Edit Profile (opens in new tab) Varchenko, Alexander Nikolaevich Co-Author Distance Author ID: varchenko.alexander-n Published as: Varchenko, Alexander; Varchenko, A. N.; Varchenko, A.; Varchenko, Alexander N.; Varchenko, Alexandre; Varchenko, Alexandre N. more...less External Links: MGP · Wikidata · Math-Net.Ru · GND · IdRef Documents Indexed: 293 Publications since 1969, including 11 Books and 13 Additional arXiv Preprints 5 Contributions as Editor · 1 Further Contribution Co-Authors: 103 Co-Authors with 205 Joint Publications 3,581 Co-Co-Authors all top 5 Co-Authors 86 single-authored 56 Tarasov, Vitaly Olegovich 44 Mukhin, Evgeny 22 Felder, Giovanni 19 Schechtman, Vadim 18 Rimányi, Richárd 13 Etingof, Pavel Il’ich 11 Arnol’d, Vladimir Igorevich 10 Khovanskiĭ, Askold Georgievich 9 Gusein-Zade, Sabir M. 6 Givental, Alexander Borisovich 6 Vasil’ev, Viktor Anatol’evich 5 Chmutov, Sergei V. 5 Smirnov, Andrey V. 4 Falk, Michael J. 4 Stevens, Laura 3 Cohen, Daniel C. 3 Cotti, Giordano 3 Feĭgin, Boris L’vovich 3 Khesin, Boris A. 3 Scherbak, Inna 3 Slinkin, Alexey M. 3 Woodruff, Tyler 2 Beilinson, Alexander A. 2 Denham, Graham 2 Gel’fand, Israil’ Moiseevich 2 Goncharov, Alexander Borisovich 2 Grushevsky, Samuel 2 Hertling, Claus 2 Karev, Maksim V. 2 Krasil’shchik, Joseph 2 Lando, Sergei K. 2 Lu, Kang 2 Mnëv, Nikolai Evgen’evich 2 Nekrasov, Nikita Alexandrovich 2 Novikov, Sergeĭ Petrovich 2 Okun’kov, Andreĭ Yur’evich 2 Panina, Gaiane Yu. 2 Petersen, Karl E. 2 Sosinskiĭ, Alekseĭ Bronislavovich 2 Tyurina, Svetlana 2 Vershik, Anatoliĭ Moiseevich 2 Veselov, Alexander Petrovich 2 Viro, Oleg Ya. 2 Vologodsky, Vadim 2 Young, Charles A. S. 2 Zabrodin, Anton V. 2 Zhou, Zijun 2 Zudilin, Wadim 1 Abramov, Aleksandr Mikhailovich 1 Arbarello, Enrico 1 Arinkin, Dima 1 Barlet, Daniel 1 Belkale, Prakash 1 Berry, Michael 1 Blok, B. 1 Bolsinov, Alexey V. 1 Braverman, Alexander 1 Brazovski, Serguei 1 Brillon, Laura 1 Bukhshtaber, Viktor Matveevich 1 Chekhov, Leonid O. 1 Dobrokhotov, Sergei Yurievich 1 Drinfeld, Vladimir Gershonovich 1 Dzhamay, Anton 1 Felder, D. Zh. 1 Felder, T. G. 1 Frenkel, Igor B. 1 Galgani, Luigi 1 Gorbounov, Vassily 1 Gorskiĭ, Aleksandr Sergeevich 1 Grinevich, Pëtr Georgievich 1 Il’yashenko, Yuliĭ 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 Olshanetsky, Mikhail A. 1 Phong, Duong Hong 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, Stephen 1 Smoliarova, Tatiana 1 Sperber, Steven I. 1 Sun, Yi ...and 14 more Co-Authors all top 5 Serials 16 Functional Analysis and its Applications 11 Communications in Mathematical Physics 11 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 6 Arnold Mathematical Journal 5 Journal of Geometry and Physics 5 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 5 Selecta Mathematica. New Series 4 Mathematical Notes 4 Compositio Mathematica 4 Pure and Applied Mathematics Quarterly 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 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 Notices of the American Mathematical Society 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 the London Mathematical Society. Second Series 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 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 Journal of the Australian Mathematical Society 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 Research in the Mathematical Sciences 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) 96 Several complex variables and analytic spaces (32-XX) 79 Quantum theory (81-XX) 74 Special functions (33-XX) 67 Algebraic geometry (14-XX) 50 Statistical mechanics, structure of matter (82-XX) 37 Global analysis, analysis on manifolds (58-XX) 23 Dynamical systems and ergodic theory (37-XX) 22 Difference and functional equations (39-XX) 19 Number theory (11-XX) 17 Partial differential equations (35-XX) 16 Ordinary differential equations (34-XX) 16 Convex and discrete geometry (52-XX) 16 Differential geometry (53-XX) 15 Manifolds and cell complexes (57-XX) 13 Algebraic topology (55-XX) 11 History and biography (01-XX) 11 Combinatorics (05-XX) 11 Commutative algebra (13-XX) 5 Geometry (51-XX) 4 Group theory and generalizations (20-XX) 3 General and overarching topics; collections (00-XX) 3 Field theory and polynomials (12-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 Category theory; homological algebra (18-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 245 Publications have been cited 4,193 times in 2,517 Documents Cited by ▼ Year ▼ 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 0554.58001 Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N. 313 1985 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 1290.58001 Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. 