Nicolai Reshetikhin

Affiliation: YMSC, BIMSA

Office: A3-2-307

Email: nreshetikhin@bimsa.cn

Research Field: Quantum Field Theory, Representation Theory, Low-dimensional Topology

Webpage: https://ymsc.tsinghua.edu.cn/en/info/1031/1880.htm

Biography

Professor Nicolai Reshetikhin was born in Leningrad, former Soviet Union, now St. Petersburg, Russia. In 1982, he graduated from Leningrad State University with a bachelor's degree and a master's degree. In 1984, he graduated from the Steklov Institute of Mathematics and obtained a PhD degree. He has taught at well-known universities such as Harvard University, the University of California, Berkeley and the University of Amsterdam. He was invited twice to give a talk at the ICM International Conference of Mathematicians, one of which was a plenary talk. Professor Reshetikhin's main research interests include quantum topology, quantum groups and their representations, classical and quantum integrable systems, and integrable models statistical mechanics. He is one of the founders of quantum group theory, one of the authors of Reshetikhin-Turaev invariant, has important results in the theory of quantum integrable system, in Poisson and symplectic geometry, in the theory of quantum Kac Moody algebra. In 2010, he was elected as a Foreign member of the Royal Danish Academy. In 2021, he became a Fellow of the American Mathematical Society.

Research Interest

Representation theory, Quantum field theory, Integrable systems

Education Experience

1982 - 1984 Leningrad Branch, Steklov Mathematical Institute (LOMI) Doctor
1979 - 1982 Leningrad University Master,Bachelor
1975 - 1979 Leningrad Polytechnic Institute Bachelor

Work Experience

2022 - BIMSA
2021 - Tsinghua University Professor
1997 - 2021 University of California, Berkeley Professor
1991 - 1997 University of California, Berkeley Associate Professor
1989 - 1991 Harvard University Assistant Professor
1984 - 1989 Steklov Mathematical Institute Research Fellow

Honors and Awards

2022 Weyl-Wigner Award
2010 "The Mathematics of Quantum Field Theory" plenary talk at the ICM-2010 Hyderabad, India, August 2010
1990 45-minute talk, ICM1990, Kyoto Japan

