Photo of Anatoly Vershik Anatoly Vershik

Head of the Laboratory of Representation Theory
and Dynamical Systems
,
St.Petersburg Department of Steklov Institute of Mathematics,
27 Fontanka, St.Petersburg 191023, Russia

Professor of the Chair of Mathematical Analysis,
Department of Mathematics and Mechanics,
St.Petersburg State University

Phone: +7(812) 312-88-29
Fax:     +7(812) 310-53-77
E-mail : vershik@pdmi.ras.ru



List of publications

Research papers

Other publications

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2012 2011 2010 2009 2008 2007
2006 2005 2004 2003 2002 2001
2000 1999 1998 1997 1996 1995
1990-1994 1985-1989 1980-1984
1975-1979 1970-1974 1958-1969
On Mathematics and Mathematicians
Science and life
Jubilees, obituaries, personalia
Editing


2017


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2012


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2011


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2009



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2008



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2005



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2004

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2003

  • Kolmogorov's example (a survey of actions of infinite-dimensional groups with invariant measure).
    Teor. Veroyatnost. i Primenen. 48, No. 2, 386-391 (2003). English translation: Theory Probab. Appl. 48, No. 2, 373-378 (2004).
  • Two lectures on the asymptotic representation theory and statistics of Young diagrams.
    In "Asymptotic Combinatorics with Applications to Mathematical Physics" (A.M.Vershik, ed.). Lecture Notes in Math. 1815, 161-182. Springer-Verlag, Berlin-Heidelberg, 2003.
  • Asymptotics of the uniform measure on the simplex, random compositions and partitions (with Yu.Yakubovich).
    Funkts. Anal. i Prilozh. 37, No. 4, 39-48 (2003). English translation: Funct. Anal. Appl. 37, No. 4, 273-180 (2003).
  • Fock factorizations, and decompositions of the L^2 spaces over general Levy processes (with N.Tsilevich).
    Uspekhi Mat. Nauk 58, No. 3(351), 3-50 (2003). English translation: Russian Math. Surveys 58, No. 3, 427-472 (2003).
  • Strange factor representations of type II_1, and pairs of dual dynamical systems.
    Moscow Mathematical Journal 3, No. 4, 1141-1157 (2003).
    Preprint version
  • Canonical semigroups of states and cocycles for the group of automorphisms of a homogeneous tree (with G.Kuhn).
    Algebr. Represent. Theory 6, no. 3, 333-352 (2003).
    Preprint version .
  • Frobenius-Schur functions (with G.Olshansky, A.Regev, and an Appendix by V.Ivanov).
    In "I.Schur Memorial Conference". Rehovot, Israel, 2000. Progress in Mathematics 210, 251-299. Birkhauser, 2003.
  • Random and universal metric spaces.
    In "Fundamental Mathematics Today" (S.K.Lando and O.K.Sheinman, eds.), Independent University of Moscow, 2003, pp.54-88.
    Preprint version.
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2002

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2001

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2000

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1999

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1998

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1997

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1996

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1995

  • Asymptotic combinatorics and algebraic analysis.
    In Proc. International Congress of Mathematicians (Zurich, 1994), vol.II, 1384-1394. Birkhauser, Basel, 1995.
  • The adic realizations of the ergodic actions with the homeomorphisms of the Markov compact and the ordered Bratteli diagrams. Zapiski Nauchn. Semin. POMI 223, 120-126 (1995). English translation: J. Math. Sci. 87, No.6, 4054-4058 (1997).
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1990-1994