218 2012 Arrangements of hyperplanes and Lie algebra homology. Zbl 0754.17024 Shekhtman, V. V.; Varchenko, Alexander N. 162 1991 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 1297.32001 Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. 160 2012 Singularities of differentiable maps. Volume II: Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous. Zbl 0659.58002 Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N. 147 1988 Newton polyhedra and estimation of oscillating integrals. Zbl 0351.32011 Varchenko, A. N. 103 1977 The complex exponent of a singularity does not change along strata mu=const. Zbl 0498.32010 Varchenko, A. N. 88 1982 Zeta-function of monodromy and Newton’s diagram. Zbl 0333.14007 Varchenko, A. N. 86 1976 Multidimensional hypergeometric functions and representation theory of Lie algebras and quantum groups. Zbl 0951.33001 Varchenko, A. 74 1995 Schubert calculus and representations of the general linear group. Zbl 1205.17026 Mukhin, E.; Tarasov, V.; Varchenko, A. 69 2009 The elliptic gamma function and \(\text{SL}(3,\mathbb Z)\ltimes\mathbb Z^3\). Zbl 1038.11029 Felder, Giovanni; Varchenko, Alexander 67 2000 Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors. Zbl 0849.32025 Schechtman, Vadim; Terao, Hiroaki; Varchenko, Alexander 59 1995 Geometry and classification of solutions of the classical dynamical Yang-Baxter equation. Zbl 0915.17018 Etingof, Pavel; Varchenko, Alexander 49 1998 Geometry of \(q\)-hypergeometric functions, quantum affine algebras and elliptic quantum groups. Zbl 0938.17012 Tarasov, V.; Varchenko, A. 49 1997 Algebraic Bethe ansatz for the elliptic quantum group \(E_{\tau,\eta} (sl_2\)). Zbl 0925.17020 Felder, Giovanni; Varchenko, Alexander 47 1996 Bethe eigenvectors of higher transfer matrices. Zbl 1456.82301 Mukhin, E.; Tarasov, V.; Varchenko, A. 47 2006 Differential equations compatible with KZ equations. Zbl 0984.35134 Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A. 45 2000 On representations of the elliptic quantum group \(E_ \tau,\eta(sl_ 2)\). Zbl 0870.17012 Felder, Giovanni; Varchenko, Alexander 45 1996 Estimate of the number of zeros of an Abelian integral depending on a parameter and limit cycles. Zbl 0578.58035 Varchenko, A. N. 44 1984 Why the boundary of a round drop becomes a curve of order four. Zbl 0768.76073 Varchenko, A. N.; Etingof, P. I. 43 1992 Solutions of the quantum dynamical Yang-Baxter equation and dynamical quantum groups. Zbl 0957.17019 Etingof, Pavel; Varchenko, Alexander 43 1998 Asymptotic Hodge structure in the vanishing cohomology. Zbl 0489.14003 Varchenko, A. N. 43 1982 Quasiclassical asymptotics of solutions to the KZ equations. Zbl 0867.58065 Reshekikhin, Nicolai; Varchenko, Alexander 42 1995 Critical points of master functions and flag varieties. Zbl 1050.17022 Mukhin, E.; Varchenko, A. 41 2004 Geometric \(q\)-hypergeometric functions as a bridge between Yangians and quantum affine algebras. Zbl 0877.33013 Tarasov, V.; Varchenko, A. 38 1997 Duality for Knizhnik-Zamolodchikov and dynamical equations. Zbl 1013.17006 Tarasov, V.; Varchenko, A. 36 2002 Dynamical Weyl groups and applications. Zbl 1033.17010 Etingof, P.; Varchenko, A. 36 2002 Bethe algebra of homogeneous \(XXX\) Heisenberg model has simple spectrum. Zbl 1173.82006 Mukhin, E.; Tarasov, V.; Varchenko, A. 36 2009 Bispectral and \((\mathfrak{gl}_N,\mathfrak{gl}_M)\) dualities, discrete versus differential. Zbl 1142.82005 Mukhin, E.; Tarasov, V.; Varchenko, A. 36 2008 Special functions, KZ type equations, and representation theory. Zbl 1053.33001 Varchenko, Alexander 36 2003 Exchange dynamical quantum groups. Zbl 0943.17010 Etingof, P.; Varchenko, A. 36 1999 The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz. Zbl 1213.14101 Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander 