratum mu=const in terms of the mixed Hodge structure. Zbl 0517.32004Varchenko, A. N. 10 1982 Singularities of differentiable mappings. Classification of critical points, caustics and wave fronts. (Osobennosti differentsiruemykh otobrazhenij. Klassifikatsiya kriticheskikh tochek, kaustik i volnovykh frontov). Zbl 0513.58001Arnol’d, V. I.; Varchenko, A. N.; Gusejn-Zade, S. M. 10 1982 Asymptotic solutions to the quantized Knizhnik-Zamolodchikov equation and Bethe vectors. Zbl 0883.17021Tarasov, V. O.; Varchenko, A. N. 10 1996 Elliptic Selberg integrals and conformal blocks. Zbl 1041.33003Felder, G.; Stevens, L.; Varchenko, A. 10 2003 Solutions of KZ differential equations modulo \(p\). Zbl 1416.81080Schechtman, Vadim; Varchenko, Alexander 10 2019 Projective geometry and \(K\)-theory. Zbl 0728.14008Beilinson, A. A.; Varchenko, A. N.; Goncharov, A. B.; Shekhtman, V. V. 9 1991 Completeness of Bethe vectors and difference equations with regular singular points. Zbl 0860.17022Tarasov, Vitaly; Varchenko, Alexander 9 1995 Three-dimensional mirror symmetry and elliptic stable envelopes. Zbl 1495.14058Rimányi, Richárd; Smirnov, Andrey; Zhou, Zijun; Varchenko, Alexander 8 2022 Determinant of \(\mathbb{F}_p\)-hypergeometric solutions under ample reduction. Zbl 1497.13019Varchenko, Alexander 1 2022 The \({{\mathbb{F}}}_p\)-Selberg integral. Zbl 1496.13008Rimányi, Richárd; Varchenko, Alexander 1 2022 Hypergeometric integrals modulo \(p\) and Hasse-Witt matrices. Zbl 1477.13016Slinkin, Alexey; Varchenko, Alexander 4 2021 An invariant subbundle of the KZ connection mod \(p\) and reducibility of \(\widehat{{\mathfrak{sl}_2}}\) Verma modules mod \(p\). Zbl 1490.81090Varchenko, A. 3 2021 The \(\mathbb{F}_p\)-Selberg integral of type \(A_n\). Zbl 1487.33018Rimányi, Richárd; Varchenko, Alexander 3 2021 Equivariant quantum differential equation, Stokes bases, and \(K\)-theory for a projective space. Zbl 1475.14111Tarasov, Vitaly; Varchenko, Alexander 3 2021 Equivariant quantum differential equation and \(qKZ\) equations for a projective space: Stokes bases as exceptional collections, Stokes matrices as Gram matrices, and B-Theorem. Zbl 1466.14060Cotti, Giordano; Varchenko, Alexander 3 2021 Incarnations of XXX \(\widehat{\mathfrak{sl}_N}\) Bethe ansatz equations and integrable hierarchies. Zbl 1503.17028Krichever, Igor; Varchenko, Alexander 1 2021 Hyperelliptic integrals modulo \(p\) and Cartier-Manin matrices. Zbl 1456.14036Varchenko, Alexander 8 2020 Elliptic and \(K\)-theoretic stable envelopes and Newton polytopes. Zbl 1452.55009Rimányi, R.; Tarasov, V.; Varchenko, A. 18 2019 Three-dimensional mirror self-symmetry of the cotangent bundle of the full flag variety. Zbl 1451.53116Rimányi, Richárd; Smirnov, Andrey; Varchenko, Alexander; Zhou, Zijun 17 2019 Solutions of KZ differential equations modulo \(p\). Zbl 1416.81080Schechtman, Vadim; Varchenko, Alexander 10 2019 Twisted de Rham complex on line and singular vectors in \(\widehat{\mathfrak{sl}_2}\) Verma modules. Zbl 1460.17029Slinkin, Alexey; Varchenko, Alexander 3 2019 \(q\)-hypergeometric solutions of quantum differential