  • Calculation of the Grothendieck group of the algebra C(SL(2,k)), where k is a countable algebraically closed field (with K.P.Kokhas).
    Algebra i Anal. 2, No.6, 98-106 (1990). English translation: Leningrad Math. J. 2, No.6, 1251-1259 (1991).
  • A nonholonomic Laplace operator (with V.Ya.Gershkovich).
    Probl. Mat. Anal. 11, 96-108 (1990). English translation: J. Sov. Math. 64, No.6, 1289-1296 (1993).
  • Local algebras and a new version of Young's orthogonal form.
    In "Topics in Algebra, part 2: Commutative Rings and Algebraic Groups" (Warsaw 1988), Banach Cent. Publ. 26, Part 2, 467-473 (1990).
  • Metagonal groups of finite and infinite dimensions.
    In "Representation of Lie groups and related topics". Adv. Stud. Contemp. Math. 7, 1-37 (1990).
  • New examples of continuum graded Lie algebras (with M.V.Saveliev).
    Phys. Lett. A 143, No.3, 121-128 (1990).
  • On topological questions of real complexity theory and combinatorial optimization.
    Lect. Notes in Math. 1453, 263-270 (1990).
  • The Grothendieck group of the infinite symmetric group and symmetric functions (with the elements of the theory of K0-functor of AF-algebras) (with S.V.Kerov).
    In "Representation of Lie groups and related topics". Adv. Stud. Contemp. Math. 7, 39-117 (1990).
  • Polynomially computable approximation of families of semi-algebraic sets, and combinatorial complexitiy (with A.I.Barvinok).
    Trudy Leningr. Mat. Obshchestva 1, 8-26 (1991). English translation: Amer. Math. Soc. Transl. Ser. 2 155, 1-17 (1993).
  • Reduction of nonholonomic variational problems to isoperimetric ones and connections in principal bundles (with O.A.Granichina).
    Mat. Zametki 49, No.5, 37-44 (1991). English translation: Math. Notes 49, No.5, 467-472 (1991).
  • A new class of infinite-dimensional Lie algebras (continuum Lie algebras) and associated nonlinear systems (with M.V.Saveliev).
    In "Differential geometric methods in theoretical physics" (Rapallo, 1990). Lect. Notes in Phys. 375, 162-170 (1991).
  • The fibadic expansions of real numbers and adic transformation.
    Preprint Institut Mittag-Leffler 4, 1-9 (1991).
  • On the classification of Z-graded Lie algebras of constant growth which have the algebra C[h] as Cartan subalgebra.
    In "Quantum groups" (Leningrad 1990). Lect. Notes in Math. 1510, 395 (1992).
  • Adic models of ergodic transformations, spectral theory, substitutions, and related topics (with A.N.Livshits).
    In "Representation theory and dynamical systems". Adv. Sov. Math. 9, 185-204 (1992).
  • Formulation of Bell type problems, and "noncommutative" convex geometry (with B.S.Tsirelson).
    In "Representation theory and dynamical systems". Adv. Sov. Math. 9, 95-114 (1992).
  • Manifolds with intrinsic metric, and nonholonomic spaces (with V.N.Berestovsky).
    In "Representation theory and dynamical systems". Adv. Sov. Math. 9, 253-267 (1992).
  • Asymptotic behaviour of the number of faces of random polyhedra and the neighbourliness problem (with P.V.Sporyshev).
    Selecta Math. Sov. 11, No.2, 181-201 (1992).
  • New examples of continuum graded Lie algebras (with M.V.Saveliev).
    In Proc. Int. Conf. on Algebra, Part 2 (Novosibirsk, 1989). Contemp. Math. 131, Part 2, 123-133 (1992).
  • Asymptotic aspects of the representation theory of symmetric groups.
    Selecta Math. Sov. 11, No.2. 159-179 (1992). Translation from the Addendum to the Russian translation of the book by G.James "Theory of the representations of symmetric groups". Mir, Moscow, 1982.
  • On nonlinear equations assosiated with Lie algebras of diffeomorphism groups of two-dimensional manifols (with M.Saveliev, S.Savelieva, and R.Kashaev).
    In "Ideas and methods in mathematical analysis, stochastics and applications" (Oslo, 1988), 295-307. Cambridge Univ. Press, Cambridge, 1992.
  • Arithmetic isomorphism of hyperbolic automorphism of a torus and of sofic shifts.
    Funkts. Anal. Prilozh. 26, No.3, 22-27 (1992). English translation: Funct. Anal. Appl. 26, No.3, 170-173 (1992).
  • On the number of convex lattice polytopes (with I.Barany).
    Geom. Funct. Anal. 2, No.4, 381-393 (1992).
  • The topology of configuration spaces, convex polytopes, and representations of lattices (with A.I.Barvinok and N.E.Mnev).
    Trudy Mat. Inst. Steklova 193, 37-41 (1992). English translation: Proc. Steklov Inst. Math. 193, 37-41 (1993).
  • Lie algebras generated by dynamical systems.
    Algebra i Analiz 4, No.6, 103-113 (1992). English translation: St.Petersburg Math. J. 4, No.6, 1143-1151 (1993).
  • Harmonic analysis on the infinite symmetric group. A deformation of the regular representation (with G.Olshansky and S.Kerov)
    C.R.Acad. Sci. Paris, Ser. I. 316, No.8, 773-778 (1993).
  • Arithmetic expansions associated with rotation of the circle and continued fractions (with N.A.Sidorov)
    Algebra i Analiz 5, No.6, 97-115 (1993). English translation: St.Petersburg Math. J. 5, No.6 (1993)
  • The limit form of convex integral polygons and related problems.
    Funkts. Anal. Prilozh. 28, No.1, 16-25 (1994). English translation: Funct. Anal. Appl. 28, No.1, 13-20 (1994).
  • Theory of decreasing sequences of measurable partitions.
    Algebra i Analiz 6, No.4, 1-68 (1994). English translation: St.Petersburg Math. J. 6, No.4, 705-761 (1995).
  • Random walks on multiconnected manifolds and conformal field theory (with S.Nechaev)
    J. Phys. A 27, No.7, 2289-2298 (1994).
  • Locally transversal symbolic dynamics.
    Algebra i Analiz 6, No.3, 94-106 (1994). English translation: St.Petersburg Math. J. 6, No.3, 529-540 (1995).
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1985-1989