Publication

[1] Andrii Liashyk, Nicolai Reshetikhin, Ivan Sechin, Quantum integrable systems on a classical integrable background, arXiv preprint arXiv:2405.17865 (2024)
[2] E Koelink, S Kolb, N Reshetikhin, B Vlaar, Hypergeometry, Integrability and Lie Theory, American Mathematical Society (2022)
[3] Nicolai Reshetikhin, Gus Schrader, Superintegrability of generalized Toda models on symmetric spaces, International Mathematics Research Notices, 2021(17), 12993-13010 (2021)
[4] S. Arthamonov, N. Reshetikhin, Superintegrable systems on moduli spaces of flat connections, Communications in Mathematical Physics, 386, 1337-1381 (2021)
[5] Christian Blanchet, Nathan Geer, Bertrand Patureau-Mirand, Nicolai Reshetikhin, Holonomy braidings, biquandles and quantum invariants of links with SL2(C) flat connections, Selecta Math., 26(2) (2020)
[6] Alberto S. Cattaneo, Pavel Mnev, Nicolai Reshetikhin, A cellular topolog- ical field theory, Communications in Mathematical Physics, 374(2), 1229-1320 (2020)
[7] Alberto S. Cattaneo, Pavel Mnev, Nicolai Reshetikhin, Poisson sigma model and semiclassical quantization of integrable systems, Reviews in Mathematical Physics, 30(06), 1840004 (2018)
[8] Nicolai Reshetikhin, Semiclassical geometry of integrable systems, Journal of Physics A: Mathematical and Theoretical, 51(16), 164001 (2018)
[9] N Reshetikhin, J Stokman, B Vlaar, Integral solutions to boundary quantum Knizhnik–Zamolodchikov equations, Advances in Mathematics, 323, 486-528 (2018)
[10] Alberto S. Cattaneo, Pavel Mnev, Nicolai Reshetikhin, Perturbative quan- tum gauge theories on manifolds with boundary, Communications in Math-ematical Physics, 357(2), 631730 (2018)
[11] Nicolai Reshetikhin, Jasper Stokman, Bart Vlaar, Integral solutions to bound- ary quantum Knizhnik-Zamolodchikov equations, Advances in Mathematics, 323(7 January 2018), 486-528 (2018)
[12] D. Keating, N. Reshetikhin, A. Sridhar, Conformal limit for Dimer models on the hexagonal lattice, Записки научных семинаров ПОМИ, 473(0), 174-193 (2018)
[13] Nicolai Reshetikhin, Ananth Sridhar, Integrability of limit shapes of the six vertex model, Communications in Mathematical Physics, 356, 535-565 (2017)
[14] Nicolai Reshetikhin, Degenerate integrability of quantum spin Calogero-Moser systems, Lett.Math.Phys., 107(1), 187-200 (2017)
[15] Nicolai Reshetikhin, Degenerately integrable systems, Journal of Mathematical Sciences, 213, 769-785 (2016)
[16] Reshetikhin N.Y., Stokman J.V., Vlaar B., Boundary Quantum Knizhnik- Zamolodchikov Equations and Fusion, Annales Henri Poincar January 2016, 17(1), 137177 (2016)
[17] Nicolai Reshetikhin, Jasper Stokman and Bart Vlaar, Boundary quantum Knizhnik–Zamolodchikov equations and fusion, Annales Henri Poincaré, 17(1), 137-177 (2016)
[18] Nicolai, Reshetikhin, Jasper, Stokman, Bart, Vlaar, Boundary quantum Knizhnik-Zamolodchikov equations and Bethe vectors, Communications in Mathematical Physics, 336, 953-986 (2015)
[19] Nicolai Reshetikhin, Boris Vertman, Combinatorial Quantum Field The- ory and Gluing Formula for Determinants, Lett. Math. Phys., 105(3), 309340 (2015)
[20] Nicolai Reshetikhin, Jasper Stokman and Bart Vlaar, Boundary Quantum Knizhnik–Zamolodchikov Equations and Bethe Vectors, Commun. Math. Phys., 336, 953-986 (2015)
[21] A Gerasimov, S Kharchev, D Lebedev, S Oblezin, Contemporary Mathematics Volume 391, 2005, Noncommutative Geometry and Representation Theory in Mathematical Physics: Satellite Conference to the Fourth European Congress of Mathematics, July 5-10, 2004, Karlstad University, Karlstad, Sweden, 391, 101 (2005)
[22] A.Kirillov, N.Yu.Reshetikhin, The Bethe ansatz and the combinatorics of Young tableaux, Zap. Nauch. Sem. LOMI, 155(1986), 65-115 (1987)
[23] A.Kirillov, N.Yu.Reshetikhin, The Yangians, Bethe ansatz and combinatorics, letters in mathematical physics, 12, 199-208 (1986)
[24] S Gukov, B Haghighat, N Reshetikhin, Foams and KZ-equations in Rozansky-Witten theories, Nuclear Physics B, 116856 (2025)
[25] P Mnev, Lecture notes on conformal field theory, arXiv preprint arXiv:2501.06616 (2025)
[26] H De Clercq, N Reshetikhin, J Stokman, Graphical calculus for quantum vertex operators, I: The dynamical fusion operator, Communications in Mathematical Physics, 405(6) (2024)
[27] S Gukov, B Haghighat, Y Liu, N Reshetikhin, Irregular KZ equations and Kac-Moody representations, arXiv preprint arXiv:2412.16929 (2024)
[28] H De Clercq, N Reshetikhin, J Stokman, Graphical calculus for quantum vertex operators, II: q-KZB and coordinate Macdonald-Ruijsenaars equations, arXiv preprint arXiv:2411.17306 (2024)
[29] JV Stokman, N Reshetikhin, Correction to: -point spherical functions and asymptotic boundary KZB equations, Inventiones mathematicae, 237(2), 869-870 (2024)
[30] A Lachowska, O Postnova, N Reshetikhin, D Solovyev, Tensor powers of vector representation of at even roots of unity, Other (2024)
[31] F Colomo, J de Gier, P Di Francesco, N Reshetikhin, D Serban, H Spohn, Randomness, Integrability and Universality (2024)
[32] N Reshetikhin, Spin Calogero-Moser periodic chains and two dimensional Yang-Mills theory with corners, arXiv preprint arXiv:2303.10579 (2023)
[33] N Reshetikhin, Periodic and open classical spin Calogero-Moser chains, arXiv preprint arXiv:2302.14281 (2023)
[34] N Reshetikhin, J Stokman, Quantum superintegrable spin systems on graph connections, arXiv preprint arXiv:2305.02767 (2023)
[35] N Reshetikhin, The acceptance speech of the 2022 Weyl-Wigner award, SciPost Physics Proceedings (2023)
[36] B Haghighat, Y Liu, N Reshetikhin, Flat Connections from Irregular Conformal Blocks, arXiv preprint arXiv:2311.07960 (2023)
