My publications (Math.Reviews)
Chekhov, Leonid; Mazzocco, Marta; Rubtsov, Vladimir; Quantised Painlevé monodromy manifolds, Sklyanin and Calabi-Yau algebras.
Adv. Math. 376 (2021), 107442, 52 pp.
Rubtsov, Vladimir; On energy-information balance in automatic control systems revisited. Entropy 22 (2020), no. 11, Paper No. 1300, 18 pp.
Huru, Hilja; Krasil'shchik, Iosif; Kruglikov, Boris; Roubtsov, Vladimir; Editors' preface to the topical issue on the geometry and algebra of PDEs.
J. Geom. Phys. 141 (2019), 159–160.
Lychagin, Valentin V.; Roubtsov, Volodya; Monge-Ampère Grassmannians, characteristic classes and all that. Nonlinear PDEs, their geometry,
and applications, 233–257, Tutor. Sch. Workshops Math. Sci., Birkhäuser/Springer, Cham, 2019.
Banos, Bertrand; Roubtsov, Volodya; Roulstone, Ian; On the geometry arising in some meteorological models in two and three
dimensions. Nonlinear PDEs, their geometry, and applications, 185–207, Tutor. Sch. Workshops Math. Sci., Birkhäuser/Springer, Cham, 2019.
Rubtsov, Volodya; Geometry of Monge-Ampère structures. Nonlinear PDEs, their geometry, and applications, 95–156, Tutor. Sch. Workshops
Math. Sci., Birkhäuser/Springer, Cham,2019.
Chekhov, Leonid; Mazzocco, Marta; Rubtsov, Vladimir; Algebras of quantum monodromy data and character varieties. Geometry and physics.
Vol. I, 39–68, Oxford Univ. Press, Oxford, 2018.
Bertola, M.; Cafasso, M.; Rubtsov, V.; Noncommutative Painlevé equations and systems of Calogero type. Comm. Math. Phys. 363 (2018), no. 2,
503–530.
Aldrovandi, E.; Bruzzo, U.; Rubtsov, V.; Lie algebroid cohomology and Lie algebroid extensions. J. Algebra 505 (2018), 456–481.
Chekhov, Leonid O.; Mazzocco, Marta; Rubtsov, Vladimir N.; Painlevé monodromy manifolds, decorated character varieties, and cluster
algebras. Int. Math. Res. Not. IMRN2017, no. 24, 7639–7691.
Landi, Giovanni; Rubtsov, Vladimir; Sala, Francesco; Interactions between geometry and physics: a special issue in honor of Ugo Bruzzo's
60th birthday [Editorial]. J. Geom. Phys. 118 (2017), 1–3.
Matveev, Vladimir S.; Miranda, Eva; Rubtsov, Vladimir; Przybylska, Maria; Tabachnikov, Sergei; Preface [FDIS 2015:
Finite dimensional integrable systems in geometry and mathematical physics]. Held in Będlewo, July 12–17, 2015. J. Geom. Phys. 115 (2017), 1.
Krasil'shchik, Joseph; Rubtsov, Volodya; Nonlinear partial differential equations: integrability, geometry and related topics [Editorial].
- Banos, B.; Roubtsov, V. N.; Roulstone, I.; Monge-Ampère structures and the geometry of incompressible flows. J. Phys. A 49 (2016), no. 24, 244003, 17 pp.
- Avan, Jean; Ragoucy, Eric; Rubtsov, Vladimir; Quantization and dynamisation of trace-Poisson brackets. Comm. Math. Phys. 341 (2016), no. 1, 263–287.
- Gurevich, Dimitri; Rubtsov, Vladimir; Saponov, Pavel; Škoda, Zoran; Generalizations of Poisson structures related to rational Gaudin model. Ann. Henri Poincaré 16 (2015), no. 7, 1689–1707.
- Bruzzo, Ugo; Mencattini, Igor; Rubtsov, Vladimir N.; Tortella, Pietro; Nonabelian holomorphic Lie algebroid extensions. Internat. J. Math. 26 (2015), no. 5, 1550040, 26 pp.