  • Amenability and approximability of groups and algebras.
    Uspekhi Mat. Nauk 40, No.2, 217-219 (1985) (in Russian).
  • Asymptotics of maximal and typical dimensions of irreducible representations of a symmetric group (with S.V.Kerov).
    Funkts. Anal. Prilozh. 19, No.1, 25-36 (1985). English translation: Funct. Anal. Appl. 19, 21-31 (1985).
  • General ergodic theory of groups of measure preserving transformations (with I.P.Kornfel'd and Ya.G.Sinai).
    In "Itogi Nauki i Tekhniki, Ser. Sovrem. Probl. Mat." 2, 5-111. VINITI, Moscow, 1985. English translation in "Dynamical systems. II. Ergodic theory with applications to dynamical systems and statistical mechanics". Encycl. Math. Sci. 2, 1-98 (1989).
  • Locally semisimple algebras. Combinatorial theory and the K-functor (with S.V.Kerov).
    In "Itogi Nauki i Tekhniki, Ser. Sovrem. Probl. Mat." 26, 3-56. VINITI, Moscow, 1985. English translation: J. Sov. Math. 38, 1701-1733 (1987).
  • Trajectory theory (with A.L.Fedorov).
    In "Itogi Nauki i Tekhniki, Ser. Sovrem. Probl. Mat." 26, 171-211. VINITI, Moscow, 1985. English translation: J. Sov. Math. 38, 1799-1822 (1987).
  • Models of representations of current groups (with I.M.Gelfand and M.I.Graev).
    In "Representations of Lie groups and Lie algebras" (Budapest, 1971), 121-179. Akad. Kiado, Budapest, 1985.
  • Approximation for actions of amenable groups and transversal automorphism (with A.A.Lodkin).
    In "Operator algebras and their connections with topology and ergodic theory" (Busteni, 1983). Lect. Notes in Math. 1132, 331-346 (1985).
  • The commutative model of the principal representation of the current group SL(2,R)X with respect to a unipotent subgroup (with I.M.Gelfand and M.I.Graev).
    In "Group theoretical methods in physics" (Zvenigorod, 1982), 3-22. Harwood Academic Publ., Chur, 1985.
  • Infinite-dimensional metagonal and metaplectic groups.
    In "Group theoretical methods in physics" (Zvenigorod, 1982), 23-27. Harwood Academic Publ., Chur, 1985.
  • A bijective proof of the Jacobi identity, and reshapings of the Young diagrams.
    Zapiski Nauchn. Semin. LOMI 155, 3-6 (1986). English translation: J. Sov. Math. 41, No.2, 889-891 (1988).
  • Geodesic flow on SL(2,R) with nonholonomic constraints (with V.Ya. Gershkovich).
    Zapiski Nauchn. Semin. LOMI 155, 7-17 (1986). English translation: J. Sov. Math. 41, No.2, 891-898 (1988).
  • The characters of the infinite symmetric group and probability properties of the Robinson-Schensted-Knuth algoritm (with S.V.Kerov).
    SIAM J. Alg. Discr. Methods 7, No.1, 116-124 (1986).
  • An asymptotic estimate of the average number of steps of the parametric simplex method (with P.V.Sporyshev).
    Zhurnal Vychisl. Matem. i Matem. Fiziki 26, No.6, 813-826 (1986). English translation: USSR Comput. Math. Math. Phys. 26, No.3, 104-113 (1986).
  • The asymptotic distribution of factorizations of natural numbers into prime divisors.
    Dokl. Akad. Nauk SSSR 289, No.2, 269-272 (1986). English translation: Sov. Math. Dokl. 34, 57-61 (1987).
  • Nonholonomic problems and the theory of distributions (with V.Ya. Gershkovich).
    Acta Appl. Math. 12, No.2, 181-209 (1988). Translation from the Addendum to the Russian translation of the book by Ph. Greaffits "External Differential Form and Variational Calculus". Mir, Moscow, 1986.
  • Growth and asymptotics of random configurations.
    Uspekhi Mat. Nauk 41, No.1 (1986) (in Russian).
  • The geometry of the nonholonomic sphere of three-dimensional Lie groups (with V.Ya.Gershkovich).
    In "Geometriya i Teoriya Osobennostej v Nelinejnykh Uravneniyakh". Novoe v Global'nom Analize, 61-75. Voronezh, 1987. English translation: Lect. Notes in Math. 1334, 309-331 (1988).
  • Statistics on the set of naturals' partitions, limit forms of Young random diagrams and asymptotic distributions of the space of positive series.
    In "Probability theory and mathematical statistics" (Vilnius 1985), vol. 2, 683-694. VNU Sci. Press, Utrecht, 1987.
  • Superstability of hyperbolic automorphisms and unitary dilatations of Markov operators.
    Vestn. Leningr. Univ., Ser. I, No.3, 28-33 (1987). English translation: Vestnik Leningrad Univ. Math. 20, No.3, 22-29 (1987).
  • Measurable realizations of automorphism groups and integral representations of positive operators.
    Sib. Mat. Zh. 28, No.1(161), 52-60 (1987). English translation: Sib. Math. J. 28, 36-43 (1987).
  • Nonholonomic dynamical systems, geometry of distributions and variational problems (with V.Ya.Gershkovich).
    In "Itogi Nauki i Tekhniki, Ser. Sovrem. Probl. Mat." 16, 5-85. VINITI, Moscow, 1987. English translation: Encycl. Math. Sci. 16, 1-81 (1994).
  • A partition function connected with Young diagrams.
    Zapiski Nauchn. Semin. LOMI 164, 20-29 (1987). English translation: J. Sov. Math. 47, No.2, 2379-2386 (1989).
  • Convex hulls of orbits of representations of finite groups and combinatorial optimization (with A.I.Barvinok).
    Funkts. Anal. Prilozh. 22, No.3, 66-67 (1988). English translation: Funct. Anal. Appl. 22, No.3, 224-225 (1988).
  • A geometric approach to representation of a partial ordered set.
    Vestn. Leningr. Univ., Ser. I, No.1, 12-14 (1988). English translation: Vestn. Leningr. Univ., Math. 21, No.1, 11-15 (1988).
  • Local stationary algebras.
    In "Algebra and Analysis" (Kemerovo, 1988). VINITI, Kemerovo, 1988. English translation: Amer. Math. Soc. Transl. Ser. 2 148, 1-13 (1991).
  • Methods of representations theory in combinatorial optimization problems (with A.I.Barvinok).
    Izv. Akad. Nauk SSSR, Tekh. Kibern., No.6, 64-71 (1988). English translation: Sov. J. Comput. Syst. Sci. 27, No.5, 1-7 (1989).
  • Estimation of the functional dimension of the orbit space of germs of distributions in general position (with V.Ya.Gershkovich).
    Mat. Zametki 44, No.5, 596-603 (1988). English translation: Math. Notes 44, No.5, 806-810 (1988).
  • The Fock space and its relation to non-linear theory of functionals on realizations of a Gaussian random process (in Russian).
    In "Razrabotka i primenenie approksimatsionnyh metodov k zadacham sinteza elektricheskih tsepej", 1988.
  • Characters and realizations of representations of an infinite-dimensional Hecke algebra, and knot invariants (with S.V.Kerov).
    Dokl. Akad. Nauk SSSR 301, No.4, 777-780 (1988). English translation: Sov. Math. Dokl. 38, No.1, 134-137 (1989).
  • Nonholonomic manifolds and nilpotent analysis (with V.Ya.Gershkovich).
    J. Geom. Phys. 5, No.3, 407-452 (1988).
  • Topology of the convex polytopes' manifolds, the manifold of the projective configurations of a given combinatorial type and representations of lattices.
    In "Topology and geometry - Rokhlin Seminar". Lect. Notes in Math. 1346, 557-581 (1988).
  • Topological problems in combinatorial and convex geometry and the theory of representations of partially ordered sets.
    In "Topological and geometric methods of analysis". Novoe v Global'nom Anal., 58-74. Voronezh, 1989 (in Russian).
  • A bundle of nilpotent Lie algebras over a non-holonomic manifold (nilpotentization) (with V.Ya.Gershkovich).
    Zapiski Nauchn. Semin. LOMI 172, 21-40 (1989). English translation: J. Sov. Math. (1991).
  • Hook formula and related identities.
    Zapiski Nauchn. Semin. LOMI 172, 3-20 (1989). English translation: J. Sov. Math. (1991).
  • A new model of the ergodic transformations.
    In "Dynamical systems and ergodic theory" (Warsaw 1986), Banach Cent. Publ. 23, 381-384 (1989).
  • Continuum analogues of contragredient Lie algebras (Lie algebras with a Cartan operator and nonlinear dynamical systems) (with M.V.Saveliev).
    Comm. Math. Phys. 126, No.2, 367-378 (1989).
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1980-1984

