Symplectic geometry, Poisson geometry, algebraic geometry, differential geometry and Riemannian geometry, nonlinear equations of mathematical physics, integrable systems, Hamiltonian and bi-Hamiltonian systems, discrete geometry and discrete equations, systems of hydrodynamic type, commuting differential operators.
Main publications:
O. I. Mokhov, Symplectic and Poisson geometry on loop spaces of smooth manifolds and integrable equations, Reviews in Mathematics and Mathematical Physics, 11, part 2, eds. S. P. Novikov and I. M. Krichever, Harwood Academic Publishers, Amsterdam, 2001, 204
O. I. Mokhov, “Soglasovannye i pochti soglasovannye psevdorimanovy metriki”, Funktsionalnyi analiz i ego prilozheniya, 35:2 (2001), 24–36
O. I. Mokhov, “Simplekticheskie i puassonovy struktury na prostranstvakh petel gladkikh mnogoobrazii i integriruemye sistemy”, Uspekhi matematicheskikh nauk, 53:3 (1998), 85–192
O. I. Mokhov, “O gruppakh kogomologii kompleksov odnorodnykh form na prostranstvakh petel gladkikh mnogoobrazii”, Funktsionalnyi analiz i ego prilozheniya, 32:3 (1998), 22–34
O. I. Mokhov, “Kommutiruyuschie differentsialnye operatory ranga 3 i nelineinye uravneniya”, Izvestiya AN SSSR, seriya matematicheskaya, 53:6 (1989), 1291–1315
E. V. Glukhov, O. I. Mokhov, “Algebraic-geometry approach to construction
of semi-Hamiltonian systems of hydrodynamic type”, Izv. RAN. Ser. Mat., 87:6 (2023), 35–48; Izv. Math., 87:6 (2023), 1148–1160
2021
2.
A. M. Gagonov, O. I. Mokhov, “On compatible diagonal metrics”, Uspekhi Mat. Nauk, 76:6(462) (2021), 195–196; Russian Math. Surveys, 76:6 (2021), 1140–1142
2020
3.
E. V. Glukhov, O. I. Mokhov, “On algebraic-geometry methods for constructing submanifolds with flat normal bundle and holonomic net of curvature lines”, Funktsional. Anal. i Prilozhen., 54:3 (2020), 26–37; Funct. Anal. Appl., 54:3 (2020), 169–178
E. V. Glukhov, O. I. Mokhov, “On algebraic-geometry methods for constructing flat diagonal metrics of a special form”, Uspekhi Mat. Nauk, 74:4(448) (2019), 185–186; Russian Math. Surveys, 74:4 (2019), 761–763
O. I. Mokhov, N. A. Strizhova, “Liouville integrability of the reduction of the associativity equations on the set of stationary points of an integral in the case of three primary fields”, Uspekhi Mat. Nauk, 74:2(446) (2019), 191–192; Russian Math. Surveys, 74:2 (2019), 369–371
2018
6.
O. I. Mokhov, N. A. Strizhova, “Classification of the associativity equations possessing a Hamiltonian structure of Dubrovin–Novikov type”, Uspekhi Mat. Nauk, 73:1(439) (2018), 183–184; Russian Math. Surveys, 73:1 (2018), 175–177
O. I. Mokhov, N. A. Pavlenko, “Classification of the associativity equations with a first-order Hamiltonian operator”, TMF, 197:1 (2018), 124–137; Theoret. and Math. Phys., 197:1 (2018), 1501–1513
O. I. Mokhov, “On Commutative Subalgebras of the Weyl Algebra Related to Commuting Operators of Arbitrary Rank and Genus”, Mat. Zametki, 94:2 (2013), 314–316; Math. Notes, 94:2 (2013), 298–300
O. I. Mokhov, “Deformations of Poisson Structures by Closed $3$-Forms”, Mat. Zametki, 89:6 (2011), 944–947; Math. Notes, 89:6 (2011), 899–902
12.
Oleg I. Mokhov, “On Initial Data in the Problem of Consistency on Cubic Lattices for $3\times3$ Determinants”, SIGMA, 7 (2011), 075, 19 pp.
13.