- Odesskii, Alexander; Rubtsov, Vladimir; Sokolov, Vladimir; Parameter-dependent associative Yang-Baxter equations and Poisson brackets. Int. J. Geom. Methods Mod. Phys. 11 (2014), no. 9, 1460036, 18 pp.
- Chervov, A.; Falqui, G.; Rubtsov, V.; Silantyev, A. Algebraic properties of Manin matrices II: $q$-analogues and integrable systems. Adv. in Appl. Math. 60 (2014), 25–89.
- Odesskii, Alexander; Rubtsov, Vladimir; Sokolov, Vladimir Double Poisson brackets on free associative algebras. "Noncommutative birational geometry, representations and combinatorics", 225–239, Contemp. Math., 592, Amer. Math. Soc., Providence, RI, 2013.
- Odesskii, A. V.; Rubtsov, V. N.; Sokolov, V. V. Bi-Hamiltonian ordinary differential equations with matrix variables. Translation of Teoret. Mat. Fiz. 171 (2012), no. 1, 26–32. Theoret. and Math. Phys. 171 (2012), no. 1, 442–447.
- Bruzzo, Ugo; Rubtsov, Vladimir On localization in holomorphic equivariant cohomology. Cent. Eur. J. Math. 10 (2012), no. 4, 1442–1454.
- Ortenzi, G.; Rubtsov, V.; Tagne Pelap, S. R. Integer solutions of integral inequalities and $H$-invariant Jacobian Poisson structures. Adv. Math. Phys. 2011, Art. ID 252186, 18 pp.
- Ortenzi, Giovanni; Rubtsov, Vladimir; Tagne Pelap, Serge Roméo On the Heisenberg invariance and the elliptic Poisson tensors. Lett. Math. Phys. 96 (2011), no. 1-3, 263–284.
- Retakh, Vladimir; Rubtsov, Vladimir Noncommutative Toda chains, Hankel quasideterminants and the Painlevé II equation. J. Phys. A 43 (2010), no. 50, 505204, 13 pp.
- Kosmann-Schwarzbach, Yvette; Rubtsov, Vladimir Compatible structures on Lie algebroids and Monge-Ampère operators. Acta Appl. Math. 109 (2010), no. 1, 101–135.
- Rubtsov, Vladimir; Silantyev, Alexey; Talalaev, Dmitri Manin matrices, quantum elliptic commutative families and characteristic polynomial of elliptic Gaudin model. SIGMA Symmetry Integrability Geom. Methods Appl. 5 (2009), Paper 110, 22 pp.
- Roubtsov, V.; Skrypnyk, T. Compatible Poisson brackets, quadratic Poisson algebras and classical $r$-matrices. "Differential equations: geometry, symmetries and integrability," 311–333, Abel Symp., 5, Springer, Berlin, 2009.
- Dolgushev, V. A.; Rubtsov, V. N. An algebraic index theorem for Poisson manifolds. J. Reine Angew. Math. 633 (2009), 77–113.
- Chervov, A.; Falqui, G.; Rubtsov, V. Algebraic properties of Manin matrices. I. Adv. in Appl. Math. 43 (2009), no. 3, 239–315.
- Roulstone, I.; Banos, B.; Gibbon, J. D.; Roubtsov, V. N. A geometric interpretation of coherent structures in Navier-Stokes flows. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009), no. 2107, 2015–2021.
- Brutstso, U.; Chirio, L.; Rossi, P.; Rubtsov, V. N. Equivariant cohomology and localization for Lie algebroids. (Russian) Funktsional. Anal. i Prilozhen. 43 (2009), no. 1, 22--36; translation in Funct. Anal. Appl. 43 (2009), no. 1, 18–29
- Odesskii, Alexander; Rubtsov, Vladimir Integrable systems associated with elliptic algebras. "Quantum groups", 81–105, IRMA Lect. Math. Theor. Phys., 12, Eur. Math. Soc., Zürich, 2008.