  • Functional Lie groups: geometry, analysis,representations.
    Uspekhi Mat. Nauk 35, No.6, 181-182 (1980) (in Russian).
  • Representations of the group of functions taking values in a compact Lie group (with I.M.Gelfand and M.I.Graev).
    Compos. Math. 42, No.2, 217-243 (1980).
  • Characters and factor representations of the infinite symmetric group (with S.V.Kerov).
    Dokl. Akad. Nauk SSSR 257, No.5, 1037-1040 (1981). English translation: Sov. Math. Dokl. 23, 389-392 (1981).
  • Random walks on groups and related problems.
    Teor. Veroyatn. i Primen. 26, No.1, 190-191 (1981) (in Russian).
  • Uniform algebraic approximations of shift and multiplication operators.
    Dokl. Akad. Nauk SSSR 259, No.3, 526-529 (1981). English translation: Sov. Math. Dokl. 24, 97-100 (1981).
  • Asymptotic theory of characters of the symmetric group (with S.V.Kerov).
    Funkts. Anal. Prilozh. 15, No.4, 15-27 (1981). English translation: Funct. Anal. Appl. 15, 246-255 (1982).
  • Cohomology of groups in unitary representations, the neighborhood of the identity, and conditionally positive definite functions (with S.I.Karpushev).
    Matem. Sborn. 119, No.4, 521-533 (1982). English translation: Math. in USSR 47, 513-526 (1984).
  • Fields of convex polyhedra and the Pareto-Smale optimum (with A.G. Chernyakov).
    Optimizatsiya 28(45), 112-145 (1982). English translation in "Functional Analysis, Optimization, and Mathematical Economics", 290-313. Oxford University Press, New York, 1990.
  • Characters and factor representations of the infinite unitary group (with S.V.Kerov).
    Dokl. Akad. Nauk SSSR 267, No.2, 272-276 (1982). English translation: Sov. Math. Dokl. 26, 570-574 (1982).
  • The commutative model of the principle representation of the current group $SL(2,R)^X$ with respect to unipotent subgroup.
    In "Group theoretical methods in physics", vol.2, 472-486. Nauka, Moscow, 1982. English translation in "Group theoretical methods in physics", 3-21. Harv. Acad. Publ., London, 1985.
  • Amenability and approximation of infinite groups.
    Selecta Math. Sov. 2, No 4, 311-330 (1982). Revised translation from the Addendum to the Russian translation of the book by F.Greenleaf "Invariant means on topological groups". Mir, Moscow, 1973.
  • Critical points of fields of convex polytopes and the Pareto-Smale optimum with respect to a convex cone (with A.G.Chernyakov).
    Dokl. Akad. Nauk SSSR 266, No.3, 529-532 (1982). English translation: Sov. Math. Dokl. 26, 353-356 (1982).
  • A theorem on periodical Markov approximation in ergodic theory.
    Zapiski Nauchn. Semin. LOMI 115, 72-82 (1982). English translation: J. Sov. Math. 28, 667-674 (1985). Another English translation in "Ergodic theory and related topics" (Vitte, 1981). Math. Res. 12, 195-206. Akademie-Verlag, Berlin, 1982.
  • Commutative model of the representation of the group of flows $SL(2,R)^X$ connected with a unipotent subgroup (with I.M.Gelfand and M.I.Graev).
    Funkts. Anal. Prilozh. 17, No.2, 70-72 (1983). English translation: Funct. Anal. Appl. 17, 137-139 (1983).
  • Infinite-dimensional metagonal and metaplectic groups. I: General concepts and metagonal groups.
    Zapiski Nauchn. Semin. LOMI 123, 3-35 (1983). English translation: J. Sov. Math. 28, 459-481 (1985).
  • The K-functor (Grothendieck group) of the infinite symmetric group (with S.V.Kerov).
    Zapiski Nauchn. Semin. LOMI 123, 126-151 (1983). English translation: J. Sov. Math. 28, 549-568 (1985).
  • Experiments in calculating the dimension of a typical representation of the symmetric group (with S.V.Kerov and A.B.Gribov).
    Zapiski Nauchn. Semin. LOMI 123, 152-154 (1983). English translation: J. Sov. Math. 28, 568-570 (1985).
  • An estimate of the average number of steps in the simplex method, and problems in asymptotic integral geometry (with P.V.Sporyshev).
    Dokl. Akad. Nauk SSSR 271, No.5, 1044-1048 (1983). English translation: Sov. Math. Dokl. 28, 195-199 (1983).
  • Factorial representations of path groups (with S.Albeverio, R.Hoegh-Krohn, and D.Testard).
    J. Funct. Anal. 51, No.1, 115-131 (1983).
  • Random walks on discrete groups: Boundary and entropy (with V.A. Kaimanovich).
    Ann. Prob. 11, No.3, 457-490 (1983).
  • Classical and nonclassical dynamics with constraints.
    In "Geometriya i Topologiya v Global'nykh Nelinejnykh Zadachakh". Novoe v Global'nom Analize, 23-48. Voronezh, 1983. English translation: Lect. Notes in Math. 1108, 278-301 (1984).
  • Star algebras associated with endomorphisms (with V.A.Arzumanian).
    In "Operator algebras and group representations", vol.I (Neptun, 1980). Monogr. Stud. Math. 17, 17-27. Pitman, Boston, 1984.
  • Characters, factor representations and K-functor of the infinite symmetric group (with S.V.Kerov).
    In "Operator algebras and group representation", vol.II (Neptun, 1980). Monogr. Stud. Math. 18, 23-32. Pitman, Boston, 1984.
  • The theory of Markov processes from the standpoint of theory of contractions.
    Lect. Notes in Math. 1043, 101-103 (1984).
  • Quadratic forms that are positive on the cone, and quadratic duality.
    Zapiski Nauchn. Semin. LOMI 134, 59-83 (1984). English translation: J. Sov. Math. 36, 39-56 (1987).
  • Algebras with quadratic relations.
    In "Spectral theory of operators and infinite-dimensional analysis", 32-57. Akad. Nauk Ukrain. SSR., Inst. Mat., Kiev, 1984. English translation: Selecta Math. Sov. 11, No.4, 293-315 (1992).
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1975-1979