equations, quantum Pieri rules, and Gamma theorem. Zbl 1419.82020Tarasov, Vitaly; Varchenko, Alexander 2 2019 Potentials of a family of arrangements of hyperplanes and elementary subarrangements. Zbl 1425.32025Prudhom, Andrew; Varchenko, Alexander 2 2019 Cyclotomic discriminantal arrangements and diagram automorphisms of Lie algebras. Zbl 1476.17013Varchenko, Alexander; Young, Charles 1 2019 Equivariant Chern-Schwartz-MacPherson classes in partial flag varieties: interpolation and formulae. Zbl 1391.14108Rimányi, Richárd; Varchenko, Alexander 18 2018 Elliptic dynamical quantum groups and equivariant elliptic cohomology. Zbl 1423.17015Felder, Giovanni; Rimányi, Richárd; Varchenko, Alexander 8 2018 Remarks on the Gaudin model modulo \(p\). Zbl 1405.17019Varchenko, Alexander 7 2018 Potentials of a Frobenius-like structure. Zbl 1391.05073Hertling, Claus; Varchenko, Alexander 3 2018 Solutions modulo \(p\) of Gauss-Manin differential equations for multidimensional hypergeometric integrals and associated Bethe ansatz. Zbl 1406.33013Varchenko, Alexander 8 2017 Self-dual Grassmannian, Wronski map, and representations of \(\mathfrak{gl}_N\), \(\mathfrak{sp}_{2r}\), \(\mathfrak{so}_{2r+1}\). Zbl 1437.17002Lu, Kang; Mukhin, E.; Varchenko, A. 5 2017 Rational differential forms on the line and singular vectors in Verma modules over \(\widehat{\mathfrak {sl}}_2\). Zbl 1460.17028Schechtman, Vadim; Varchenko, Alexander 2 2017 On the Gaudin model associated to Lie algebras of classical types. Zbl 1353.82024Lu, Kang; Mukhin, E.; Varchenko, A. 3 2016 Dynamical Gelfand-Zetlin algebra and equivariant cohomology of Grassmannians. Zbl 1380.81167Rimanyi, R.; Varchenko, A. 3 2016 On axioms of Frobenius like structure in the theory of arrangements. Zbl 1400.37087Varchenko, Alexander 2 2016 Trigonometric weight functions as \(K\)-theoretic stable envelope maps for the cotangent bundle of a flag variety. Zbl 1349.19002Rimányi, R.; Tarasov, V.; Varchenko, A. 27 2015 Partial flag varieties, stable envelopes, and weight functions. Zbl 1361.14030Rimányi, Richárd; Tarasov, Vitaly; Varchenko, Alexander 19 2015 Arrangements and Frobenius like structures. Zbl 1349.53114Varchenko, Alexander 5 2015 Critical set of the master function and characteristic variety of the associated Gauss-Manin differential equations. 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Zbl 1354.01038Arnold, Vladimir I. 6 2014 On the number of populations of critical points of master functions. Zbl 1382.17015Mukhin, Evgeny; Varchenko, Alexander 4 2014 Cohomology classes of conormal bundles of Schubert varieties and Yangian weight functions. Zbl 1328.14082Rimányi, R.; Tarasov, V.; Varchenko, A. 4 2014 Critical points of master functions and the mKdV hierarchy of type \(A_2^{(2)}\). Zbl 1332.82026Varchenko, A.; Woodruff, T.; Wright, D. 3 2014 BGG resolutions via configuration spaces. (Résolutions BGG via les espaces de configurations.) Zbl 1323.55013Falk, Michael; Schechtman, Vadim; Varchenko, Alexander 2 2014 Characteristic variety of the Gauss-Manin differential equations of a generic parallelly translated arrangement. Zbl 