D. A. Domanevsky, A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Integrable deformations of principal chiral model from solutions of associative Yang–Baxter equation”, Izv. Math., 90:1 (2026), 109–143, arXiv: 2501.08777
2.
A. M. Mostovskii, A. V. Zotov, “Classical elliptic ${\rm BC}_1$ Ruijsenaars–van Diejen model: relation to Zhukovsky–Volterra gyrostat and 1-site classical $XYZ$ model with boundaries”, Theoret. and Math. Phys., 226:2 (2026), 189–216, arXiv: 2601.06826
3.
M. Matushko, A. Mostovskii, A. Zotov, “$R$-matrix valued Lax pair for elliptic Calogero–Inozemtsev system and associative Yang–Baxter equations of $\mathrm{BC}_n$ type”, Lett. Math. Phys., 116 (2026), 11, 35 pp., arXiv: 2503.22659
D. Murinov, A. Zotov, “Elliptic Ruijsenaars-Toda and elliptic Toda chains: classical r-matrix structure and relation to XYZ chain”, Journal of Geometry and Physics, 226 (2026), 105848, 23 pp., arXiv: 2602.08143
Andrei Zotov, “On the Field Analogue of the Elliptic Spin Calogero–Moser Model: Lax Pair and Equations of Motion”, Functional Analysis and Its Applications, 59:2 (2025), 142–158, arXiv: 2407.13854
6.
R. A. Potapov, A. V. Zotov, “Interrelations between dualities in classical integrable systems and a classical–classical version of the quantum–classical duality”, Theoret. and Math. Phys., 222:2 (2025), 252–275, arXiv: 2410.19035
7.
D. Domanevsky, A. Zotov, “Classical Integrable Spin Chains of Landau–Lifshitz type from R-matrix Identities”, JETP Letters, 121:12 (2025), 921–926, arXiv: 2505.09918
8.
A. V. Zotov, “2D Classical Integrable Field Theories from Hitchin Systems on $\mathrm {SL}(NM,\mathbb C)$-Bundles with Non-trivial Characteristic Classes”, Proc. Steklov Inst. Math., 330 (2025), 479–510
9.
K. Atalikov, A. Zotov, “Field generalization of elliptic Calogero–Moser system in the form of higher rank Landau–Lifshitz model”, Journal of Experimental and Theoretical Physics, 168:4 (2025), 476–484, arXiv: 2506.00938
10.
R. Potapov, A. Zotov, “Large $N$ limit of spectral duality in classical integrable systems”, Eur. Phys. J. C, Part. Fields, 85 (2025), 1331, 12 pp., arXiv: 2508.16470
11.
Dmitrii Murinov, Andrei Zotov, “Classical $r$-matrix structure for elliptic Ruijsenaars chain and $1+1$ field analogue of Ruijsenaars–Schneider model”, J. Phys. A, 58:50 (2025), 505205, 27 pp., arXiv: 2508.12656
M. Matushko, A. Zotov, “Supersymmetric generalization of $q$-deformed long-range spin chains of Haldane–Shastry type and trigonometric $\mathrm{GL}(N|M)$ solution of associative Yang–Baxter equation”, Nuclear Phys. B, 1001 (2024), 116499, 14 pp., arXiv: 2312.04525
K. R. Atalikov, A. V. Zotov, “Gauge equivalence of $1+1$ Calogero–Moser–Sutherland field theory and a higher-rank trigonometric Landau–Lifshitz model”, Theoret. and Math. Phys., 219:3 (2024), 1004–1017, arXiv: 2403.00428
14.
Andrei Zotov, “Non-ultralocal classical $r$-matrix structure for $1+1$ field analogue of elliptic Calogero–Moser model”, J. Phys. A, 57 (2024), 315201, 28 pp., arXiv: 2404.01898
K. R. Atalikov, A. V. Zotov, “Higher-rank generalization of the 11-vertex rational $R$-matrix: IRF–vertex relations and the associative Yang–Baxter equation”, Theoret. and Math. Phys., 216:2 (2023), 1083–1103, arXiv: 2303.02391
18.