[37] OV Postnova, NY Reshetikhin, On the Asymptotics of Multiplicities for Large Tensor Product of Representations of Simple Lie Algebras., Journal of Mathematical Sciences, 275(3) (2023)
[38] JV Stokman, N Reshetikhin, N-point spherical functions and asymptotic boundary KZB equations, Inventiones mathematicae, 229(1), 1-86 (2022)
[39] E Frenkel, D Hernandez, N Reshetikhin, Folded quantum integrable models and deformed W-algebras, Letters in Mathematical Physics, 112(4) (2022)
[40] P Belov, N Reshetikhin, The two-point correlation function in the six-vertex model, Journal of Physics A: Mathematical and Theoretical, 55(15) (2022)
[41] D Keating, N Reshetikhin, A Sridhar, Integrability of limit shapes of the inhomogeneous six vertex model, Communications in Mathematical Physics, 391(3), 1181-1207 (2022)
[42] OV Postnova, NY Reshetikhin, On the asymptotics of multiplicities for large tensor product of representations of simple Lie algebras, Записки научных семинаров ПОМИ(509), 185-200 (2021)
[43] E Frenkel, D Hernandez, N Reshetikhin, arXiv: Folded quantum integrable models and deformed W-algebras (2021)
[44] AS Cattaneo, P Mnev, N Reshetikhin, A cellular topological field theory, Communications in Mathematical Physics, 374, 1229-1320 (2020)
[45] C Blanchet, N Geer, B Patureau-Mirand, N Reshetikhin, Holonomy braidings, biquandles and quantum invariants of links with$SL2(C)$flat connections, Selecta Mathematica, 26(2) (2020)
[46] O Postnova, N Reshetikhin, On multiplicities of irreducibles in large tensor product of representations of simple Lie algebras, Letters in Mathematical Physics, 110(1), 147-178 (2020)
[47] N Reshetikhin, J Stokman, Asymptotic boundary KZB operators and quantum Calogero-Moser spin chains, arXiv preprint arXiv:2012.13497 (2020)
[48] D Dumbaugh, P Daskalopoulos, A Vershik, L Kapitanski, N Reshetikhin et al., The ties that bind Olga Alexandrovna Ladyzhenskaya and the 2022 ICM in St. Petersburg, Notices of the American Mathematical Society, 67(3) (2020)
[49] N Reshetikhin, Spin Calogero-Moser models on symmetric spaces, arXiv preprint arXiv:1903.03685 (2019)
[50] D Keating, N Reshetikhin, A Sridhar, Conformal Limit for Dimer Models on the Hexagonal Lattice., Journal of Mathematical Sciences, 242(5) (2019)
[51] AS Cattaneo, P Mnev, N Reshetikhin, Perturbative quantum gauge theories on manifolds with boundary, Communications in Mathematical Physics, 357, 631-730 (2018)
[52] N Reshetikhin, A Sridhar, Limit shapes of the stochastic six vertex model, Communications in Mathematical Physics, 363, 741-765 (2018)
[53] N Kitanine, RI Nepomechie, N Reshetikhin, Quantum integrability and quantum groups: a special issue in memory of Petr P Kulish, Journal of Physics A: Mathematical and Theoretical, 51(11) (2018)
[54] A Its, N Reshetikhin, Preface: Introduction to special issue: In memory of Ludwig Faddeev, Journal of Mathematical Physics, 59(9) (2018)
[55] N RESHETIKHIN, GUS SCHRADER, SUPERINTEGRABILITY OF SYMMETRIC TODA, arXiv preprint arXiv:1802.00356 (2018)
[56] N Reshetikhin, Degenerate integrability of quantum spin Calogero–Moser systems, Letters in Mathematical Physics, 107, 187-200 (2017)
[57] IY Aref'eva, VE Zakharov, VV Kozlov, IM Krichever, VP Maslov et al., Ludwig Dmitrievich Faddeev, Russian Mathematical Surveys, 72(6) (2017)
[58] N Reshetikhin, M Semenov-Tian-Shansky, L Takhtajan, LD Faddeev:(March 23, 1934-February 26, 2017), International Association of Mathematical Physics (IAMP) News Bulletin (2017)
[59] AS Cattaneo, P Mnev, N Reshetikhin, Perturbative BV theories with Segal-like gluing, arXiv preprint arXiv:1602.00741 (2016)
[60] F Colomo, P Fendley, A Pronko, N Reshetikhin, P Wiegmann et al., Statistical Mechanics, Integrability and Combinatorics, Il Colle di Galileo, 5(1), 77-81 (2016)
[61] R Borcherds, M Haiman, N Reshetikhin, V Serganova, T Johnson-Freyd, Part I: Lie Groups (2016)
[62] B Booss-Bavnbek, M Lesch, G Marinescu, N Reshetikhin, B Vertman, Interfaces between Geometric Analysis and Mathematical Physics: July 2016, Scientific report (2016)
[63] L FADDEEV, N RESHETIKHIN, L TAKHTAJAN, Leningrad Branch of VA Steklov Mathematical Institute of the Academy of, Fifty Years of Mathematical Physics: Selected Works of Ludwig Faddeev, 2 (2016)
[64] N Reshetikhin, B Vertman, Combinatorial quantum field theory and gluing formula for determinants, Letters in Mathematical Physics, 105, 309-340 (2015)
[65] AS Cattaneo, P Mnev, N Reshetikhin, Semiclassical quantization of classical field theories, Mathematical Aspects of Quantum Field Theories, 275-324 (2015)
[66] M Aganagic, I Agol, D Auroux, G Bergman, R Bryant, A Chorin, M Christ et al., Sincerely, University of California, Berkeley (2015)
[67] AS Cattaneo, P Mnev, N Reshetikhin, Classical BV theories on manifolds with boundary, Communications in Mathematical Physics, 332, 535-603 (2014)
[68] Q Chen, N Reshetikhin, Recursion formulas for HOMFLY and Kauffman invariants, Journal of Knot Theory and Its Ramifications, 23(5) (2014)
[69] N Reshetikhin, J Stokman, B Vlaar, Reflection quantum Knizhnik-Zamolodchikov equations and Bethe vectors, arXiv preprint arXiv:1305.1113 (2013)
[70] C De Concini, D Hernandez, N Reshetikhin, Geometry of the analytic loop group, Advances in Mathematics, 238, 290-321 (2013)
[71] AS Cattaneo, P Mnev, N Reshetikhin, Classical and quantum Lagrangian field theories with boundary, arXiv preprint arXiv:1207.0239 (2012)
[72] C Boutillier, S Mkrtchyan, N Reshetikhin, P Tingley, Random skew plane partitions with a piecewise periodic back wall, Annales Henri Poincaré, 13, 271-296 (2012)