35 2009 Asymptotic Hodge structure in vanishing cohomologies. Zbl 0476.14002 Varchenko, A. N. 33 1981 Trigonometric weight functions as \(K\)-theoretic stable envelope maps for the cotangent bundle of a flag variety. Zbl 1349.19002 Rimányi, R.; Tarasov, V.; Varchenko, A. 32 2015 Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra. Zbl 1287.81063 Gorbounov, V.; Rimányi, R.; Tarasov, V.; Varchenko, A. 32 2013 Remarks on the Vassiliev knot invariants coming from \(sl_ 2\). Zbl 0876.57013 Chmutov, S. V.; Varchenko, A. N. 31 1997 Critical points of the product of powers of linear functions and families of bases of singular vectors. Zbl 0842.17044 Varchenko, A. 30 1995 Hypergeometric solutions of Knizhnik-Zamolodchikov equations. Zbl 0719.35079 Shekhtman, V. V.; Varchenko, A. N. 29 1990 Singularities of differentiable mappings. Classification of critical points, caustics and wave fronts. (Osobennosti differentsiruemykh otobrazhenij. Klassifikatsiya kriticheskikh tochek, kaustik i volnovykh frontov). Zbl 0513.58001 Arnol’d, V. I.; Varchenko, A. N.; Gusejn-Zade, S. M. 28 1982 Integral representation of solutions of the elliptic Knizhnik-Zamolodchikov-Bernard equations. Zbl 0840.17020 Felder, Giovanni; Varchenko, Alexander 28 1995 Difference equations compatible with trigonometric KZ differential equations. Zbl 0971.39009 Tarasov, V.; Varchenko, A. 27 2000 On semicontinuity of the spectrum and an upper estimate for the number of singular points of a projective hypersurface. Zbl 0537.14003 Varchenko, A. N. 26 1983 Bilinear form of real configuration of hyperplanes. Zbl 0777.52006 Varchenko, Alexandre 26 1993 Topological conformal field theories and the flat coordinates. Zbl 0802.53034 Blok, B.; Varchenko, A. 25 1992 Norm of a Bethe vector and the Hessian of the master function. Zbl 1072.82012 Mukhin, Evgeny; Varchenko, Alexander 25 2005 Three-dimensional mirror self-symmetry of the cotangent bundle of the full flag variety. Zbl 1451.53116 Rimányi, Richárd; Smirnov, Andrey; Varchenko, Alexander; Zhou, Zijun 25 2019 Aomoto dilogarithms, mixed Hodge structures and motivic cohomology of pairs of triangles on the plane. Zbl 0737.14003 Beilinson, A. A.; Goncharov, A. B.; Schechtman, V. V.; Varchenko, A. N. 24 1990 Equivariant Chern-Schwartz-MacPherson classes in partial flag varieties: interpolation and formulae. Zbl 1391.14108 Rimányi, Richárd; Varchenko, Alexander 23 2018 Elliptic and \(K\)-theoretic stable envelopes and Newton polytopes. Zbl 1452.55009 Rimányi, R.; Tarasov, V.; Varchenko, A. 22 2019 Partial flag varieties, stable envelopes, and weight functions. Zbl 1361.14030 Rimányi, Richárd; Tarasov, Vitaly; Varchenko, Alexander 22 2015 Jackson integral representations for solutions of the quantized Knizhnik- Zamolodchikov equation. Zbl 0818.33012 Varchenko, A. N.; Tarasov, V. O. 21 1994 Number of lattice points in families of homothetic domains in \(R^ n\). Zbl 0522.10031 Varchenko, A. N. 21 1983 KZ characteristic variety as the zero set of classical Calogero-Moser Hamiltonians. Zbl 1269.82018 Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander 21 2012 Traces of intertwiners for quantum groups and difference equations. I. Zbl 1004.17006 Etingof, Pavel; Varchenko, Alexander 21 2000 Solutions of the elliptic qKZB equations and Bethe ansatz. I. Zbl 0884.65127 Felder, T. G.; Tarasov, V.; Varchenko, A. 20 1997 The asymptotics of holomorphic forms determine a mixed Hodge structure. Zbl 0516.14007 Varchenko, A. N. 19 1980 Multiple orthogonal polynomials and a counterexample to the Gaudin Bethe ansatz conjecture. Zbl 1127.82019 Mukhin, E.; Varchenko, A. 19 2007 Combinatorial formulae for nested Bethe vectors. Zbl 1288.82024 Tarasov, Vitaly; Varchenko, Alexander 19 2013 Critical points of functions, \({\mathfrak {sl}}_2\) representations, and Fuchsian differential equations with only univalued solutions. Zbl 1039.34077 Scherbak, I.; Varchenko, A. 18 2003 Quantized Knizhnik-Zamolodchikov equations, quantum Yang-Baxter equation, and difference equations for \(q\)-hypergeometric functions. Zbl 0807.17014 Varchenko, Alexander 18 1994 On algebraic equations satisfied by hypergeometric correlators in WZW models. I. Zbl 0835.17019 Feigin, Boris; Schechtman, Vadim; Varchenko, Alexander 