M. Matushko, Andrei Zotov, “Anisotropic spin generalization of elliptic Macdonald–Ruijsenaars operators and $R$-matrix identities”, Ann. Henri Poincaré, 24 (2023), 3373–3419, arXiv: 2201.05944
A. Gorsky, M. Vasilyev, A. Zotov, “Dualities in quantum integrable many-body systems and integrable probabilities. Part I”, JHEP, 2022:4 (2022), 159, 86 pp., arXiv: 2109.05562
A. Levin, M. Olshanetsky, A. Zotov, “2D Integrable systems, 4D Chern–Simons theory and affine Higgs bundles”, Eur. Phys. J. C, Part. Fields, 82 (2022), 635, 14 pp., arXiv: 2202.10106
K. Atalikov, A. Zotov, “Higher Rank 1 + 1 Integrable Landau–Lifshitz Field Theories from the Associative Yang–Baxter Equation”, JETP Letters, 115 (2022), 757-762, arXiv: 2204.12576
23.
E. Trunina, A. Zotov, “Lax equations for relativistic $\mathrm{G}\mathrm{L}(NM,\mathbb{C})$ Gaudin models on elliptic curve”, J. Phys. A, 55:39 (2022), 395202, 31 pp., arXiv: 2204.06137
M. G. Matushko, A. V. Zotov, “On the $R$-matrix identities related to elliptic anisotropic spin Ruijsenaars–Macdonald operators”, Theoret. and Math. Phys., 213:2 (2022), 1543–1559, arXiv: 2211.08529
2021
25.
K. Atalikov, A. Zotov, “Field theory generalizations of two-body Calogero–Moser models in the form of Landau–Lifshitz equations”, J. Geom. Phys., 164 (2021), 104161, 14 pp., arXiv: 2010.14297
A. Grekov, A. Zotov, “Characteristic determinant and Manakov triple for the double elliptic integrable system”, SciPost Phys., 10:3 (2021), 055, 34 pp., arXiv: 2010.08077
I. A. Sechin, A. V. Zotov, Theoret. and Math. Phys., 208:2 (2021), 1156–1164, arXiv: 2104.04963
28.
E. S. Trunina, A. V. Zotov, “Multi-pole extension of the elliptic models of interacting integrable tops”, Theoret. and Math. Phys., 209:1 (2021), 1331–1356, arXiv: 2104.08982
29.
A. Levin, M. Olshanetsky, A. Zotov, “Generalizations of parabolic Higgs bundles, real structures, and integrability”, J. Math. Phys., 62:10 (2021), 103502, 28 pp., arXiv: 2012.15529
A. Grekov, A. Zotov, “On Cherednik and Nazarov–Sklyanin large $N$ limit construction for integrable many-body systems with elliptic dependence on momenta”, JHEP, 2021:12 (2021), 062, 43 pp., arXiv: 2102.06853
M. Vasilyev, A. Zabrodin, A. Zotov, “Quantum-classical duality for Gaudin magnets with boundary”, Nuclear Phys. B, 952 (2020), 114931, 20 pp., arXiv: 1911.11792
I. A. Sechin, A. V. Zotov, “Integrable system of generalized relativistic interacting tops”, Theoret. and Math. Phys., 205:1 (2020), 1292–1303, arXiv: 2011.09599
35.
A. Levin, M. Olshanetsky, A. Zotov, “Odd supersymmetric Kronecker elliptic function and Yang–Baxter equations”, J. Math. Phys., 61 (2020), 103504, 9 pp., arXiv: 1910.01814
36.