[73] P Di Francesco, N Reshetikhin, Asymptotic shapes with free boundaries, Communications in Mathematical Physics, 309, 87-121 (2012)
[74] AS Cattaneo, P Mnëv, N Reshetikhin, Classical BV theories on manifolds with boundaries, arXiv preprint math-ph/1201.0290 (2012)
[75] N Reshetikhin, C Stroppel, B Webster, Schur–Weyl-Type Duality for Quantized(1|1), the Burau Representation of Braid Groups, and Invariants of Tangled Graphs, Perspectives in Analysis, Geometry, and Topology (2012)
[76] N Reshetikhin, Quantum Deformations of SL/B and its Schubert Varieties n, ICM-90 Satellite Conference Proceedings: Special Functions (2012)
[77] R Borcherds, M Haiman, N Reshetikhin, V Serganova, Berkeley Lectures on Lie Groups and Quantum Groups, ed. Anton Geraschenko and Theo Johnson-Freyd (2011)
[78] K Hasegawa, T Hayashi, S Hosono, Y Yamada, Program of the Conference, Exploring New Structures and Natural Constructions in Mathematical Physics 61 (2011)
[79] N Reshetikhin, Lectures on the integrability of the six-vertex model, Exact methods in low-dimensional statistical physics and quantum computing … (2010)
[80] N Reshetikhin, Lectures on quantization of gauge systems, New Paths Towards Quantum Gravity, 125-190 (2010)
[81] R Kashaev, N Reshetikhin, Invariants of tangles with flat connections in their complements, arXiv preprint arXiv:1008.1384 (2010)
[82] K Palamarchuk, N Reshetikhin, The 6-vertex model with fixed boundary conditions, arXiv preprint arXiv:1010.5011 (2010)
[83] I Affleck, F Alet, JL Cardy, NR Cooper, B Duplantier, MV Feigel'man et al., Exact Methods in Low-dimensional Statistical Physics and Quantum Computing: École D'été de Physique Des Houches, Session LXXXIX, 30 June-1 August 2008, École Thématique Du CNRS, Oxford University Press (2010)
[84] T JOLICOEUR, R KENYON, A KITAEV, I KOSTOV, W KRAUTH et al., STUDENTS AND AUDITORS, Exact Methods in Low-dimensional Statistical Physics and Quantum Computing … (2010)
[85] N Geer, N Reshetikhin, On Invariants of Graphs Related to Quantum at Roots of Unity, Letters in Mathematical Physics, 88(1), 321-331 (2009)
[86] D Orlando, S Reffert, N Reshetikhin, On domain wall boundary conditions for the XXZ spin Hamiltonian, arXiv preprint arXiv:0912.0348 (2009)
[87] VK Murty, SELECTED MATHEMATICAL REVIEWS, AMERICAN MATHEMATICAL SOCIETY, 46(3), 485-487 (2009)
[88] D Cimasoni, N Reshetikhin, Dimers on surface graphs and spin structures. II, Communications in mathematical physics, 281, 445-468 (2008)
[89] N Reshetikhin, Topological quantum field theory: 20 years later, European Congress of Mathematics, 333-377 (2008)
[90] A Okounkov, N Reshetikhin, Random skew plane partitions and the Pearcey process, Communications in Mathematical Physics, 269, 571-609 (2007)
[91] D Cimasoni, N Reshetikhin, Dimers on surface graphs and spin structures. I, Communications in Mathematical Physics, 275, 187-208 (2007)
[92] RM Kashaev, N Reshetikhin, Symmetrically factorizable groups and set-theoretical solutions of the pentagon equation, Contemporary Mathematics, 433, 267-280 (2007)
[93] N Reshetikhin, The Mathematical Work of the 2006 Fields Medalists, Notices of the AMS, 54(3) (2007)
[94] N Reshetikhin, The work of Andrei Okounkov, Notices of the American Mathematical Society, 54(3), 388-390 (2007)
[95] A Okounkov, N Reshetikhin, C Vafa, Quantum Calabi-Yau and classical crystals, The unity of Mathematics: In Honor of the Ninetieth Birthday of IM Gelfand … (2006)
[96] AY Okounkov, NY Reshetikhin, The birth of a random matrix, Moscow Mathematical Journal, 6(3), 553-566 (2006)
[97] A Okounkov, N Reshetikhin, C Vafa, The unity of mathematics, Progress in Mathematics, 244, 597-618 (2006)
[98] N Reshetikhin, Some algebraic and analytic structures in integrable systems, Low-Dimensional Models in Statistical Physics and Quantum Field Theory (2006)
[99] N Reshetikhin, K Palamarchuk, PoS (Solvay) 012 The 6-vertex model with fixed boundary conditions. (2006)
[100] D Allison, N Reshetikhin, Numerical stu\-dy of the 6-vertex model with domain wall boundary conditions, Annales de l'institut Fourier, 55(6), 1847-1869 (2005)
[101] C De Concini, C Procesi, N Reshetikhin, M Rosso, Hopf algebras with trace and representations, Inventiones mathematicae, 161, 1-44 (2005)
[102] N Reshetikhin, A Veselov, Poisson Lie groups and Hamiltonian theory of the Yang-Baxter maps, arXiv preprint math/0512328 (2005)
[103] R Kashaev, N Reshetikhin, Braiding for the quantum gl_2 at roots of unity, arXiv preprint math/0410182 (2004)
[104] AS Cattaneo, P Mnëv, N Reshetikhin, Perturbative BV-BFV theories on manifolds with boundary, preparation (2004)
[105] A Okounkov, N Reshetikhin, Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram, Journal of the American Mathematical Society, 16(3), 581-603 (2003)
[106] N Reshetikhin, Degenerate integrability of the spin Calogero–Moser systems and the duality with the spin Ruijsenaars systems, Letters in Mathematical Physics, 63, 55-71 (2003)
[107] N Reshetikhin, Integrability of characteristic Hamiltonian systems on simple Lie groups with standard Poisson Lie structure, Communications in mathematical physics, 242, 1-29 (2003)
[108] N RESHETIKHIN, M ROSSO, Hopf algebras with trace and representations DE CONCINI, Corrado PROCESI, Claudio (2003)
[109] R Kashaev, N Reshetikhin, Invariants of tangles with flat connections in their complements. I. Invariants and holonomy R-matrices, arXiv preprint math/0202211 (2002)
[110] R Kashaev, N Reshetikhin, Invariants of links with flat connections in their complements. II. Holonomy R-matrices related to quantized universal enveloping algebras at roots of 1, arXiv preprint math/0202212 (2002)