18 1994 Elliptic quantum groups and Ruijsenaars models. Zbl 0924.17011 Felder, Giovanni; Varchenko, Alexander 18 1997 An estimate of the number of zeros of an Abelian integral depending on a parameter and limiting cycles. Zbl 0545.58038 Varchenko, A. N. 18 1984 Spaces of quasi-exponentials and representations of the Yangian \(Y(\mathfrak{gl}_N)\). Zbl 1365.17006 Mukhin, E.; Tarasov, V.; Varchenko, A. 18 2014 Gauss-Manin connection of isolated singular point and Bernstein polynomial. Zbl 0434.32008 Varchenko, Alexandre N. 18 1980 Bispectral and \((\mathfrak{gl}_{N},\mathfrak{gl}_{M})\) dualities. Zbl 1156.82005 Mukhin, Evgenii E.; Tarasov, Vitaly O.; Varchenko, Alexander N. 17 2006 Quantum integrable model of an arrangement of hyperplanes. Zbl 1217.82026 Varchenko, Alexander 17 2011 Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of \(\mathfrak{gl}_{N}\). Zbl 1219.82121 Mukhin, E.; Tarasov, V.; Varchenko, A. 17 2011 The Euler beta-function, the Vandermonde determinant, Legendre’s equation, and critical values of linear functions on a configuration of hyperplanes. I. Zbl 0709.33001 Varchenko, A. N. 17 1990 Selberg-type integrals associated with \(\mathfrak{sl}_3\). Zbl 1055.33016 Tarasov, V.; Varchenko, A. 16 2003 A generalization of the Capelli identity. Zbl 1287.17026 Mukhin, E.; Tarasov, V.; Varchenko, A. 16 2009 Solutions to the \(XXX\) type Bethe ansatz equations and flag varieties. Zbl 1029.82008 Mukhin, E.; Varchenko, A. 16 2003 Quasi-polynomials and the Bethe ansatz. Zbl 1138.82010 Mukhin, E.; Varchenko, A. 15 2008 A lower bound for the codimension of the strata mu=const in terms of the mixed Hodge structure. Zbl 0511.32004 Varchenko, A. N. 15 1982 Critical points and resonance of hyperplane arrangements. Zbl 1228.32028 Cohen, D.; Denham, G.; Falk, M.; Varchenko, A. 15 2011 Solutions of KZ differential equations modulo \(p\). Zbl 1416.81080 Schechtman, Vadim; Varchenko, Alexander 15 2019 Discrete Miura opers and solutions of the Bethe ansatz equations. Zbl 1127.82020 Mukhin, Evgeny; Varchenko, Alexander 15 2005 Three-dimensional mirror symmetry and elliptic stable envelopes. Zbl 1495.14058 Rimányi, Richárd; Smirnov, Andrey; Zhou, Zijun; Varchenko, Alexander 15 2022 Miura opers and critical points of master functions. Zbl 1108.82011 Mukhin, Evgeny; Varchenko, Alexander 14 2005 Three formulae for eigenfunctions of integrable Schrödinger operators. Zbl 0907.17004 Felder, Giovanni; Varchenko, Alexander 14 1997 Quantum groups and homology of local systems. Zbl 0760.17014 Shekhtman, Vadim V.; Varchenko, Alexander N. 14 1991 On algebraic equations satisfied by hypergeometric correlators in WZW models. II. Zbl 0842.17043 Feigin, Boris; Schechtman, Vadim; Varchenko, Alexander 14 1995 Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety. Zbl 1294.82016 Tarasov, Vitaly; Varchenko, Alexander 14 2014 Singularities of differentiable mappings. Monodromy and asymptotics of integrals. (Osobennosti differentsiruemykh otobrazhenij. Monodromiya i asimptotiki integralov). Zbl 0545.58001 Arnol’d, V. I.; Varchenko, A. N.; Gusejn-Zade, S. M. 14 1984 Asymptotics of integrals over vanishing cycles and the Newton polyhedron. Zbl 0595.32012 Varchenko, A. N.; Khovanskij, A. G. 14 1985 Remarks on critical points of phase functions and norms of Bethe vectors. Zbl 1040.17001 Mukhin, Evgeny; Varchenko, Alexander 13 2000 Monodromy of solutions of the elliptic quantum Knizhnik-Zamolodchikov-Bernard difference equations. Zbl 1038.32500 Felder, G.; Tarasov, V.; Varchenko, A. 13 1999 Traces of intertwiners for quantum groups and difference equations. Zbl 1018.17013 Etingof, P.; Schiffmann, O.; Varchenko, A. 13 2002 The determinant formula for a matroid bilinear form. Zbl 0918.05038 Brylawski, T.; Varchenko, A. 13 1997 On Heaviside functions of a hyperplane configuration. Zbl 0647.32013 Varchenko, A. N.; Gel’fand, I. M. 13 1987 Spaces of quasi-exponentials and representations of \(\mathfrak{gl}_N\). Zbl 1142.81011 Mukhin, E.; Tarasov, V.; Varchenko, A. 13 2008 Bethe algebra of Gaudin model, Calogero-Moser space, and Cherednik algebra. Zbl 1304.82021 Mukhin, E.; Tarasov, V.; Varchenko, A. 13 2014 Elliptic dynamical quantum groups and equivariant elliptic cohomology. Zbl 1423.17015 Felder, Giovanni; Rimányi, Richárd; Varchenko, Alexander 