  • Lagrangian mechanics in invariant form (with L.D.Faddeev).
    In "Problems of Theoretical Physics", vol.2. Functional methods in quantum field theory and statistical physics, 129-141. Izdat. LGU, 1975. English translation: Selecta Math. Sov. 1, No.4, 339-350 (1981).
  • Best piecewise polynomial approximation (with V.N.Malozemov and A.B.Pevnyi).
    Sib. Math. J. 16, No.5, 925-938 (1975). English translation: Siber. Math. J. 16, 706-717 (1976).
  • Representations of the group of diffeomorphisms which are connected with infinite configurations (with I.M.Gel'fand and M. I. Graev).
    Uspekhi Mat. Nauk 30, No.6(186), 3-50 (1975). English translation: Russian Math. Surveys 30, No.6, 1-50 (1975). Another English translation: Lect. Notes London Math. Soc. 69, 15-60 (1982).
  • On the evolution of measures defined by the Navier-Stokes equations, and on the solvability of the Cauchy problem for Hopf's statistical equation (with O.A.Ladyzenskaya).
    Dokl. Akad. Nauk SSSR 226, No.1, 26-29 (1976). English translation: Sov. Math. Dokl. 17, 18-22 (1976).
  • The evolution of measures determined by the Navier-Stokes equations and the solvability of the Cauchy problem for the Hopf statistical equation (with O.A.Ladyzenskaya).
    Zapiski Nauchn. Semin. LOMI 59, 3-24 (1976). English translation: J. Sov. Math. 8, 195-212 (1978). French translation: Sur l'evolution des mesures determinees par les equations de Navier-Stokes et la resolution du probleme de Cauchy pour l'equation statistique de E.Hopf. Ann. Scuola Norm. Sup. Pisa Cl. Sci., Ser. 4 4, 209-230 (1977).
  • On D.Ornstein's papers, weak dependence conditions and classes of stationary measures.
    Teor. Veroyatn. Primen. 21, No.3, 673-675 (1976). English translation: Theory Probab. Appl. 21, 655-657 (1977).
  • Representations of the group of smooth mappings from a manifold X into a compact Lie group (with I.M.Gel'fand and M.I.Graev).
    Dokl. Akad. Nauk SSSR 232, No.4, 745-748 (1977). English translation: Sov. Math. Dokl. 18, 118-121 (1977).
  • Representations of the group of smooth mappings of a manifold X into a compact Lie group (with I.M.Gel'fand and M.I.Graev).
    Compos. Math. 35, No.3, 299-334 (1977).
  • Asymptotics of the Plancherel measure of the symmetric group and the limiting form of Young tableaux (with S.V.Kerov).
    Dokl. Akad. Nauk SSSR 233, No.6, 1024-1027 (1977). English translation: Sov. Math. Dokl. 18, 527-531 (1977).
  • Limit measures arising in the asymptotic theory of symmetric groups. I (with A. A. Shmidt).
    Teor. Veroyatn. Primen. 22, 72-88 (1977). English translation: Theory Probab. Appl. 22, No.1, 70-85 (1977).
  • Multivalued mappings with invariant measure (polymorphisms) and Markov operators.
    Zapiski Nauchn. Semin. LOMI 72, 26-61 (1977). English translation: J. Sov. Math. 23, 2243-2266 (1983).
  • Asymptotic problems in the theory of classical groups and their representations.
    Uspekhi Mat. Nauk 32, No.5, 165 (1977) (in Russian).
  • Limit measures arising in the asymptotic theory of symmetric groups. II (with A.A.Shmidt).
    Teor. Veroyatn. Primen. 23, No.1, 42-54 (1978). English translation: Theory Probab. Appl. 23, 36-49 (1978).
  • The action of PSL(2,Z) in R1 is approximable.
    Uspekhi Mat. Nauk 33, No.1(199), 209-210 (1978). English translation: Russian Math. Surveys 33, No.1, 221-222 (1978).
  • Factor representations of the crossed product of a commutative C*-algebra and a semigroup of its endomorphisms (with V.A.Arzumanian).
    Dokl. Akad. Nauk SSSR 238, No.3, 513-516 (1978). English translation: Sov. Math. Dokl. 19, 48-52 (1978).
  • Are multiplicator and shift uniformly algebraically approximated?
    Zapiski Nauchn. Semin. LOMI 81, 77-81 (1978). English translation: Lect. Notes in Math. 1043, 189-196 (1984).
  • Product of commuting spectral measures need not be countably additive (with M.S.Birman and M.Z.Solomyak).
    Funkts. Anal. Prilozh. 13, No.1, 61-62 (1979). English translation: Funct. Anal. Appl. 13, 48-49 (1979).
  • Random walks on groups: boundary, entropy, uniform distribution (with V.A.Kaimanovich).
    Dokl. Akad. Nauk SSSR 249, No.1, 15-18 (1979). English translation: Sov. Math. Dokl. 20, 1170-1173 (1979).
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1970-1974