M. Vasilyev, A. Zabrodin, A. Zotov, “Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary”, J. Phys. A, 53:49 (2020), 494002, 20 pp., arXiv: 2006.06717
Sovremennye problemy matematicheskoi i teoreticheskoi fiziki, Sbornik statei. K 80-letiyu so dnya rozhdeniya akademika Andreya Alekseevicha Slavnova, Trudy MIAN, 309, ed. A. K. Pogrebkov, N. A. Slavnov, A. A. Belavin, A. V. Zotov, I. V. Tyutin, MIAN, M., 2020, 346 pp.
2019
38.
A. Grekov, A. Zabrodin, A. Zotov, “Supersymmetric extension of qKZ-Ruijsenaars correspondence”, Nuclear Phys. B, 939 (2019), 174–190, arXiv: 1810.12658
Yu. Chernyakov, S. Kharchev, A. Levin, M. Olshanetsky, A. Zotov, “Generalized Calogero and Toda models”, JETP Letters, 109:2 (2019), 136–143
40.
I. A. Sechin, A. V. Zotov, “${\rm GL}_{NM}$ quantum dynamical $R$-matrix based on solution of the associative Yang–Baxter equation”, Russian Math. Surveys, 74:4 (2019), 767–769, arXiv: 1905.08724
41.
T. Krasnov, A. Zotov, “Trigonometric Integrable Tops from Solutions of Associative Yang–Baxter Equation”, Ann. Henri Poincaré, 20:8 (2019), 2671–2697, arXiv: 1812.04209
A. V. Zabrodin, A. V. Zotov, “Self–dual form of Ruijsenaars–Schneider models and ILW equation with discrete Laplacian”, Nuclear Phys. B, 927 (2018), 550–565, arXiv: 1711.01036
A. V. Zotov, “Calogero–Moser model and $R$-matrix identities”, Theoret. and Math. Phys., 197:3 (2018), 1755–1770
49.
S. Kharchev, A. Levin, M. Olshanetsky, A. Zotov, “Quasi-compact Higgs bundles and Calogero–Sutherland systems with two types of spins”, J. Math. Phys., 59:10 (2018), 103509, 36 pp., arXiv: 1712.08851
A. V. Zabrodin, A. V. Zotov, A. N. Liashyk, D. S. Rudneva, “Asymmetric six-vertex model and the classical Ruijsenaars–Schneider system of particles”, Theoret. and Math. Phys., 192:2 (2017), 1141–1153, arXiv: 1611.02497
52.
A. Zabrodin, A. Zotov, “QKZ–Ruijsenaars correspondence revisited”, Nuclear Phys. B, 922 (2017), 113–125, arXiv: 1704.04527
A. Zotov, “Relativistic elliptic matrix tops and finite Fourier transformations”, Modern Phys. Lett. A, 32:32 (2017), 1750169, 22 pp., arXiv: 1706.05601
A. Levin, M. Olshanetsky, A. Zotov, “Yang–Baxter equations with two Planck constants”, J. Phys. A: Math. Theor., 49:1 (2016), 14003, 19 pp., Exactly Solved Models and Beyond: a special issue in honour of R. J. Baxter's 75th birthday, arXiv: 1507.02617
M. Beketov, A. Liashyk, A. Zabrodin, A. Zotov, “Trigonometric version of quantum–classical duality in integrable systems”, Nuclear Phys. B, 903 (2016), 150–163, arXiv: 1510.07509
A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero–Moser systems, and KZB equations”, Theoret. and Math. Phys., 188:2 (2016), 1121–1154, arXiv: 1507.04265
59.
Andrey Levin, Mikhail Olshanetsky, Andrei Zotov, “Noncommutative extensions of elliptic integrable Euler–Arnold tops and Painlevé VI equation”, J. Phys. A, 49:39 (2016), 395202, 26 pp., arXiv: 1603.06101
A. V. Zotov, “Higher-order analogues of the unitarity condition for quantum $R$-matrices”, Theoret. and Math. Phys., 189:2 (2016), 1554–1562
2015
61.