- Pakuliak, S.; Rubtsov, V.; Silantyev, A. The SOS model partition function and the elliptic weight functions. J. Phys. A 41 (2008), no. 29, 295204, 20 pp.
- Pakuliak, Stanislav; Rubtsov, Vladimir; Silantyev, Alexey Classical elliptic current algebras. II. J. Gen. Lie Theory Appl. 2 (2008), no. 2, 79–93.
- Pakuliak, Stanislav; Rubtsov, Vladimir; Silantyev, Alexey Classical elliptic current algebras. I. J. Gen. Lie Theory Appl. 2 (2008), no. 2, 65–78.
- Ortenzi, Giovanni; Pedroni, Marco; Rubtsov, Vladimir On the higher Poisson structures of the Camassa-Holm hierarchy. Acta Appl. Math. 101 (2008), no. 1-3, 243–254.
- Enriquez, B.; Rubtsov, V. Hecke-Tyurin parametrization of the Hitchin and KZB systems. "Moscow Seminar on Mathematical Physics. II", 1–31, Amer. Math. Soc. Transl. Ser. 2, 221, Amer. Math. Soc., Providence, RI, 2007.
- Rubtsov, Vladimir Hitchin and Beauville-Mukai system: classical and quantum correspondence. Acta Appl. Math. 99 (2007), no. 3, 283–292.
- Enriquez, B.; Pakuliak, S.; Rubtsov, V. Basic representations of quantum current algebras in higher genus. "Quantum groups", 177–190, Contemp. Math., 433, Amer. Math. Soc., Providence, RI, 2007.
- Kushner, Alexei; Lychagin, Valentin; Rubtsov, Vladimir Contact geometry and non-linear differential equations. "Encyclopedia of Mathematics and its Applications", 101. Cambridge University Press, Cambridge, 2007. xxii+496 pp. ISBN: 978-0-521-82476-7; 0-521-82476-1.
- Iorgov, Nikolai; Roubtsov, Vladimir; Shadura, Vitaly; Tykhyy, Yuri Relativistic Toda chain with boundary interaction at root of unity. SIGMA Symmetry Integrability Geom. Methods Appl. 3 (2007), Paper 013, 14 pp.
- Enriquez, B.; Rubtsov, V. Quantizations of the Hitchin and Beauville-Mukai integrable systems. Mosc. Math. J. 5 (2005), no. 2, 329–370, 493.
- Enriquez, Benjamin; Rubtsov, Vladimir Commuting families in skew fields and quantization of Beauville's fibration. Duke Math. J. 119 (2003), no. 2, 197–219.
- Odesskiĭ, A. V.; Rubtsov, V. N. Polynomial Poisson algebras with a regular structure of symplectic leaves. (Russian) Teoret. Mat. Fiz. 133 (2002), no. 1, 3--23; translation in Theoret. and Math. Phys. 133 (2002), no. 1, 1321–1337.
- Braden, H. W.; Gorsky, A.; Odesskii, A.; Rubtsov, V. Double-elliptic dynamical systems from generalized Mukai-Sklyanin algebras. Nuclear Phys. B 633 (2002), no. 3, 414–442.
- Gorsky, A.; Rubtsov, V. Dualities in integrable systems: geometrical aspects. "Integrable structures of exactly solvable two-dimensional models of quantum field theory" (Kiev, 2000), 173–198, NATO Sci. Ser. II Math. Phys. Chem., 35, Kluwer Acad. Publ., Dordrecht, 2001.
- Gorsky, A.; Nekrasov, N.; Rubtsov, V. Hilbert schemes, separated variables, and D-branes. Comm. Math. Phys. 222 (2001), no. 2, 299–318.
- Roubtsov, V. N.; Roulstone, I. Holomorphic structures in hydrodynamical models of nearly geostrophic flow. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 457 (2001), no. 2010, 1519–1531.