  • Decreasing sequences of measurable partitions and their applications.
    Sov. Math. Dokl. 11, 1007--1011 (1970).
  • Some remarks on the infinite-dimensional problems of linear programming.
    Russian Math. Surveys 25, No.5, 117-124 (1970).
  • Nonmeasurable decompositions, orbit theory, algebras of operators.
    Dokl. Akad. Nauk SSSR 199, 1004-1007 (1971). English translation: Sov. Math. Dokl. 12, 1218-1222 (1971).
  • Continuum of pairwise nonisomorphic diadic sequences.
    Funkts. Anal. i Prilozh. 5, No.3, 16-18 (1971). English translation: Funct. Anal. Appl. 5, 182-184 (1971).
  • Diagonalizable factors are decomposable.
    Uspekhi Mat. Nauk 26, No.5, p.161 (1971) (in Russian).
  • Differential geometry and Lagrangian mechanics with constraints (with L.D.Faddeev).
    Dokl. Akad. Nauk SSSR 202, 555-557 (1972). English translation: Sov. Phys. Dokl. 17, 34-36 (1972).
  • Symmetric groups of higher degree (with A.A.Shmidt).
    Sov. Math. Dokl. 206, No.2, 269-272 (1972).
  • A structure of the tame partitions.
    Uspekhi Mat. Nauk 27, No.3(165), 195-196 (1972).
  • Geometrical theory of states, the von Neumann boundary, and duality of the C*-algebras.
    Zapiski Nauchn. Semin. LOMI 29, 147-154 (1972). English translation: J. Sov. Math. 3, 840-845 (1975).
  • A metric invariant for the automorphisms of measure space, that is connected with uniform approximation and sequences of partitions.
    Sov. Math. Dokl. 209, No 1, 15-18 (1973).
  • Four definitions of the scale of an automorphism.
    Funct. Anal. Appl. 7, 169-181 (1973).
  • Factors and representations of dynamical systems.
    Uspekhi Mat. Nauk 28, No.2, 170 (1973) (in Russian).
  • Representations of the group SL(2,R), where R is a ring of functions (with I.M.Gel'fand and M.I.Graev).
    Uspekhi Mat. Nauk 28, No.5(173), 83-128 (1973). Another English translation: Lect. Notes London Math. Soc. 69, 15-60 (1982).
  • Countable groups which are close to finite groups.
    Addendum to the Russian translation of the book by F.Greenleaf "Invariant means on topological groups". Mir, Moscow, 1973.
  • A general duality theorem in linear programming (with M.M.Rubinov).
    In "Mathematical Economics and Functional Analysis", 35-55. Nauka, Moscow, 1974.
  • Decreasing sequences of sigma-algebras and ergodic theorems.
    Teor. Veroyatn. i Primen. 19, No.3, 657-658 (1974) (in Russian).
  • Description of invariant measures for the actions of some infinite-dimensional groups.
    Dokl. Akad. Nauk SSSR 218, No.4, 749-752 (1974). English translation: Sov. Math. Dokl. 15, 1396-1400 (1974).
  • Irreducible representations of the group $G^X$ and cohomology (with I.M. Gel'fand and M.I.Graev).
    Funct. Anal. i Prilozh. 8, No.2, 67-69 (1974). Another English translation: Lect. Notes London Math. Soc. 69, 15-60 (1982).
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1958-1969

  • On the reciprocal continuous extension of linear operations (with G.P.Akilov).
    Vestn. Leningr. Univ. 13, No.7, 27-33 (1958) (in Russian).
  • On the theory of normal dynamical systems.
    Dokl. Akad. Nauk SSSR 144, 9-12 (1962). English translation: Sov. Math. Dokl. 3, 625-628 (1962).
  • Spectral and metric isomorphism of some normal dynamical systems.
    Dokl. Akad. Nauk SSSR 144, No.2, 255-257 (1962). English translation: Sov. Math. Dokl. 3, 693-696 (1962).
  • Topological questions of the measure theory in linear spaces (with V.N.Sudakov).
    Uspekhi Mat. Nauk 17, No.4, 217-219 (1962) (in Russian).
  • General theory of Gaussian measures in linear spaces.
    Uspekhi Mat. Nauk 19, No.1, 210-212 (1964) (in Russian).
  • Some characteristic properties of Gaussian stochastic processes.
    Teor. Veroyatn. i Primen. 9, No.2, 390-394 (1964) (in Russian).
  • Measurable realization of continuous automorphism groups of a unitary ring.
    Izv. Akad. Nauk SSSR, Ser. Mat. 29, 127-136 (1965). English translation: Amer. Math. Soc. Transl. Ser. 2 84, 69-81 (1969).
  • Duality in the theory of measure in linear spaces.
    Dokl. Akad. Nauk SSSR 170, 497-500 (1966). English translation: Sov. Math. Dokl. 7, 1210-1214 (1967).
  • A theorem on the lacunary isomorphism of monotonic sequence of partitions.
    Funkts. Anal. i Prilozh. 2, No.3, 17-21 (1968) (in Russian).
  • The axiomatics of measure theory in linear spaces.
    Dokl. Akad. Nauk SSSR 178, 278-281 (1968). English translation: Sov. Math. Dokl. 9, 68-72 (1968).
  • Some questions concerning the approximation of the optimal value of infinite-dimensional problems in linear programming (with V.Temelt).
    Sib. Mat. Zh. 9, 790-803 (1968). English translation: Siber. Math. J. 9, No.3, 591-601 (1968).
  • Probability measures in infinite-dimensional spaces (with V.N.Sudakov).
    Zapiski Nauchn. Semin. LOMI 12, 7-67 (1969). English translation: Seminars in Math., V.A.Steklov Math. Inst., Leningrad 12, 1-28 (1971).
  • Dynamical systems with invariant measure (with S.A.Yuzvinsky).
    In "Itogi Nauki i Tehniki, Matem. Anal.", 133-187. VINITI, Moscow, 1969. English translation: Progress Math. 8, 151-215 (1970).
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On Mathematics and Mathematicians