[111] E Frenkel, N Reshetikhin, Quantum affine algebras and deformations of the Virasoro and, arXiv preprint q-alg/9505025 (2002)
[112] N Reshetikhin, M Yakimov, Quantum invariant measures, Communications in Mathematical Physics, 224, 399-426 (2001)
[113] T Hoffmann, J Kellendonk, N Kutz, N Reshetikhin, Factorization Dynamics and Coxeter--Toda Lattices, Communications in Mathematical Physics, 212, 297-321 (2000)
[114] N Reshetikhin, M Yakimov, Deformation quantization of Lagrangian fiber bundles, Conférence Moshé Flato (2000)
[115] N Reshetikhin, Characteristic systems on Poisson Lie groups and their quantization, CRM Proc (2000)
[116] N Reshetikhin, L Takhtajan, Deformation quantization of Kahler manifolds, arXiv preprint math/9907171 (1999)
[117] E Frenkel, N Reshetikhin, Contemporary Mathematics Volume 248, 1999, Recent Developments in Quantum Affine Algebras and Related Topics (1999)
[118] E Frenkel, N Reshetikhin, The q-characters of representations of quantum affine algebras and deformations of W-algebras, arXiv preprint math/9810055 (1998)
[119] E Frenkel, N Reshetikhin, MA Semenov-Tian-Shansky, Drinfeld–sokolov reduction for difference operators and deformations of-algebras¶ i. the case of virasoro algebra, Communications in mathematical physics, 192(3), 605-629 (1998)
[120] JE Andersen, J Mattes, N Reshetikhin, Quantization of the algebra of chord diagrams, Mathematical Proceedings of the Cambridge Philosophical Society, 124(3), 451-467 (1998)
[121] PJ Sally Jr, M Flato, J Lepowsky, N Reshetikhin, GJ Zuckerman, Mathematical aspects of conformal and topological field theories and quantum groups, 1994, Contemporary Mathematics, 217, 175-175 (1998)
[122] E Frenkel, N Reshetikhin, Deformations of W-algebras associated to simple Lie algebras, arXiv preprint q-alg/9708006 (1997)
[123] E Frenkel, N Reshetikhin, Towards deformed chiral algebras, arXiv preprint q-alg/9706023 (1997)
[124] RM Kashaev, N Reshetikhin, Affine Toda field theory as a 3-dimensional integrable system, Communications in Mathematical Physics, 188, 251-266 (1997)
[125] N Reshetikhin, J Mattes, From Infinite Dimensional Lie Algebras to Invariants of Knots, American Mathematical Society (1997)
[126] E Frenkel, N Reshetikhin, Quantum affine algebras and deformations of the Virasoro and 237-1237-1237-1, Communications in mathematical physics, 178(1), 237-264 (1996)
[127] JE Andersen, J Mattes, N Reshetikhin, The Poisson structure on the moduli space of flat connections and chord diagrams, Topology, 35(4), 1069-1083 (1996)
[128] V Bazhanov, A Bobenko, N Reshetikhin, Quantum discrete sine-Gordon model at roots of 1: integrable quantum system on the integrable classical background, Communications in Mathematical Physics, 175, 377-400 (1996)
[129] N Reshetikhin, AA Voronov, A Weinstein, Semiquantum geometry, arXiv preprint q-alg/9606007 (1996)
[130] AN Kirillov, NY Reshetikhin, Formulas for multiplicities of occurence of irreducible components in the tensor product of representations of simple Lie algebras, Journal of Mathematical Sciences, 80, 1768-1772 (1996)
[131] N Reshetikhin, Integrable discrete systems, Quantum Groups and their Applications in Physics, 445-487 (1996)
[132] M Polyak, N Reshetikhin, On 2D Yang-Mills theory and invariants of links, Deformation Theory and Symplectic Geometry, 223-246 (1996)
[133] N Reshetikhin, Quasitriangularity of quantum groups at roots of 1, Communications in mathematical physics, 170(1), 79-99 (1995)
[134] VV Bazhanov, NY Reshetikhin, Remarks on the quantum dilogarithm, Journal of Physics A: Mathematical and General, 28(8) (1995)
[135] VV Bazhanov, NY Reshetikhin, Chiral Potts model and the discrete Sine-Gordon model at roots of unity, Preprint arXiv: hep-th/0809.2351 (1995)
[136] B Feigin, E Frenkel, N Reshetikhin, Gaudin model, Bethe ansatz and critical level, Communications in Mathematical Physics, 166, 27-62 (1994)
[137] N Reshetikhin, A Varchenko, Quasiclassical asymptotics of solutions to the KZ equations, arXiv preprint hep-th/9402126 (1994)
[138] V Ginzburg, QUANTUM GROUPS AND FLAG VARIETIES. VICTOR GINZBURG, NICOLAI RESHETIKHIN ERIC VASSEROT, Mathematical aspects of conformal and topological field theories and quantum … (1994)
[139] NY Reshetikhin, H Saleur, Lattice regularization of massive and massless integrable field theories, Nuclear Physics B, 419(3), 507-528 (1994)
[140] P Sally, M Flato, J Lepowsky, N Reshetikhin, G Zuckerman, Mathematical aspects of conformal and topological field theories and quantum groups, American Mathematical Society (1994)
[141] J Mattes, N Reshetikhin, On invariants of tangles derived from balanced categories, Conference on Quantum Topology, 269-299 (1994)
[142] N Reshetikhin, Integrable systems with discrete time, Lectures given at “Enrico Fermi” international school of physics, Varenna (1994)
[143] J Mattes, M Polyak, N Reshetikhin, On invariants of 3-manifolds derived from abelian groups, Quantum topology, 324-338 (1993)
[144] AN Kirillov, NY Reshetikhin, Formulas for multiplicities of occurrence of irreducible components into the tensor product of representations of simple Lie algebras, Zapiski Nauchnykh Seminarov POMI, 205, 30-37 (1993)
[145] IB Frenkel, NY Reshetikhin, Quantum affine algebras and holonomic difference equations, Communications in Mathematical Physics, 146(1), 1-60 (1992)
[146] N Reshetikhin, The Knizhnik-Zamolodchikov system as a deformation of the isomonodromy problem, Letters in Mathematical Physics, 26, 167-177 (1992)