13 2018 Combinatorics and topology of the situation of affine hyperplanes in real space. Zbl 0615.52005 Varchenko, A. N. 12 1987 Generating operator of \(XXX\) or Gaudin transfer matrices has quasi-exponential kernel. Zbl 1140.82015 Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander 12 2007 On reality property of Wronski maps. Zbl 1181.81065 Mukhin, E.; Tarasov, V.; Varchenko, A. 12 2009 Dynamical differential equations compatible with rational qKZ equations. Zbl 1064.32012 Tarasov, V.; Varchenko, A. 11 2005 Extended Joseph polynomials, quantized conformal blocks, and a \(q\)-Selberg type integral. Zbl 1254.22013 Rimányi, Richard; Tarasov, Vitaly O.; Varchenko, A.; Zinn-Justin, Paul 11 2012 The Euler beta-function, the Vandermonde determinant, the Legendre equation, and critical values of linear functions on a configuration of hyperplanes. I. Zbl 0695.33004 Varchenko, A. N. 11 1989 Elliptic Selberg integrals and conformal blocks. Zbl 1041.33003 Felder, G.; Stevens, L.; Varchenko, A. 10 2003 Congruences for Hasse-Witt matrices and solutions of \(p\)-adic KZ equations. Zbl 1546.11172 Varchenko, Alexander; Zudilin, Wadim 1 2024 Landau-Ginzburg mirror, quantum differential equations and qKZ difference equations for a partial flag variety. Zbl 1512.14032 Tarasov, Vitaly; Varchenko, Alexander 3 2023 Dwork-type congruences and \(p\)-adic KZ connection. Zbl 1532.11164 Varchenko, Alexander 1 2023 Three-dimensional mirror symmetry and elliptic stable envelopes. Zbl 1495.14058 Rimányi, Richárd; Smirnov, Andrey; Zhou, Zijun; Varchenko, Alexander 15 2022 The \(\ast \)-Markov equation for Laurent polynomials. Zbl 1500.11027 Cotti, Giordano; Varchenko, Alexander 3 2022 Notes on solutions of KZ equations modulo \(p^s\) and \(p\)-adic limit \(s\to\infty\). Zbl 1497.13020 Varchenko, Alexander 2 2022 Dynamical and qKZ equations modulo \(p^s\): an example. Zbl 1506.37089 Varchenko, A. 1 2022 Determinant of \(\mathbb{F}_p\)-hypergeometric solutions under ample reduction. Zbl 1497.13019 Varchenko, Alexander 1 2022 The \({{\mathbb{F}}}_p\)-Selberg integral. Zbl 1496.13008 Rimányi, Richárd; Varchenko, Alexander 1 2022 Derived KZ equations. Zbl 1536.17031 Schechtman, Vadim; Varchenko, Alexander 1 2022 An invariant subbundle of the KZ connection mod \(p\) and reducibility of \(\widehat{{\mathfrak{sl}_2}}\) Verma modules mod \(p\). Zbl 1490.81090 Varchenko, A. 5 2021 The \(\mathbb{F}_p\)-Selberg integral of type \(A_n\). Zbl 1487.33018 Rimányi, Richárd; Varchenko, Alexander 4 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 1466.14060 Cotti, Giordano; Varchenko, Alexander 4 2021 Hypergeometric integrals modulo \(p\) and Hasse-Witt matrices. Zbl 1477.13016 Slinkin, Alexey; Varchenko, Alexander 4 2021 Equivariant quantum differential equation, Stokes bases, and \(K\)-theory for a projective space. Zbl 1475.14111 Tarasov, Vitaly; Varchenko, Alexander 3 2021 Igor’ Moiseevich Krichever. Zbl 1489.01018 Buchstaber, V. M.; Varchenko, A. N.; Veselov, A. P.; Grinevich, P. G.; Grushevsky, S. M.; Dobrokhotov, S. Yu.; Zabrodin, A. V.; Marshakov, A. V.; Mironov, A. E.; Nekrasov, N. A.; Novikov, S. P.; Okounkov, A. Yu.; Olshanetsky, M. A.; Pogrebkov, A. K.; Taimanov, I. A.; Tsfasman, M. A.; Chekhov, L. O.; Sheinman, O. K.; Shlosman, S. B. 1 2021 Incarnations of XXX \(\widehat{\mathfrak{sl}_N}\) Bethe ansatz equations and integrable hierarchies. Zbl 1503.17028 Krichever, Igor; Varchenko, Alexander 1 2021 Hyperelliptic integrals modulo \(p\) and Cartier-Manin matrices. Zbl 1456.14036 Varchenko, Alexander 8 2020 Positive populations. Zbl 1519.13013 Schechtman, Vadim; Varchenko, Alexander 3 2020 Three-dimensional mirror self-symmetry of the cotangent bundle of the full flag variety. Zbl 1451.53116 Rimányi, Richárd; Smirnov, Andrey; Varchenko, Alexander; Zhou, Zijun 25 2019 Elliptic and \(K\)-theoretic stable envelopes and Newton polytopes. Zbl 1452.55009 Rimányi, R.; Tarasov, V.; Varchenko, A. 22 2019 Solutions of KZ differential equations modulo \(p\). Zbl 1416.81080 Schechtman, Vadim; Varchenko, Alexander 15 2019 \(q\)-hypergeometric solutions of quantum differential equations, quantum Pieri rules, and Gamma theorem. Zbl 1419.82020 Tarasov, Vitaly; Varchenko, Alexander 3 2019 Twisted de Rham complex