  • About Grisha Mints,
    IfColog Journal of Logics and Their Applications 4, No. 42017, 841-843.
  • Several words about Mikhail Iosifovich Gordin (in Russian).
    Zapiski Nauchn. Semin. POMI 441, 9-11 (2015).
  • About A.N.Livshits (in Russian).
    In: A.N.Livshits, Dynamical Systems, Ergodic Theory, Formal Languages (A.A.Lodkin, ed.). St.Petersburg, 2014.
  • Gromov's geometry.
    In: The Abel Prize 2008-2012, H.Holden and R.Piene (eds.), Springer (2014), pp.143-148.
  • Long history of the Monge-Kantorovich transportation problem.
    Math. Intelligencer 35, No. 4 (2013).
  • Several thoughts about Arnold.
    In: Arnold: Swimming Against the Tide (B.A.Khesin and S.L.Tabachnikov, eds.). Amer. Math. Soc., 2014, pp. 187-196. The Russian version.
  • Gelfand, My Inspiration.
    Notices AMS, 60, No. 1, 32-38 (2013).
  • Leonid Vital'evich Kantorovich (on the 100th anniversary of his birth) (with S.S.Kutateladze and S.P. Novikov).
    Russian Math. Surveys 67, No. 3, 589 (2012). Russian preprint version.
  • A commentary (in Russian).
    In: J.C.Maxwell, Works on Kinetic Theory. Binom, Moscow, 2011.
  • The work of Andrei Okounkov.
    Notices of the AMS 54, no. 3, 391-393, March 2007.
  • What is good for mathematics? Thoughts on the Clay Millenium Prizes.
    Notices of the AMS 54, no. 1, 45-47, January 2007.
  • The life and fate of functional analysis in the twentieth century.
    In: Mathematical Events of the Twentieth Century, Phasis, Moscow, 2003.
    English translation: Springer, Berlin, 2006, pp. 437-447.
  • Alexandrov's inequality. Alexander Danilovich as I knew him (in Russian).
    St.Petersburg University, No. 3-4 (2004), 36-40.
    Full version.
  • A look at the university in the light of mathematics.
    St.Petersburg University, No. 3-4 (2004), 14-18.
  • A talk at the session of the St.Petersburg Mathematical Society dedicated to the memory of L.V.Kantorovich (in Russian).
    In: "History of Computer Science in Russia". Nauka, Moscow, 2003, pp. 52-56.
  • About L.V.Kantorovich and linear programming.
    In: "Leonid Vital'evich Kantorovich: a man and a scientist", vol.1, 130-152. Izd. SO RAN, Novosibirsk, 2002.
    English translation (2007).
  • Randomization of algebra and algebraization of probability. An attempt of prediction.
    In: "Mathematics Unlimited - 2001 and Beyond" (B.Engquist and W.Schmid, eds.), part II, 1157-1166. Springer, Berlin-Heidelberg-New York, 2001.
  • Vladimir Abramovich Rokhlin [1919-1984].
    Amer. Math. Soc. Transl. Ser. 2 202, 1-10 (2001).
  • What will happen to our mathematics.
    Notices Amer. Math. Soc. 40, No.2, 129-131 (1993).
  • To guard the future of Soviet mathematics. (with O.Ya.Viro and L.A.Bokut').
    Math. Intell. 14, No.1, 12-15 (1992).
  • V.A.Rokhlin's work in ergodic theory.
    Algebra i Analiz 2, No.2, 236-241 (1990). English translation: Leningrad Math. J. 2, No.2, 427-431 (1991).
  • On the Leningrad Mathematical Society.
    Trudy Leningrad. Mat. Obshchestva 1, 4-8 (1991) (in Russian). English translation: Proc. of Leningrad Math. Soc. Amer. Math. Soc. Transl. Ser. 2 155, IX-XIII (1992). Another English translation: Newsletter EMS, No.10, 21-23 (1993).
  • Vladimir Abramovich Rokhlin 1919-1984 (on the 70th anniversary of his birth).
    Algebra i Analiz 2, No.2, 227-235 (1990). English translation: Leningrad Math. J. 2, No.2, 419-426 (1991).
  • Gleb Pavlovich Akilov.
    Optimizatsiya 48(65), 41-46 (1990) (in Russian).
  • Student Mathematical competition in Leningrad State University (with A.A.Lodkin).
    In "Mathematics today", No.6, 126-142. Vyscha shkola, Kiev, 1990 (in Russian).
  • 50 years of linear programming (with L.M.Bragman, A.B.Gribov, and I.V.Romanovskiy).
    Ekonomika i mat. metody 26, No.2, 376-378 (1990) (in Russian).
  • Vladimir Abramovich Rokhlin - a biographical tribute (23.8.1919-3.12.1984).
    Ergodic Theory Dynam. Systems 9, No.4, 629-641 (1989).
  • John von Neumann (with A.N.Kolmogorov and Ya.G.Sinai).
    In: John von Neumann, "Collected works", vol.1, 337-351. Nauka, Moscow, 1987.
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Science and life

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Jubilees, obituaries, personalia