- Fock, Vladimir; Gorsky, Alexander; Nekrasov, Nikita; Rubtsov, Vladimir Duality in integrable systems and gauge theories. J. High Energy Phys. 2000, no. 7, Paper 28, 40 pp.
- Enriquez, B.; Rubtsov, V. Some examples of quantum groups in higher genus. "Moscow Seminar in Mathematical Physics", 33–65, Amer. Math. Soc. Transl. Ser. 2, 191, Amer. Math. Soc., Providence, RI, 1999.
- Enriquez, Benjamin; Rubtsov, Vladimir Quasi-Hopf algebras associated with $\germ{sl}_2$ and complex curves. Israel J. Math. 112 (1999), 61–108.
- Gurevich, D.; Donin, J.; Rubtsov, V. Two types of Poisson pencils and related quantum objects. "Lie groups and Lie algebras," 27–46, Math. Appl., 433, Kluwer Acad. Publ., Dordrecht, 1998.
- Enriquez, B.; Feigin, B.; Rubtsov, V. Separation of variables for Gaudin-Calogero systems. Compositio Math. 110 (1998), no. 1, 1–16.
- Bugrij, A. I.; Shadura, V. N.; Rubtsov, V. Covariant differential and integral calculi for lattice $(1,q)$-deformed fields. Hadronic J. 20 (1997), no. 2, 191–211.
- Donin, J.; Gurevich, D.; Rubtsov, V. Quantum hyperboloid and braided modules. "Algèbre non commutative, groupes quantiques et invariants"(Reims, 1995), 103–118, Sémin. Congr., 2, Soc. Math. France, Paris, 1997.
- Enriquez, B.; Rubtsov, V. N. Quantum groups in higher genus and Drinfeld's new realizations method (${\germ s\germ l}_2$ case). Ann. Sci. École Norm. Sup. (4) 30 (1997), no. 6, 821–846.
- Rubtsov, V. N.; Roulstone, I. Corrigendum: "Examples of quaternionic and Kähler structures in Hamiltonian models of nearly geostrophic flow''. J. Phys. A 30 (1997), no. 10, 3739.
- Rubtsov, V. N.; Roulstone, I. Examples of quaternionic and Kähler structures in Hamiltonian models of nearly geostrophic flow. J. Phys. A 30 (1997), no. 4, L63–L68.
- Enriquez, B.; Rubtsov, V. Compatible Poisson-Lie structures on the loop group of ${\rm sl}_2$. Lett. Math. Phys. 38 (1996), no. 4, 429–436.
- Enriquez, B.; Rubtsov, V. Hitchin systems, higher Gaudin operators and $R$-matrices. Math. Res. Lett. 3 (1996), no. 3, 343–357.
- Enriquez, B.; Orlov, A. Yu.; Rubtsov, V. N. Dispersionful analogues of Benney's equations and $N$-wave systems. Inverse Problems 12 (1996), no. 3, 241–250.
- Gurevich, D.; Rubtsov, V. Quantization of Poisson pencils and generalized Lie algebras. Teoret. Mat. Fiz. 103 (1995), no. 3, 476--488; reprinted in Theoret. and Math. Phys. 103 (1995), no. 3, 713–722.
- Gorsky, A.; Marshakov, A.; Orlov, A.; Rubtsov, V. On third Poisson structure of KdV equation. Teoret. Mat. Fiz. 103 (1995), no. 3, 461--466; reprinted in Theoret. and Math. Phys. 103 (1995), no. 3, 701–705
- Enriquez, B.; Khoroshkin, S.; Radul, A.; Rosly, A.; Rubtsov, V. Poisson-Lie aspects of classical $W$-algebras. "The interplay between differential geometry and differential equations" , 37–59, Amer. Math. Soc. Transl. Ser. 2, 167, Amer. Math. Soc., Providence, RI, 1995.