[147] N Reshetikhin, Jackson-type integrals, Bethe vectors, and solutions to a difference analog of the Knizhnik-Zamolodchikov system, Letters in Mathematical Physics, 26(3), 153-165 (1992)
[148] V Lakshmibai, N Reshetikhin, Quantum flag and Schubert schemes, Contemp. Math, 134, 145-181 (1992)
[149] N Reshetikhin, Quantization of Lie bialgebras, International Mathematics Research Notices, 1992(7), 143-151 (1992)
[150] N Reshetikhin, Quantum supergroups, Quantum field theory, statistical mechanics, quantum groups and topology … (1992)
[151] IB Frenkel, NY Reshetikhin, Quantum affine algebras, commutative systems of difference equations and elliptic solutions to the Yang-Baxter equations, XXth International Conference on Differential Geometric (1992)
[152] M Herman, PJL Lebowitz, NY Reshetikhin, YG Sinai, MT Spencer et al., Chief Editor A. Jaffe, Cambridge, MA Editorial Board (1992)
[153] N Reshetikhin, VG Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Inventiones mathematicae, 103(1), 547-597 (1991)
[154] N Reshetikhin, S-matrices in integrable models of isotropic magnetic chains. I, Journal of Physics A: Mathematical and General, 24(14) (1991)
[155] NY Reshetikhin, A new exactly solvable case of an O (n)-model on a hexagonal lattice, Journal of Physics A: Mathematical and General, 24(10) (1991)
[156] NY Reshetikhin, Algebraic Bethe ansatz for SO (N)-invariant transfer matrices, Journal of Soviet Mathematics, 54, 940-951 (1991)
[157] V Lakshmibai, N Reshetikhin, Quantum Deformations of SL/B and its Schubert Varieties, ICM-90 Satellite Conference Proceedings: Special Functions, 149-168 (1991)
[158] N Reshetikhin, Invariants of links and 3-manifolds related to quantum groups, Int. Congr. Math., 2, 1373-1375 (1991)
[159] N Reshetikhin, Boston, MA 02115, Special Functions: Proceedings of the Hayashibara Forum (1991)
[160] M Aizenman, M Herman, PJL Lebowitz, NY Reshetikhin, R Schrieffer, Chief Editor A. Jaffef Cambridge, MA (1991)
[161] NY Reshetikhin, VG Turaev, Ribbon graphs and their invaraints derived from quantum groups, Communications in Mathematical Physics, 127, 1-26 (1990)
[162] N Reshetikhin, Multiparameter quantum groups and twisted quasitriangular Hopf algebras, Letters in Mathematical Physics, 20, 331-335 (1990)
[163] NY Reshetikhin, MA Semenov-Tian-Shansky, Central extensions of quantum current groups, Letters in Mathematical Physics, 19, 133-142 (1990)
[164] AN Kirillov, N Reshetikhin, $q$-Weyl group and a multiplicative formula for universal$R$-matrices (1990)
[165] N Reshetikhin, F Smirnov, Hidden quantum group symmetry and integrable perturbations of conformal field theories, Communications in Mathematical Physics, 131(1), 157-177 (1990)
[166] VV Bazhanov, N Reshetikhin, Restricted solid-on-solid models connected with simply laced algebras and conformal field theory, Journal of Physics A: Mathematical and General, 23(9) (1990)
[167] AN Kirillov, NY Reshetikhin, Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras, Journal of Soviet Mathematics, 52, 3156-3164 (1990)
[168] VV Bazhanov, NY Reshetikhin, Scattering amplitudes in offcritical models and RSOS integrable models, Progress of Theoretical Physics Supplement, 102, 301-318 (1990)
[169] V Lakshimibai, NY Reshetikhin, Quantum deformations of flag and Schubert schemes (1990)
[170] LD Faddeev, NY Reshetikhin, LA Takhtajan, Algebra i Analiz, 1 No. 1 (1989) 178, English transl: Leningr. Math. J 1, 193 (1990)
[171] A Babelon, N Reshetikhin, S Shatashvili, F Smirnoff, L Takhtajan, From Integrable Models to Quantum Groups, Fields and Particles (1990)
[172] AN Kirillov, NY Reshetikhin, Representations of the algebra Uq (sl (2)), q-orthogonal polynomials and invariants of links, Infinite dimensional Lie algebras and groups, 7, 285-339 (1989)
[173] PP Kulish, NY Reshetikhin, Universal-matrix of the quantum superalgebra osp(2 | 1), Letters in Mathematical Physics, 18, 143-149 (1989)
[174] G Moore, N Reshetikhin, A comment on quantum group symmetry in conformal field theory, Nuclear Physics B, 328(3), 557-574 (1989)
[175] LD Faddeev, Quantum groups, Boletim da Sociedade Brasileira de Matemática-Bulletin/Brazilian … (1989)
[176] NY Reshetikhin, Quasitriangular Hopf algebras and invariants of links, Algebra i Analiz, 1(2), 169-188 (1989)
[177] AG Izergin, VE Korepin, NY Reshetikhin, Conformal dimensions in Bethe ansatz solvable models, Journal of Physics A: Mathematical and General, 22(13) (1989)
[178] NY Reshetikhin, Calculation of the norm of Bethe vectors in models with SU (3)-symmetry, Journal of Soviet Mathematics, 46, 1694-1706 (1989)
[179] AN Kirillov, NY Reshetikhin, VG Kac, Infinite dimensional Lie algebras and groups, Advanced Series in Mathematical Physics, 7, 285-339 (1989)
[180] LD Faddeev, NY Reshetikhin, LA Takhtajan, Leningrad Math. J., 1, 193 (1990), Alg. Anal, 1 (1989)
[181] AG Izergin, VE Korepin, NY Reshetikhin, Field correlation functions in a one-dimensional Bose gas, Journal of Soviet Mathematics, 46, 1581-1588 (1989)
[182] NY Reshetikhin, MA Semenov-Tian-Shansky, Quantum R-matrices and factorization problems, Journal of Geometry and Physics, 5(4), 533-550 (1988)
[183] SV Kerov, AN Kirillov, NY Reshetikhin, Combinatorics, Bethe Ansatz, and representations of the symmetric group, Journal of Soviet Mathematics, 41, 916-924 (1988)
[184] LD Faddeev, NY Reshetikhin, LA Takhtajan, Quantization of Lie groups and Lie algebras, in Algebraic Analysis, Academic Press, 1, 129-139 (1988)
[185] N Reshetikhin, Quantized universal enveloping algebras, the Yang-Baxter equation and inveriants of links: I, II, preprints LOMI E-4-87, E-17-87 (1988)