  • Yakov Grigorievich Sinai (on the occasion of his seventieth birthday) (with D.V.Anosov, R.V.Plykin et al.).
    Russian Math. Surveys 60 (2005), no. 5, 995-998.
  • Gennadii Shlemovich Rubinstein (with V.A.Zalgaller, S.S.Kutateladze et al.).
    Russian Math. Surveys 60 (2005), no. 2, 337-339.
  • Olga Aleksandrovna Ladyzhenskaya (with V.I.Arnold, M.Sh.Birman et al.).
    Russian Math. Surveys 59 (2004), no. 3, 553-555.
  • Garald Isidorovich Natanson (with V.M.Babich, V.S.Videnskii et al.).
    Russian Math. Surveys 59 (2004), no. 4, 771-776.
  • Vasilii Mikhailovich Babich (on the occasion of his seventieth birthday) (with V.S.Buldyrev, I.A.Ibragimov, et al.).
    Russian Math. Surveys 57 (2002), no. 3, 627-635.
  • Anatoly Mikhailovich Stepin (on the occasion of his sixtieth birthday) (with D.V.Anosov, A.A.Bolibrukh, et al.).
    Russian Math. Surveys 56 (2001), no. 1, 201-205.
  • Robert Adol'fovich Minlos (on the occasion of his seventieth birthday) (with N.D.Vvedenskaya, E.A.Zhizhina, et al.).
    Russian Math. Surveys 56 (2001), no. 4, 789-792.
  • Viktor Abramovich Zalgaller (on the occasion of his eightieth birthday) (with Yu.D.Burago, I.A.Ibragimov, et al.).
    Zapiski Nauchn. Semin. POMI 280 (2001), 7-13. English translation: J. Math. Sci. 119 (2004), no. 2, 129--132.
  • Vladimir Andreevich Yakubovich (on the occasion of his 75th birthday) (with V.I.Derguzov, I.A.Ibragimov, O.A.Ladyzhenskaya, G.A.Leonov).
    Algebra i Analiz 13 (2001), no. 4, 254-256. English translation: St. Petersburg Math. J. 13 (2002), no. 4, 703--704.
  • Sergei Vassilievich Kerov (12.06.1946--28.07.2000) (in Russian).
    Zapiski Nauchn. Semin. POMI 283, 7-13 (2001). English translation: J. Math. Sci. 121, no. 3, 2295-2299 (2004).
  • Mikhail Shlemovich Birman (on the occasion of his seventieth birthday) (with V.S.Buslaev, I.M.Gelfand et al.).
    Uspekhi Mat. Nauk 55, No.1(331), 204-207 (2000). English translation: Russian Math. Surveys 55, No.1, 201-205 (2000).
  • To the memory of M.V.Saveliev.
    In: "Symmetries and integrable systems", 290-292. Dubna, 1999.
  • Yakov Grigorievich Sinai (on the occasion of his sixtieth birthday) (with S.P.Novikov, L.A.Bunimovich, B.M.Gurevich, E.I.Dinaburg, G.A.Margulis, V.I.Oseledets, S.A.Pirogov, K.M.Khanin, N.N.Chentsova).
    Uspekhi Mat. Nauk 51, No.4(310), 179-191 (1996). English translation: Russian Math. Surveys 51, No.4, 765-778 (1996).
  • Vladimir Andreevich Yakubovich (on the occasion of his seventieth birthday (with O.A.Ladyzhenskaya, G.A.Leonov, V.N.Fomin).
    Uspekhi Mat. Nauk 51, No.6, 231-232 (1996). English translation: Russian Math. Surveys 51, No.6, 1237-1240 (1996).
  • Alik Berezin in the recollections of friends (with V.P.Maslov, M.A.Shubin, N.D.Vvedenskaya).
    Amer. Math. Soc. Transl. Ser. 2 175, 225-236 (1996).
  • Dmitrij Andreevich Gudkov (obituary) (with V.I.Arnold, O.Ya.Viro, A.B.Korchagin, E.A.Leontovich-Andronova, S.P.Novikov, O.A.Oleinik, G.M.Polotovskij, G.A.Utkin, E.I.Shustin).
    Uspekhi Mat. Nauk 47, No.6, 195-198 (1992). English translation: Russian Math. Surveys 47, No.6, 193-197 (1992).
  • Gleb Pavlovich Akilov (with A.D.Aleksandrov, V.V.Ivanov, A.G. Kusraev, S.S.Kutateladze, B.M.Makarov, Yu.G.Reshetnyak, V.P.Khavin).
    Uspekhi Mat. Nauk 43, No.1(259), 181-182 (1988). English translation: Russian Math. Surveys 43, No.1, 221-223 (1988).
  • Vladimir Andreevich Yakubovich (on the occasion of his sixtieth birthday) (with S.M.Ermakov, O.A.Ladyzhenskaya, V.N.Fomin).
    Uspekhi Mat. Nauk 42, No.4(256), 219-220 (1987) (in Russian).
  • Vladimir Abramovich Rohklin. An Obituary. (with V.I.Arnold, O.Ya.Viro, A.N.Kolmogorov, S.P.Novikov, Ya.G.Sinai, D.B.Fuks).
    Uspekhi Mat. Nauk. 41, No.3(249), 159-163 (1986).
  • Sergei Mikhailovich Lozinskii (with S.M.Ermakov, O.A.Ladyzhenskaya, I.P.Mysovskikh, V.A.Pliss, Kh.L.Smolitskii, D.K.Faddeev).
    Uspekhi Mat. Nauk 41, No.5(251), 153-154 (1986) (in Russian).
  • Gleb Pavlovich Akilov (on the occasion of his fiftieth birthday) (with D.A. Vladimirov, B.Z.Vulikh, L.V.Kantorovich, B.M.Makarov, A.M.Rubinov, G.S.Rubinshtein, V.N.Sudakov, V.P.Havin).
    Optim. Planirov. 17, 7-9 (1970) (in Russian).
  • Commentaries to the papers by John von Neumann.
    In: John von Neumann, "Collected works", vol.1, 362-369, 372-375; vol.2, 338-348, 360-365. Nauka, Moscow, 1987.
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Editing


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