1311.58003Varchenko, Alexander 1 2014 Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra. Zbl 1287.81063Gorbounov, V.; Rimányi, R.; Tarasov, V.; Varchenko, A. 28 2013 Combinatorial formulae for nested Bethe vectors. Zbl 1288.82024Tarasov, Vitaly; Varchenko, Alexander 19 2013 Bethe subalgebras of the group algebra of the symmetric group. Zbl 1276.82014Mukhin, E.; Tarasov, V.; Varchenko, A. 8 2013 Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol’d. Reprint of the 1985 hardback edition. Zbl 1290.58001Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. 199 2012 Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi. Reprint of the 1988 hardback edition. Zbl 1297.32001Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. 153 2012 KZ characteristic variety as the zero set of classical Calogero-Moser Hamiltonians. 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Marsden, Alexander N. Varchenko, Victor A. Vissilev, Oleg Ya. Viro and Vladimir M. Zakalyukin. Zbl 1187.01033Arnold, Vladimir I. 2 2010 Schubert calculus and representations of the general linear group. Zbl 1205.17026Mukhin, E.; Tarasov, V.; Varchenko, A. 61 2009 The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz. Zbl 1213.14101Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander 32 2009 Bethe algebra of homogeneous \(XXX\) Heisenberg model has simple spectrum. Zbl 1173.82006Mukhin, E.; Tarasov, V.; Varchenko, A. 28 2009 A generalization of the Capelli identity. Zbl 1287.17026Mukhin, E.; Tarasov, V.; Varchenko, A. 16 2009 On reality property of Wronski maps. Zbl 1181.81065Mukhin, E.; Tarasov, V.; Varchenko, A. 12 2009 On separation of variables and completeness of the Bethe ansatz for quantum \(\mathfrak{gl}_N\) Gaudin model. Zbl 1158.81336Mukhin, E.; Tarasov, V.; Varchenko, A. 4 2009 Nikolai Nikolaevich Nekhoroshev (obituary). Zbl 1175.01064Abramov, A. M.; Arnol’d, V. I.; Bolsinov, A. V.; Varchenko, A. N.; Galgani, L.; Zhilinskii, B. I.; Il’yashenko, Yu. S.; Kozlov, Valerii V.; Neishtadt, Anatolii I.; Piterbarg, Vladimir I.; Khovanskii, Askold G.; Yashchenko, Valerii V. 1 2009 Bispectral and \((\mathfrak{gl}_N,\mathfrak{gl}_M)\) dualities, discrete versus differential. Zbl 1142.82005Mukhin, E.; Tarasov, V.; Varchenko, A. 32 2008 Spaces of quasi-exponentials and representations of \(\mathfrak{gl}_N\). Zbl 1142.81011Mukhin, E.; Tarasov, V.; Varchenko, A. 13 2008 Quasi-polynomials and the Bethe ansatz. Zbl 1138.82010Mukhin, E.; Varchenko, A. 12 2008 Bethe algebra and the algebra of functions on the space of differential operators of order two with polynomial kernel. Zbl 1171.82008Mukhin, E.; Tarasov, V.; Varchenko, A. 1 2008 Multiple orthogonal polynomials and a counterexample to the Gaudin Bethe ansatz conjecture. 