[186] NY Reshetikhin, Lomi preprints E-4-87, E-17-87 (1988)
[187] AN Kirillov, NY Reshetikhin, Properties of kernels of integral equations in XXZ models of arbitrary spin, Journal of Soviet Mathematics, 40, 35-71 (1988)
[188] NY Reshetikhin, Bethe-ansats for$SO(N)$-invariant transfermatrices, Zapiski Nauchnykh Seminarov POMI, 169, 122-140 (1988)
[189] AN Kirillov, NY Reshetikhin, Classification of the string solutions of Bethe equations in an XXZ model of arbitrary spin, Journal of Soviet Mathematics, 40, 22-35 (1988)
[190] NY Reshetikhin, LOMI preprints E-4-87 and E-17-87, Leningrad (1988)
[191] AN Kirillov, NY Reshetikhin, Multiplicity of weights in irreducibile tensor representations of a complete linear superalgebra, Functional Analysis and Its Applications, 22(4), 328-330 (1988)
[192] LD Faddeev, NY Reshetikhin, LA Takhtajan, RT, T₂= T₂T, R, Algebraic Analysis: Papers Dedicated to Professor Mikio Sato on the Occasion … (1988)
[193] L Fadeev, NY Reshetikhin, LA Takhtajan, Quantization of Lie groups and Lie algebras, Algebr. Analiz., 1, 178-206 (1987)
[194] AN Kirillov, NY Reshetikhin, Exact solution of the integrable XXZ Heisenberg model with arbitrary spin. I. The ground state and the excitation spectrum, Journal of Physics A: Mathematical and General, 20(6) (1987)
[195] NY Reshetikhin, Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links, 1 (1987)
[196] E Ogievetsky, N Reshetikhin, P Wiegmann, The principal chiral field in two dimensions on classical lie algebras: the Bethe-ansatz solution and factorized theory of scattering, Nuclear Physics B, 280, 45-96 (1987)
[197] NY Reshetikhin, The spectrum of the transfer matrices connected with Kac-Moody algebras, letters in mathematical physics, 14, 235-246 (1987)
[198] NM Bogoliubov, AG Izergin, NY Reshetikhin, Finite-size effects and infrared asymptotics of the correlation functions in two dimensions, Journal of Physics A: Mathematical and General, 20(15) (1987)
[199] NY Reshetikhin, PB Weigmann, Towards the classification of completely integrable quantum field theories (the Bethe-ansatz associated with Dynkin diagrams and their automorphisms), Physics Letters B 189 (1-2), 125-131 (1987)
[200] AN Kirillov, NY Reshetikhin, Exact solution of the integrable XXZ Heisenberg model with arbitrary spin. II. Thermodynamics of the system, Journal of Physics A: Mathematical and General, 20(6) (1987)
[201] AG Izergin, VE Korepin, NY Reshetikhin, Correlation functions in a one-dimensional Bose gas, Journal of Physics A: Mathematical and General, 20(14) (1987)
[202] AN Kirillov, NY Reshetikhin, Representation of Yangians and multiplicities of occurrence of irreducible components of the tensor product of simple algebras, Zapiski Nauchnykh Seminarov POMI, 160, 211-221 (1987)
[203] LD Faddeev, NY Reshetikhin, Integrability of the principal chiral field model in 1+ 1 dimension, Annals of Physics, 167(2), 227-256 (1986)
[204] SV Kerov, AN Kirillov, NY Reshetikhin, Combinatorics Bethe ansats and representations of symmetric group, Zapiski Nauchnykh Seminarov POMI, 155, 50-64 (1986)
[205] AN Kirillov, NY Reshetikhin, Exact solution of the Heisenberg XXZ model of spin s, Journal of Soviet Mathematics, 35, 2627-2643 (1986)
[206] AN Kirillov, NY Reshetikhin, Bethe ansatz and combinatorics of Young tableaux, Zapiski Nauchnykh Seminarov POMI, 155, 65-115 (1986)
[207] PP Kulish, NY Reshetikhin, GL-invariant solutions of the Yang-Baxter equation and associated quantum systems, Journal of Soviet Mathematics, 34, 1948-1971 (1986)
[208] NY Reshetikhin, Calculation of Bethe vector norms for models with SU (3) symmetry, Problems of quantum field theory and statistical physics. 6 (1986)
[209] NM Bogolyubov, AG Izergin, NY Reshetikhin, Finite-dimensional effects and critical indices of one-dimensional quantum models, Pis' ma Zh. Eksp. Teor. Fiz., 44(9) (1986)
[210] NM Bogolyubov, AG Izergin, NY Reshetikhin, Finite-size effects and critical indices of 1D quantum models, Soviet Journal of Experimental and Theoretical Physics Letters, 44 (1986)
[211] AG Izergin, VE Korepin, NY Reshetikhin, Field carrelation functions for the one-dimensional Bose gas, Zapiski Nauchnykh Seminarov POMI, 150, 26-36 (1986)
[212] NM Bogolyubov, AG Izergin, NY Reshetikhin, fm= a+(1rc/6U) T2+ om).(4, JETP Lett, 44(9) (1986)
[213] NY Reshetikhin, Integrable models of quantum one-dimensional magnets with O (n) and Sp (2k) symmetry, Theor. Math. Phys., 63(3) (1985)
[214] NY Reshetikhin, O (N) invariant quantum field theoretical models: Exact solution, Nuclear Physics B, 251, 565-580 (1985)
[215] NY Beshetikhin, Hamiltonian structures for integrable field theory models. II. Models with O (n) and Sp (2k) symmetry on a one-dimensional lattice, Theor. Math. Phys., 63(2) (1985)
[216] AN Kirillov, NY Reshetikhin, Exact solution of the XXZ Heisenberg model of spin S, Zapiski Nauchnykh Seminarov POMI, 145, 109-133 (1985)
[217] AN Kirillov, NY Reshetikhin, A classification of string solutions of the Bethe equations for the XXZ model of arbitrary spin, Zapiski Nauchnykh Seminarov POMI, 146, 31-46 (1985)
[218] NY Reshetikhin, Hamiltonian structures for models of integrable field theory. 2. Models with O (n) and Sp (2k) symmetry on one-dimensional lattice, Teor. Mat. Fiz., 63(2) (1985)
[219] NY Reshetikhin, Exactly solvable quantum-mechanical systems on lattices associated with classical Lie algebras, Journal of Soviet Mathematics, 28, 539-549 (1985)
[220] N RESHETIKHIN, Modèles intégrables de mgnétiques quantiques unidimensionnels à symétrie O (n) et Sp (2k), Teoretičeskaâ i matematičeskaâ fizika, 63(3), 347-366 (1985)