O. I. Mokhov, “Compatible metrics and the diagonalizability of nonlocally bi-Hamiltonian systems of hydrodynamic type”, TMF, 167:1 (2011), 3–22; Theoret. and Math. Phys., 167:1 (2011), 403–420
O. I. Mokhov, “Riemann invariants of semisimple non-locally bi-Hamiltonian systems of hydrodynamic type and compatible metrics”, Uspekhi Mat. Nauk, 65:6(396) (2010), 189–190; Russian Math. Surveys, 65:6 (2010), 1183–1185
O. I. Mokhov, “Realization of Frobenius Manifolds as Submanifolds in Pseudo-Euclidean Spaces”, Trudy Mat. Inst. Steklova, 267 (2009), 226–244; Proc. Steklov Inst. Math., 267 (2009), 217–234
O. I. Mokhov, “Consistency on Cubic Lattices for Determinants of Arbitrary Orders”, Trudy Mat. Inst. Steklova, 266 (2009), 202–217; Proc. Steklov Inst. Math., 266 (2009), 195–209
O. I. Mokhov, “The Classification of Nonsingular Multidimensional Dubrovin–Novikov Brackets”, Funktsional. Anal. i Prilozhen., 42:1 (2008), 39–52; Funct. Anal. Appl., 42:1 (2008), 33–44
O. I. Mokhov, “Duality in a special class of submanifolds and Frobenius manifolds”, Uspekhi Mat. Nauk, 63:2(380) (2008), 177–178; Russian Math. Surveys, 63:2 (2008), 378–380
O. I. Mokhov, “Theory of submanifolds, associativity equations in 2D topological quantum field theories, and Frobenius manifolds”, TMF, 152:2 (2007), 368–376; Theoret. and Math. Phys., 152:2 (2007), 1183–1190
O. I. Mokhov, “Nonlocal Hamiltonian Operators of Hydrodynamic Type with Flat Metrics, Integrable Hierarchies, and the Associativity Equations”, Funktsional. Anal. i Prilozhen., 40:1 (2006), 14–29; Funct. Anal. Appl., 40:1 (2006), 11–23
O. I. Mokhov, “Systems of integrals in involution and associativity equations”, Uspekhi Mat. Nauk, 61:3(369) (2006), 175–176; Russian Math. Surveys, 61:3 (2006), 568–570
O. I. Mokhov, “The classification of multidimensional Poisson brackets of hydrodynamic type”, Uspekhi Mat. Nauk, 61:2(368) (2006), 167–168; Russian Math. Surveys, 61:2 (2006), 356–358
O. I. Mokhov, “Non-local Hamiltonian operators of hydrodynamic type with flat metrics, and the
associativity equations”, Uspekhi Mat. Nauk, 59:1(355) (2004), 187–188; Russian Math. Surveys, 59:1 (2004), 191–192
O. I. Mokhov, “Lax Pairs for Equations Describing Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Reductions of the Lamй Equations”, TMF, 138:2 (2004), 283–296; Theoret. and Math. Phys., 138:2 (2004), 238–249
O. I. Mokhov, “The Liouville Canonical Form for Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Hierarchies”, Funktsional. Anal. i Prilozhen., 37:2 (2003), 28–40; Funct. Anal. Appl., 37:2 (2003), 103–113
O. I. Mokhov, “Quasi-Frobenius Algebras and Their Integrable $N$-Parameter Deformations Generated by Compatible $(N\times N)$ Metrics of Constant Riemannian Curvature”, TMF, 136:1 (2003), 20–29; Theoret. and Math. Phys., 136:1 (2003), 908–916
O. I. Mokhov, “Compatible Metrics of Constant Riemannian Curvature: Local Geometry, Nonlinear Equations, and Integrability”, Funktsional. Anal. i Prilozhen., 36:3 (2002), 36–47; Funct. Anal. Appl., 36:3 (2002), 196–204
O. I. Mokhov, “The Lax pair for non-singular pencils of metrics of constant Riemannian curvature”, Uspekhi Mat. Nauk, 57:3(345) (2002), 155–156; Russian Math. Surveys, 57:3 (2002), 603–605
O. I. Mokhov, “Compatible Dubrovin–Novikov Hamiltonian Operators, Lie Derivative, and Integrable Systems of Hydrodynamic Type”, TMF, 133:2 (2002), 279–288; Theoret. and Math. Phys., 133:2 (2002), 1557–1564
O. I. Mokhov, “Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Hierarchies Related to Them”, TMF, 132:1 (2002), 60–73; Theoret. and Math. Phys., 132:1 (2002), 942–954
O. I. Mokhov, “Integrability of the Equations for Nonsingular Pairs of Compatible Flat Metrics”, TMF, 130:2 (2002), 233–250; Theoret. and Math. Phys., 130:2 (2002), 198–212
O. I. Mokhov, “Compatible and Almost Compatible Pseudo-Riemannian Metrics”, Funktsional. Anal. i Prilozhen., 35:2 (2001), 24–36; Funct. Anal. Appl., 35:2 (2001), 100–110