on line and singular vectors in \(\widehat{\mathfrak{sl}_2}\) Verma modules. Zbl 1460.17029 Slinkin, Alexey; Varchenko, Alexander 3 2019 Potentials of a family of arrangements of hyperplanes and elementary subarrangements. Zbl 1425.32025 Prudhom, Andrew; Varchenko, Alexander 2 2019 Cyclotomic discriminantal arrangements and diagram automorphisms of Lie algebras. Zbl 1476.17013 Varchenko, Alexander; Young, Charles 2 2019 Equivariant Chern-Schwartz-MacPherson classes in partial flag varieties: interpolation and formulae. Zbl 1391.14108 Rimányi, Richárd; Varchenko, Alexander 23 2018 Elliptic dynamical quantum groups and equivariant elliptic cohomology. Zbl 1423.17015 Felder, Giovanni; Rimányi, Richárd; Varchenko, Alexander 13 2018 Remarks on the Gaudin model modulo \(p\). Zbl 1405.17019 Varchenko, Alexander 9 2018 Potentials of a Frobenius-like structure. Zbl 1391.05073 Hertling, Claus; Varchenko, Alexander 3 2018 Affine Macdonald conjectures and special values of Felder-Varchenko functions. Zbl 1431.33017 Rains, Eric M.; Sun, Yi; Varchenko, Alexander 1 2018 Solutions modulo \(p\) of Gauss-Manin differential equations for multidimensional hypergeometric integrals and associated Bethe ansatz. Zbl 1406.33013 Varchenko, Alexander 8 2017 Self-dual Grassmannian, Wronski map, and representations of \(\mathfrak{gl}_N\), \(\mathfrak{sp}_{2r}\), \(\mathfrak{so}_{2r+1}\). Zbl 1437.17002 Lu, 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 1460.17028 Schechtman, Vadim; Varchenko, Alexander 2 2017 Dynamical Gelfand-Zetlin algebra and equivariant cohomology of Grassmannians. Zbl 1380.81167 Rimanyi, R.; Varchenko, A. 4 2016 On the Gaudin model associated to Lie algebras of classical types. Zbl 1353.82024 Lu, Kang; Mukhin, E.; Varchenko, A. 4 2016 On axioms of Frobenius like structure in the theory of arrangements. Zbl 1400.37087 Varchenko, Alexander 2 2016 Trigonometric weight functions as \(K\)-theoretic stable envelope maps for the cotangent bundle of a flag variety. Zbl 1349.19002 Rimányi, R.; Tarasov, V.; Varchenko, A. 32 2015 Partial flag varieties, stable envelopes, and weight functions. Zbl 1361.14030 Rimányi, Richárd; Tarasov, Vitaly; Varchenko, Alexander 22 2015 Arrangements and Frobenius like structures. Zbl 1349.53114 Varchenko, Alexander 5 2015 Populations of solutions to cyclotomic Bethe equations. Zbl 1341.82025 Varchenko, Alexander; Young, Charles A. S. 1 2015 Critical set of the master function and characteristic variety of the associated Gauss-Manin differential equations. Zbl 1323.32024 Varchenko, A. 1 2015 Spaces of quasi-exponentials and representations of the Yangian \(Y(\mathfrak{gl}_N)\). Zbl 1365.17006 Mukhin, E.; Tarasov, V.; Varchenko, A. 18 2014 Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety. Zbl 1294.82016 Tarasov, Vitaly; Varchenko, Alexander 14 2014 Bethe algebra of Gaudin model, Calogero-Moser space, and Cherednik algebra. Zbl 1304.82021 Mukhin, E.; Tarasov, V.; Varchenko, A. 13 2014 Vladimir I. Arnold – Collected works. Vol. II. Hydrodynamics, bifurcation theory, and algebraic geometry 1965–1972. Edited by Alexander B. Givental, Boris A. Khesin, Alexander N. Varchenko, Victor A. Vassiliev and Oleg Ya. Viro. Zbl 1354.01038 Arnold, Vladimir I. 10 2014 Critical points of master functions and integrable hierarchies. Zbl 1311.37052 Varchenko, A.; Wright, D. 7 2014 Cohomology classes of conormal bundles of Schubert varieties and Yangian weight functions. Zbl 1328.14082 Rimányi, R.; Tarasov, V.; Varchenko, A. 6 2014 On the number of populations of critical points of master functions. Zbl 1382.17015 Mukhin, Evgeny; Varchenko, Alexander 5 2014 Critical points of master functions and the mKdV hierarchy of type \(A_2^{(2)}\). Zbl 1332.82026 Varchenko, A.; Woodruff, T.; Wright, D. 3 2014 BGG resolutions via configuration spaces. (Résolutions BGG via les espaces de configurations.) Zbl 1323.55013 Falk, Michael; Schechtman, Vadim; Varchenko, Alexander 2 2014 Characteristic variety of the Gauss-Manin differential equations of a generic parallelly translated arrangement. Zbl 1311.58003 Varchenko, Alexander 1 2014 Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra. Zbl 1287.81063 Gorbounov, V.; Rimányi, R.; Tarasov, V.; Varchenko, A. 32 2013 Combinatorial formulae for nested Bethe vectors. Zbl 1288.82024 Tarasov, Vitaly; Varchenko, Alexander 19 2013 Bethe subalgebras of the group algebra of the symmetric group. Zbl 1276.82014 Mukhin, E.; Tarasov, V.; Varchenko, A. 9 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 1290.58001 Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. 