[221] AN Kirillov, NY Reshetikhin, On the properties of integral kernels for the XXZ–model of arbitrary spin, Zapiski Nauchnykh Seminarov POMI, 146, 47-91 (1985)
[222] N RESHETIKHIN, Structures hamiltoniennes pour les modèles intégrables de la théorie du champ. II. Modèles à symétrie O (n) et Sp (2k) sur un réseau unidimensionnel, Teoretičeskaâ i matematičeskaâ fizika, 63(2), 197-207 (1985)
[223] PP Kulish, NY Reshetikhin, Integrable fermion chiral models, connected with the classical Lie algebras, Zapiski Nauchnykh Seminarov POMI, 133, 146-159 (1984)
[224] LD Faddeev, NY Reshetikhin, Integrability of a master chiral quantum field model (1984)
[225] PP Kulish, NY Reshetikhin, Quantum linear problem for the sine-Gordon equation and higher representations, Journal of Soviet Mathematics, 23, 2435-2441 (1983)
[226] PP Kulish, NY Reshetikhin, Diagonalisation of GL (N) invariant transfer matrices and quantum N-wave system (Lee model), Journal of Physics A: Mathematical and General, 16(16) (1983)
[227] NY Reshetikhin, A method of functional equations in the theory of exactly solvable quantum systems, Letters in Mathematical Physics, 7, 205-213 (1983)
[228] NY Reshetikhin, The functional equation method in the theory of exactly soluble quantum systems, Zh. Eksp. Teor. Fiz., 84(1), 190-1201 (1983)
[229] VI Vichirko, NY Reshetikhin, Excitation spectrum of the anisotropic generalization of an SU3 magnet, Theoretical and Mathematical Physics, 56(2), 805-812 (1983)
[230] NY Reshetikhin, LD Faddeev, Hamiltonian structures for integrable models of field theory, Teoreticheskaya i Matematicheskaya Fizika, 56(3), 323-343 (1983)
[231] NY Reshetikhin, LD Faddeev, Hamiltonian structures of the integrable field theory models, Teor. Mat. Fiz., 56(3) (1983)
[232] NY Reshetikhin, FA Smirnov, Quantum Floquet functions, Zapiski Nauchnykh Seminarov POMI, 131, 128-141 (1983)
[233] NY Reshetikhin, Exactly solvable quantum-meehanical systems on the lattices associated with the classical Lie algebras, Zapiski Nauchnykh Seminarov POMI, 123, 112-125 (1983)
[234] VI VICHIRKO, N RESHETIKHIN, Spectre des excitations de la généralisation anisotrope du SV3-magnétique, Teoretičeskaâ i matematičeskaâ fizika, 56(2), 260-271 (1983)
[235] N RESHETIKHIN, LD FADDEEV, Structures hamiltoniennes pour les modèles intégrables de la théorie du champ, Teoretičeskaâ i matematičeskaâ fizika, 56(3), 323-343 (1983)
[236] PP Kulish, NY Reshetikhin, On$GL_3$-invariant solutions to the Yang–Baxter equation and the assosiated quantum systems, Zapiski Nauchnykh Seminarov POMI, 120, 92-121 (1982)
[237] PP Kulish, NY Reshetikhin, EK Sklyanin, Yang-Baxter equation and representation theory: I, Letters in Mathematical Physics, 5, 393-403 (1981)
[238] PP Kulish, NY Reshetikhin, Generalized Heisenberg ferromagnet and the Gross-Neveu model, Sov. Phys. JETP, 53(1), 108-114 (1981)
[239] PP Kulish, NY Reshetikhin, Zapiski Nauchnykh Seminarov LOMI (1981)
[240] Nicolai Reshetikhin, Ananth Sridhar, Limit Shapes of the Stochastic Six Vertex Model, accepted in Communications in Mathematical Physics, arXiv:1609.01756
[241] OG Iosifovich, PF Vladimirovich, TN Vladimirovna, MA Valer'evich et al., New Perspectives in Asymptotic Representation Theory. In memory of Sergei Kerov (1946–2000)
[242] IY Sergeevich, KA Vladimirovich, SA Bronislavovich, TM Anatol'evich et al., Globus Seminar
[243] NY RESHETIKHIN, AND THEIR AUTOMORPHISMS
[244] NY Reshetikhin, A survey on the problems of deformation quantization
[245] NY Reshetikhin, On superintegrability
[246] NY Reshetikhin, On multiplicities of irreducible components in large tensor powers of representations of simple Lie groups
[247] NY Reshetikhin, On stratified structure of integrable dynamics
[248] NY Reshetikhin, On tensor powers of representations of quantum groups at roots of unity
[249] NY Reshetikhin, Integrable systems on moduli spaces of flat connections over surfaces
[250] N Reshetikhin, Poisson sigma model and quantum mechanics
[251] N Reshetikhin, On invariants of links with flat connection in the complement
[252] N Reshetikhin, On the semiclassical limit of solvable lattice models
[253] NY Reshetikhin, Spin Calogero-Moser system and two dimensional Yang-Mills theory with corners
[254] N RESHETIKHIN, Modèles intégrables de mgnétiques quantiques unidimensionnels à symétrie O (n) et Sp (2k) Integrable models of one-dimensional quantum magnetics with the O (n) and Sp (2k) symmetry
[255] VI VICHIRKO, N RESHETIKHIN, Spectre des excitations de la généralisation anisotrope du SV 3-magnétiqueExcitation spectrum of anisotropic generalization of SU (3)-ferromagnet
[256] EH Lieb, M Aizenman, JL Lebowitz, D Ruelle, IVL Flato, J Simon, E Taflin et al., Springer International,
[257] M Herman, PJL Lebowitz, NY Reshetikhin, YG Sinai, T Spencer et al., Chief Editor A. Jaffe, Cambridge, MA Editorial Board M. Aizenman, Princeton, NJ H. Araki, Kyoto A. Connes, Bures-sur-Yvette R. Dijkgraaf, Amsterdam
[258] M Sato, F Pham, BM McCoy, I Cherednik, H McKean, V Lakshmibai et al., Hayashibara Forum 1990 International Symposium on Special Functions
[259] V Chari, G Cliff, P Littelmann, N Reshetikhin, Representations of Kac-Moody Algebras and Combinatorics
[260] M Baig, A Cuervo, A Billoire, F David, M BOhm, A Denner, DV Boulatov et al., Papers to appear in forthcoming issues of Nuclear Physics BIFS
[261] N Reshetikhin, M Haiman, M Aganagic, O Ganor, Qualifying Exam Syllabus
[262] M Baig, A Cuervo, KA Benedict, Y Brihaye, P Spindel, M Creutz, R Gavai et al., Papers to appear in forthcoming issues of Nuclear Physics B [FS]

Update Time: 2025-08-12 17:00:05