G. Aminov, H. W. Braden, A. Mironov, A. Morozov, A. Zotov, “Seiberg-Witten curves and double-elliptic integrable systems”, J. High Energy Phys., 2015, no. 1, 033, 15 pp., arXiv: 1410.0698
G. Aminov, A. Levin, M. Olshanetsky, A. Zotov, “Classical integrable systems and Knizhnik–Zamolodchikov–Bernard equations”, JETP Letters, 101:9 (2015), 648–655
63.
A. Zabrodin, A. Zotov, “Classical-quantum correspondence and functional relations for Painlevé equations”, Constr. Approx., 41:3 (2015), 385–423, arXiv: 1212.5813
Zengo Tsuboi, Anton Zabrodin, Andrei Zotov, “Supersymmetric quantum spin chains and classical integrable systems”, J. High Energy Phys., 2015, no. 5, 086, 43 pp., arXiv: 1412.2586
A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Quantum Baxter–Belavin $R$-matrices and multidimensional Lax pairs for Painlevé VI”, Theoret. and Math. Phys., 184:1 (2015), 924–939, arXiv: 1501.07351
2014
66.
A. Gorsky, A. Zabrodin, A. Zotov, “Spectrum of quantum transfer matrices via classical many-body systems”, J. High Energy Phys., 2014, no. 1, 070, 28 pp., arXiv: 1310.6958
A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Classification of isomonodromy problems on elliptic curves”, Russian Math. Surveys, 69:1 (2014), 35–118, arXiv: 1311.4498
68.
G. Aminov, S. Arthamonov, A. Smirnov, A. Zotov, “Rational top and its classical $r$-matrix”, J. Phys. A: Math. Theor., 47:30 (2014), 305207, 19 pp., arXiv: 1402.3189
A. Levin, M. Olshanetsky, A. Zotov, “Relativistic classical integrable tops and quantum $R$-matrices”, J. High Energy Phys., 2014, no. 7, 012, arXiv: 1405.7523
A. Levin, M. Olshanetsky, A. Zotov, “Classical integrable systems and soliton equations related to eleven-vertex $R$-matrix”, Nuclear Physics B, 887 (2014), 400–422, arXiv: 1406.2995
A. Levin, M. Olshanetsky, A. Zotov, “Planck constant as spectral parameter in integrable systems and KZB equations”, JHEP, 2014, no. 10, 109, 29 pp., arXiv: 1408.6246v2
A. Mironov, A. Morozov, B. Runov, Y. Zenkevich, A. Zotov, “Spectral duality between Heisenberg chain and Gaudin model”, Lett. Math. Phys., 103:3 (2013), 299–329, arXiv: 1206.6349
A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov, “Characteristic classes of $\mathrm{SL}(N,\mathbb C)$-bundles and quantum dynamical elliptic $R$-matrices”, J. Phys. A: Math. Theor., 46:3 (2013), 035201, 25 pp., arXiv: 1208.5750
A. V. Zotov, A. V. Smirnov, “Modifications of bundles, elliptic integrable systems, and related problems”, Theoret. and Math. Phys., 177:1 (2013), 1281–1338
76.
G. Aminov, A. Mironov, A. Morozov, A. Zotov, “Three-particle integrable systems with elliptic dependence on momenta and theta function identities”, Phys. Lett. B, 726:4-5 (2013), 802–808, arXiv: 1307.1465
A. Mironov, A. Morozov, B. Runov, Y. Zenkevich, A. Zotov, “Spectral dualities in XXZ spin chains and five dimensional gauge theories”, J. High Energy Phys., 2013, no. 12, 034, 11 pp., arXiv: 1307.1502
A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov, “Characteristic classes and Hitchin systems. General construction”, Comm. Math. Phys., 316:1 (2012), 1–44, arXiv: 1006.0702
A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov, “Calogero-Moser systems for simple Lie groups and characteristic classes of bundles”, J. Geom. Phys., 62:8 (2012), 1810–1850, arXiv: 1007.4127
Andrey M. Levin, Mikhail A. Olshanetsky, Andrey V. Smirnov, Andrei V. Zotov, “Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles”, SIGMA, 8 (2012), 095, 37 pp., arXiv: 1207.4386
Andrey M. Levin, Mikhail A. Olshanetsky, Andrei V. Zotov, “Monopoles and Modifications of Bundles over Elliptic Curves”, SIGMA, 5 (2009), 065, 22 pp., arXiv: 0811.3056
A. V. Zotov, A. M. Levin, M. A. Olshanetsky, Yu. B. Chernyakov, “Quadratic algebras related to elliptic curves”, Theoret. and Math. Phys., 156:2 (2008), 1103–1122, arXiv: 0710.1072
2007
86.