- Lychagin, Valentin; Rubtsov, Vladimir Non-holonomic filtration: algebraic and geometric aspects of non-integrability. "Geometry in partial differential equations", 189–214, World Sci. Publ., River Edge, NJ, 1994.
- Enriquez, B.; Rubtsov, V.; Orlov, A. Higher Hamiltonian structures (the ${\rm sl}_2$ case). JETP Lett. 58 (1993), no. 8, 658–664; translated from Pisʹma Zh. Èksper. Teoret. Fiz. 58 (1993), no. 8, 677--683(Russian).
- Lychagin, V. V.; Rubtsov, V. N.; Chekalov, I. V. A classification of Monge-Ampère equations. Ann. Sci. École Norm. Sup. (4) 26 (1993), no. 3, 281–308.
- Khoroshkin, Sergei; Radul, Andrey; Rubtsov, Vladimir A family of Poisson structures on Hermitian symmetric spaces. Comm. Math. Phys. 152 (1993), no. 2, 299–315.
- Rubtsov, V. N. Topological invariants of elliptic Spencer complexes of Lie equations. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. 1992, no. 5, 74–92.
- Gurevich, D. I.; Lychagin, V. V.; Rubtsov, V. N. Nonholonomic filtration of the cohomology of Lie algebras and "large brackets''. (Russian) Mat. Zametki 52 (1992), no. 1, 36--41, 155; translation in Math. Notes 52 (1992), no. 1-2, 657–661 (1993).
- Gurevich, D.; Rubtsov, V. Yang-Baxter equation and deformation of associative and Lie algebras. "Quantum groups" (Leningrad, 1990), 47–55, Lecture Notes in Math., 1510, Springer, Berlin, 1992.
- Gurevich, D.; Radul, A.; Rubtsov, V. Noncommutative differential geometry related to the Yang-Baxter equation. (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 199 (1992), "Voprosy Kvant. Teor. Polya Statist. Fiz." 11, 51--70, 185; translation in J. Math. Sci. 77 (1995), no. 2, 3051–3062.
- Gurevich, Dmitri; Rubtsov, Vladimir; Zobin, Naum Quantization of Poisson pairs: the $R$-matrix approach. J. Geom. Phys. 9 (1992), no. 1, 25–44.
- Gourevitch, Dimitri; Rubtsov, Vladimir Équation de Yang-Baxter et $S$-traces. (French) [The Yang-Baxter equation and $S$-traces] C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 11, 809–812.
- Gourevitch, Dimitri; Lychagin, Valentin; Rubtsov, Vladimir Cohomologie de "grand crochet'' et filtration "non-holonome''. (French) ["Big bracket'' cohomology and "nonholonomic'' filtration] C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 12, 855–858.
- Rubtsov, V. N. Remarks on Lefschetz formulas for elliptic Spencer complexes. (Russian) "Algebraic problems in analysis and topology" (Russian), 142–147, 162–163, Novoe Global. Anal., Voronezh. Gos. Univ., Voronezh, 1990.
- Lychagin, V. V.; Rubtsov, V. N. Topological indices of Spencer complexes that are associated with geometric structures. (Russian) Mat. Zametki 45 (1989), no. 4, 59--68, 126; translation in Math. Notes 45 (1989), no. 3-4, 305–312.
- Lychagin, V. V.; Rubtsov, V. N. The theorems of Sophus Lie for the Monge-Ampère equations. (Russian) Dokl. Akad. Nauk BSSR 27 (1983), no. 5, 396–398.
- Lychagin, V. V.; Rubtsov, V. N. Local classification of Monge-Ampère differential equations. (Russian) Dokl. Akad. Nauk SSSR 272 (1983), no. 1, 34–38.
- Rubtsov, V. N. Relatively invariant ${\rm Der}$-cohomology of modules. (Russian) Uspekhi Mat. Nauk 38 (1983), no. 1(229), 189–190.
- Rubcov, V. N. Cohomology of the Der-complex. (Russian) Uspekhi Mat. Nauk 35 (1980), no. 4(214), 209–210.