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Zbl 1356.14042Belkale, Prakash; Mukhin, Evgeny; Varchenko, Alexander 1 2007 Bethe eigenvectors of higher transfer matrices. Zbl 1456.82301Mukhin, E.; Tarasov, V.; Varchenko, A. 43 2006 Bispectral and \((\mathfrak{gl}_{N},\mathfrak{gl}_{M})\) dualities. Zbl 1156.82005Mukhin, Evgenii E.; Tarasov, Vitaly O.; Varchenko, Alexander N. 14 2006 Bethe ansatz for arrangements of hyperplanes and the Gaudin model. Zbl 1375.32050Varchenko, Alexander 9 2006 Quiver \(D\)-modules and homology of local systems over an arrangement of hyperplanes. Zbl 1116.32005Khoroshkin, S.; Varchenko, A. 7 2006 Differential equations for Jacobi-Piñeiro polynomials. Zbl 1133.34046Mukhin, Eugene; Varchenko, Alexander 1 2006 Norm of a Bethe vector and the Hessian of the master function. Zbl 1072.82012Mukhin, Evgeny; Varchenko, Alexander 24 2005 Miura opers and critical points of master functions. Zbl 1108.82011Mukhin, Evgeny; Varchenko, Alexander 12 2005 Dynamical differential equations compatible with rational qKZ equations. Zbl 1064.32012Tarasov, V.; Varchenko, A. 10 2005 Discrete Miura opers and solutions of the Bethe ansatz equations. Zbl 1127.82020Mukhin, Evgeny; Varchenko, Alexander 8 2005 Populations of solutions of the \(XXX\) Bethe equations associated to Kac-Moody algebras. Zbl 1173.82316Mukhin, E.; Varchenko, A. 7 2005 Combinatorics of rational functions and Poincaré- Birchoff-Witt expansions of the canonical \(U ({\mathfrak n}\_)\)-valued differential form. Zbl 1088.33007Rimányi, R.; Stevens, L.; Varchenko, A. 6 2005 Orthogonality and the qKZB-heat equation for traces of \(U_q({\mathfrak g})\)-intertwiners. Zbl 1160.17305Etingof, P.; Varchenko, A. 5 2005 Multiplication formulae for the elliptic gamma function. Zbl 1195.33233Felder, Giovanni; Varchenko, Alexander 5 2005 Identities between \(q\)-hypergeometric and hypergeometric integrals of different dimensions. Zbl 1113.33015Tarasov, V.; Varchenko, A. 3 2005 Even powers of divisors and elliptic zeta values. Zbl 1117.11046Felder, Giovanni; Varchenko, Alexander 2 2005 Identities for hypergeometric integrals of different dimensions. Zbl 1088.33009Tarasov, V.; Varchenko, A. 1 2005 ...and 132 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,920 Authors 96 Varchenko, Alexander Nikolaevich 40 Tarasov, Vitaly Olegovich 34 Mukhin, Evgeny 20 Rimányi, Richárd 19 Saito, Morihiko 18 Greenblatt, Michael 17 Dimca, Alexandru 17 Felder, Giovanni 16 Schechtman, Vadim 15 Etingof, Pavel Il’ich 14 Denham, Graham 13 Feĭgin, Boris L’vovich 13 Pakuliak, Stanislav Z. 13 Reshetikhin, Nikolai Yu. 12 Gusein-Zade, Sabir M. 12 Zotov, Andrei V. 11 Khoroshkin, Sergey M. 11 Morozov, Alexei Yurievich 11 Ragoucy, Eric 11 Smirnov, Andrey V. 10 Mimachi, Katsuhisa 10 Mudrov, Andrey I. 10 Spiridonov, Vyacheslav Pavlovich 10 Stokman, Jasper V. 10 Vicedo, Benoît 9 Cohen, Daniel C. 9 Frenkel, Edward V. 9 Janeczko, Stanisław 9 Mironov, Andrei D. 9 Movasati, Hossein 9 Novikov, Dmitry 9 Vasil’ev, Viktor Anatol’evich 9 Weber, Andrzej 9 Zabrodin, Anton V. 8 Gustafsson, Bjorn 8 Han, Maoan 8 Koroteev, Peter 8 Manojlović, Nenad 8 Skrypnyk, Taras Volodymyrovych 8 Terao, Hiroaki 8 Yakovenko, Sergei 7 Aomoto, Kazuhiko 7 Awata, Hidetoshi 7 Ebeling, Wolfgang 7 Hertling, Claus 7 Ikromov, Isroil A. 7 Izumiya, Shyuichi 7 Loeser, François 7 Milanov, Todor E. 7 Némethi, András 7 Orlik, Peter 7 Rybnikov, Leonid Grigor’evich 7 Steenbrink, Joseph H. 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