A. Levin, A. Zotov, “On rational and elliptic forms of Painlevé VI equation”, Moscow Seminar on Mathematical Physics. II, Amer. Math. Soc. Transl. Ser. 2, 221, Amer. Math. Soc., Providence, RI, 2007, 173–183
A. V. Zotov, A. M. Levin, “Integrable Model of Interacting Elliptic Tops”, Theoret. and Math. Phys., 146:1 (2006), 45–52
88.
Yu. Chernyakov, A. M. Levin, M. Olshanetsky, A. Zotov, “Elliptic Schlesinger system and Painlevé VI”, J. Phys. A: Math. Gen., 39:39 (2006), 12083–12101, arXiv: nlin/0602043
A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Painlevé VI, rigid tops and reflection equation”, Comm. Math. Phys., 268:1 (2006), 67–103, arXiv: math/0508058
A. V. Zotov, “Classical integrable systems and their field-theoretical generalizations”, Physics of Particles and Nuclei, 37:3 (2006), 400-443
2005
91.
M. A. Olshanetsky, A. V. Zotov, “Isomonodromic problems on elliptic curve, rigid tops and reflection equations”, Elliptic Integrable Systems, Rokko Lectures in Mathematics, 18, eds. M. Noumi, K. Takasaki, Kobe University, Japan, 2005, 149-172http://www.math.kobe-u.ac.jp/publications/rlm18/10.pdf
2004
92.
A. Zotov, “Elliptic linear problem for the Calogero-Inozemtsev model and Painlevé VI equation”, Lett. Math. Phys., 67:2 (2004), 153–165, arXiv: hep-th/0310260
A. Zotov, “Elliptic linear problem for Painlevé VI equation with spectral parameter”, Quantum groups and integrable systems, Czechoslovak J. Phys., 53:11 (2003), 1147–1152
H. W. Braden, V. A. Dolgushev, M. A. Olshanetsky, A. V. Zotov, “Classical $r$-matrices and the Feigin-Odesskii algebra via Hamiltonian and Poisson reductions”, J. Phys. A, 36:25 (2003), 6979–7000, arXiv: hep-th/0301121
A. M. Levin, M. A. Olshanetsky, A. Zotov, “Hitchin systems—symplectic Hecke correspondence and two-dimensional version”, Comm. Math. Phys., 236:1 (2003), 93–133, arXiv: nlin/0110045
A. V. Zotov, Yu. B. Chernyakov, “Integrable Many-Body Systems via the Inosemtsev Limit”, Theoret. and Math. Phys., 129:2 (2001), 1526–1542
97.
A. Zotov, “On relation between Weyl and Kontsevich quantum products. Direct evaluation up to the $\hslash^3$-order”, Modern Phys. Lett. A, 16:10 (2001), 615–625
Àññîöèàòèâíîå óðàâíåíèå ßíãà-Áàêñòåðà, $R$-ìàòðè÷íûå òîæäåñòâà è èíòåãðèðóåìûå ñèñòåìû A. V. Zotov Seminar of the Department of Geometry and Topology of the Steklov Mathematical Institute, RAS,
and the Department of Geometry and Topology of the Faculty of Mechanics and Mathematics, MSU
"Geometry, Topology and Mathematical Physics" (Novikov Seminar) October 14, 2025 18:30
2026