218 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 1297.32001 Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. 160 2012 KZ characteristic variety as the zero set of classical Calogero-Moser Hamiltonians. Zbl 1269.82018 Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander 21 2012 Extended Joseph polynomials, quantized conformal blocks, and a \(q\)-Selberg type integral. Zbl 1254.22013 Rimányi, Richard; Tarasov, Vitaly O.; Varchenko, A.; Zinn-Justin, Paul 11 2012 Cohomology of the complement to an elliptic arrangement. Zbl 1276.14081 Levin, Andrey; Varchenko, Alexander 6 2012 Three sides of the geometric Langlands correspondence for \(\mathfrak{gl}_N\) Gaudin model and Bethe vector averaging maps. Zbl 1260.82025 Mukhin, Eugene; Tarasov, Vitaly; Varchenko, Alexander 4 2012 Reality property of discrete Wronski map with imaginary step. Zbl 1299.81027 Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander 3 2012 The contravariant form on singular vectors of a projective arrangement. Zbl 1400.14138 Falk, Michael J.; Varchenko, Alexander N. 2 2012 Singularities of functions, wave fronts, caustics and multidimensional integrals. Zbl 1255.58002 Arnold, V. I.; Varchenko, A. N.; Givental, A. B.; Khovanskii, A. G. 2 2012 Intersection cohomology of a rank one local system on the complement of a hyperplane-like divisor. Zbl 1274.14025 Arinkin, Dimitry; Varchenko, Alexander 1 2012 Vanishing products of one-forms and critical points of master functions. Zbl 1260.32007 Cohen, Daniel C.; Denham, Graham; Falk, Michael; Varchenko, Alexander 1 2012 Quantum integrable model of an arrangement of hyperplanes. Zbl 1217.82026 Varchenko, Alexander 17 2011 Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of \(\mathfrak{gl}_{N}\). Zbl 1219.82121 Mukhin, E.; Tarasov, V.; Varchenko, A. 17 2011 Critical points and resonance of hyperplane arrangements. Zbl 1228.32028 Cohen, D.; Denham, G.; Falk, M.; Varchenko, A. 15 2011 Conformal blocks and equivariant cohomology. Zbl 1259.81080 Rimányi, Richárd; Schechtman, Vadim; Varchenko, Alexander 6 2011 Cohomology of a flag variety as a Bethe algebra. Zbl 1271.14072 Rimányi, R.; Schechtman, V.; Tarasov, V.; Varchenko, A. 5 2011 Conformal blocks in the tensor product of vector representations and localization formulas. Zbl 1228.81250 Rimányi, R.; Varchenko, A. 5 2011 Bethe algebra of the \({\mathfrak {gl}}_{N+1}\) Gaudin model and algebra of functions on the critical set of the master function. Zbl 1221.82038 Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander 4 2011 The Euler adic dynamical system and path counts in the Euler graph. Zbl 1213.37008 Petersen, Karl; Varchenko, Alexander 8 2010 A Selberg integral type formula for an \(\mathfrak {sl}_{2}\) one-dimensional space of conformal blocks. Zbl 1222.81259 Varchenko, A. 6 2010 Vladimir I. Arnold – Collected works. Vol. I. Representations of functions, celestial mechanics, and KAM theory 1957-1965. Edited by Alexander B. Givental, Boris A. Khesin, Jerrold E. Marsden, Alexander N. Varchenko, Victor A. Vissilev, Oleg Ya. Viro and Vladimir M. Zakalyukin. Zbl 1187.01033 Arnold, Vladimir I. 4 2010 Schubert calculus and representations of the general linear group. Zbl 1205.17026 Mukhin, E.; Tarasov, V.; Varchenko, A. 69 2009 Bethe algebra of homogeneous \(XXX\) Heisenberg model has simple spectrum. Zbl 1173.82006 Mukhin, E.; Tarasov, V.; Varchenko, A. 36 2009 The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz. Zbl 1213.14101 Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander 35 2009 A generalization of the Capelli identity. Zbl 1287.17026 Mukhin, E.; Tarasov, V.; Varchenko, A. 16 2009 On reality property of Wronski maps. Zbl 1181.81065 Mukhin, 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 1158.81336 Mukhin, E.; Tarasov, V.; Varchenko, A. 5 2009 Nikolai Nikolaevich Nekhoroshev (obituary). Zbl 1175.01064 Abramov, 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 1142.82005 