O. I. Mokhov, “Flat pencils of metrics and integrable reductions of Lamé's equations”, Uspekhi Mat. Nauk, 56:2(338) (2001), 221–222; Russian Math. Surveys, 56:2 (2001), 416–418
O. I. Mokhov, “Compatible Poisson Structures of Hydrodynamic Type and Associativity Equations”, Trudy Mat. Inst. Steklova, 225 (1999), 284–300; Proc. Steklov Inst. Math., 225 (1999), 269–284
O. I. Mokhov, “On the Cohomology Groups of Complexes of Homogeneous Forms on Loop Spaces of Smooth Manifolds”, Funktsional. Anal. i Prilozhen., 32:3 (1998), 22–34; Funct. Anal. Appl., 32:3 (1998), 162–171
O. I. Mokhov, “Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Uspekhi Mat. Nauk, 53:3(321) (1998), 85–192; Russian Math. Surveys, 53:3 (1998), 515–622
O. I. Mokhov, “Differential geometry of symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Trudy Mat. Inst. Steklova, 217 (1997), 100–134; Proc. Steklov Inst. Math., 217 (1997), 91–125
O. I. Mokhov, E. V. Ferapontov, “The Associativity Equations in the Two-Dimensional Topological Field Theory as Integrable Hamiltonian
Nondiagonalizable Systems of Hydrodynamic Type”, Funktsional. Anal. i Prilozhen., 30:3 (1996), 62–72; Funct. Anal. Appl., 30:3 (1996), 195–203
O. I. Mokhov, “Complex homogeneous forms on loop spaces of smooth manifolds and their cohomology groups”, Uspekhi Mat. Nauk, 51:2(308) (1996), 141–142; Russian Math. Surveys, 51:2 (1996), 341–342
O. I. Mokhov, E. V. Ferapontov, “Hamiltonian Pairs Associated with Skew-Symmetric Killing Tensors on Spaces of Constant Curvature”, Funktsional. Anal. i Prilozhen., 28:2 (1994), 60–63; Funct. Anal. Appl., 28:2 (1994), 123–125
O. I. Mokhov, “Homogeneous symplectic structures of second order on loop spaces and symplectic connections”, Funktsional. Anal. i Prilozhen., 25:2 (1991), 65–67; Funct. Anal. Appl., 25:2 (1991), 136–137
O. I. Mokhov, “Canonical Hamiltonian representation of the Krichever–Novikov equation”, Mat. Zametki, 50:3 (1991), 87–96; Math. Notes, 50:3 (1991), 939–945
O. I. Mokhov, “Симплектические формы на пространстве петель и риманова геометрия”, Funktsional. Anal. i Prilozhen., 24:3 (1990), 86–87; Funct. Anal. Appl., 24:3 (1990), 247–249
O. I. Mokhov, E. V. Ferapontov, “Non-local Hamiltonian operators of hydrodynamic type related to metrics of constant curvature”, Uspekhi Mat. Nauk, 45:3(273) (1990), 191–192; Russian Math. Surveys, 45:3 (1990), 218–219
O. I. Mokhov, “A Hamiltonian structure of evolution in the space variable $x$ for the Korteweg–de Vries equation”, Uspekhi Mat. Nauk, 45:1(271) (1990), 181–182; Russian Math. Surveys, 45:1 (1990), 218–220
O. I. Mokhov, “Commuting differential operators of rank 3, and nonlinear differential equations”, Izv. Akad. Nauk SSSR Ser. Mat., 53:6 (1989), 1291–1315; Math. USSR-Izv., 35:3 (1990), 629–655
O. I. Mokhov, “Canonical variables for the two-dimensional hydrodynamics of an incompressible fluid with vorticity”, TMF, 78:1 (1989), 136–139; Theoret. and Math. Phys., 78:1 (1989), 97–99
O. I. Mokhov, “On the Hamiltonian property of an arbitrary evolution system on the set of stationary points of its integral”, Izv. Akad. Nauk SSSR Ser. Mat., 51:6 (1987), 1345–1352; Math. USSR-Izv., 31:3 (1988), 657–664
O. I. Mokhov, “The Hamiltonian property of an evolutionary flow on the set of stationary points of its integral”, Uspekhi Mat. Nauk, 39:4(238) (1984), 173–174; Russian Math. Surveys, 39:4 (1984), 133–134
O. I. Mokhov, S. P. Novikov, A. K. Pogrebkov, “Irina Yakovlevna Dorfman (obituary)”, Uspekhi Mat. Nauk, 50:6(306) (1995), 151–156; Russian Math. Surveys, 50:6 (1995), 1241–1246
Метрики диагональной кривизны O. I. Mokhov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) April 19, 2017 18:30
Согласованные метрики и римановы инварианты. II O. I. Mokhov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) November 3, 2010 18:30
16.
Согласованные метрики и римановы инварианты. I O. I. Mokhov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) October 27, 2010 18:30
О двойственности в специальном классе многообразий O. I. Mokhov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) April 30, 2008