Mukhin, E.; Tarasov, V.; Varchenko, A. 36 2008 Quasi-polynomials and the Bethe ansatz. Zbl 1138.82010 Mukhin, E.; Varchenko, A. 15 2008 Spaces of quasi-exponentials and representations of \(\mathfrak{gl}_N\). Zbl 1142.81011 Mukhin, E.; Tarasov, V.; Varchenko, A. 13 2008 Bethe algebra and the algebra of functions on the space of differential operators of order two with polynomial kernel. Zbl 1171.82008 Mukhin, E.; Tarasov, V.; Varchenko, A. 1 2008 Multiple orthogonal polynomials and a counterexample to the Gaudin Bethe ansatz conjecture. Zbl 1127.82019 Mukhin, E.; Varchenko, A. 19 2007 Generating operator of \(XXX\) or Gaudin transfer matrices has quasi-exponential kernel. Zbl 1140.82015 Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander 12 2007 Poincaré-Birkhoff-Witt expansions of the canonical elliptic differential form. Zbl 1132.33322 Felder, G.; Rimányi, R.; Varchenko, A. 5 2007 Higher Lamé equations and critical points of master functions. Zbl 1204.34122 Mukhin, E.; Tarasov, V.; Varchenko, A. 2 2007 Resonance relations, holomorphic trace functions and hypergeometric solutions to qKZB and MacDonald-Ruijsenaars equations. Zbl 1149.17010 Styrkas, K.; Varchenko, A. 1 2007 On a new form of Bethe ansatz equations and separation of variables in the \( \mathfrak{sl}_3\) Gaudin model. Zbl 1154.82308 Mukhin, E.; Schechtman, V.; Tarasov, V.; Varchenko, A. 1 2007 Multiplicity of critical points of master functions and Schubert calculus. Zbl 1356.14042 Belkale, Prakash; Mukhin, Evgeny; Varchenko, Alexander 1 2007 Bethe eigenvectors of higher transfer matrices. Zbl 1456.82301 Mukhin, E.; Tarasov, V.; Varchenko, A. 47 2006 Bispectral and \((\mathfrak{gl}_{N},\mathfrak{gl}_{M})\) dualities. Zbl 1156.82005 Mukhin, Evgenii E.; Tarasov, Vitaly O.; Varchenko, Alexander N. 17 2006 Bethe ansatz for arrangements of hyperplanes and the Gaudin model. Zbl 1375.32050 Varchenko, Alexander 9 2006 Quiver \(D\)-modules and homology of local systems over an arrangement of hyperplanes. Zbl 1116.32005 Khoroshkin, S.; Varchenko, A. 7 2006 Differential equations for Jacobi-Piñeiro polynomials. Zbl 1133.34046 Mukhin, Eugene; Varchenko, Alexander 1 2006 Norm of a Bethe vector and the Hessian of the master function. Zbl 1072.82012 Mukhin, Evgeny; Varchenko, Alexander 25 2005 ...and 145 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,419 Authors 103 Varchenko, Alexander Nikolaevich 41 Tarasov, Vitaly Olegovich 36 Mukhin, Evgeny 22 Rimányi, Richárd 19 Dimca, Alexandru 19 Greenblatt, Michael 19 Saito, Morihiko 19 Zotov, Andrei V. 17 Felder, Giovanni 17 Pakuliak, Stanislav Z. 17 Schechtman, Vadim 16 Denham, Graham 16 Etingof, Pavel Il’ich 16 Feĭgin, Boris L’vovich 16 Zabrodin, Anton V. 15 Gusein-Zade, Sabir M. 15 Ragoucy, Eric 14 Morozov, Alexei Yurievich 14 Reshetikhin, Nikolai Yu. 12 Milanov, Todor E. 12 Mironov, Andrei D. 12 Smirnov, Andrey V. 11 Ebeling, Wolfgang 11 Frenkel, Edward V. 11 Hertling, Claus 11 Khoroshkin, Sergey M. 11 Movasati, Hossein 11 Mudrov, Andrey I. 11 Slavnov, Nikita A. 11 Spiridonov, Vyacheslav Pavlovich 11 Stokman, Jasper V. 11 Weber, Andrzej 10 Fehér, László Gy. 10 Kamimoto, Joe 10 Koroteev, Peter 10 Mimachi, Katsuhisa 10 Novikov, Dmitry 10 Teramoto, Keisuke 10 Terras, Véronique 10 Vicedo, Benoît 10 Young, Charles A. 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Ole 7 Yang, Wenli 7 Zenkevich, Yegor 7 Zinn-Justin, Paul 7 Żołądek, Henryk 6 Belkale, Prakash 6 Belliard, Samuel 6 Bivià-Ausina, Carles 6 Borodzik, Maciej 6 Budur, Nero 6 Candelas, Philip 6 Cox, Ben Lewis 6 Domitrz, Wojciech 6 Givental, Alexander Borisovich 6 Greuel, Gert-Martin 6 Hussain, Naveed 6 Ito, Masahiko 6 Lichtin, Ben ...and 2,319 more Authors all top 5 Cited in 346 Serials 119 Journal of High Energy Physics 105 Communications in Mathematical Physics 103 Nuclear Physics. B 100 Advances in Mathematics 59 Journal of Mathematical Physics 57 Letters in Mathematical Physics 46 Journal of Geometry and Physics 46 Duke Mathematical Journal 46 Functional Analysis and its Applications 44 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 41 Annales de l’Institut Fourier 39 Journal of Algebra 37 Transactions of the American Mathematical Society 36 Selecta Mathematica. 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