This volume features bibliographies, papers and speeches for example at international congresses of Wolf Prize winners, such as L. Ahlfors, H. Cartan, L. Carleson, S. Chern, E. Eilenberg, P. Erdos, F. Hirzebruch, L. Hormander, K. Ito, J. Keller, K. Kodaira, R.
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Langlands and J. The work of the Wolf laureates covers a wide spectrum, featuring much of the mathematics of the 20th century. Convert currency. Share your thoughts with other customers. Write a product review. Back to top.
Get to Know Us. English Choose a language for shopping. Audible Download Audio Books. DPReview Digital Photography. Zorich, N. Panov, A. Lyskova, M. Pavlov, Le Tu Thang, L. Alania, D. Millionshikov, S. Piounikhin, V. Sadov, A. Lazarev, R. Deleo, A. Giacobbe, K. Scientific Results. Homotopy Invariance of the special Pontryagin-Hirzebruch Integrals along the cycles coming from the Homological Algebra of fundamental group Browder-Novikov theory.
There is only a finite number of manifolds with the same Rational Pontryagin Classes Volodin, V. Kuznetsov and A. Fomenko as the section A theorem of S. These results are based on the developement of algebraic and geometric technique associated with Adams Spectral Sequence. In particular, cohomology of Hopf Coalgebras and new type ''Steenrod-like'' Operations in cohomology of Hopf Algebras over the finite fields play fundamental role here Complete calculation of the ''Steenrod'' algebra of operations as the Operator Heisenberg double over the Landveber-Novikov Hopf algebra with specific Z-structure see the items nn , for the latest development of algebraic aspects.
Application for the study of the stable homotopy groups of spheres. Further development of algebraic structures associated with unitary cobordisms, the fixpoint equations, 2-valued formal group Buchstaber-Novikov, Existence of Compact Leave for any nonsingular 2-foliation on 3-sphere and many other 3-manifolds, classification of all topological types of analytical foliations in the solid torus based on the conjugacy classes of braids Resent results: Topology of the generic foliations on Riemann Surfaces generated by the real parts of holomorphic one-forms.
Transversal Canonical Bases and Fundamental Semigroup of positive closed transversal curves, its calculation based on the Continued Fractions Novikov Inequalities for the numbers of critical points Topology of foliations generated by the closed one-form with Morse singularities. The Quasiperiodic manifolds. Novikov Conjectures concerning the structure of leaves and analytical properties of the Morse-Novikov Complex generated by the closed 1-form and C 1 -generic Riemannian metric Morse Theory for the non-simply-connected manifolds.
Morse inequalities and representations of fundamental group, the jumping subvarieties for homology groups on the representation space the analogs of Alexander Polinomials. Complete calculation of the generic Betti number and all Milnor-Farber Spectral Sequence for one-dimensional representations through the Massey Operations Analog of Morse-Witten inequalitis for smooth real vector fields and diagonalization of real fermionic quadratic forms Recent results: The Exotic De Rham cohomology,differential forms and dynamical systems: new functors and exact sequences Novikov, Closed one-forms in the Variational Calculus Multivalued Action Functionals on the spaces of mappings.
Classification of the ''local'' 1-forms in the field theory Topology and Qualitative Dynamics in Physics. Full description of the nondegenerate compactification of Phase Space and System near Cosmological Singularity. Properties of the ''Typical'' Evolution and their dependence on the sign of time: the mixmaster BLKh regime survives as a typical with probability one for the Collapsing Universe only; it disappears for the Expansion Process immediately; some specific set of the power-like regimes are typical for the Expanding Universe.
Strict Isotropization of the Early Universe does not follow from the classical Einstein Equation with normal physical energy-momentum tensor positive energy and pressure : only weak isotropization in the first approximation of the Hubble constants in different directions follows from dynamics. However, the real Universe has been strictly isotropic on the large scale as it became finally clear after the later observations of the background radiation in the late 80s.
Morse type theory for the charged particle in the magnetic field and ''Other-throwing of the Cycles'' Principle , , Novikov-Taimanov-Grinevich.
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Classification of generic Electrical Conductivity Tensors in the Strong Magnetic Fields for the normal metals with topologically complicated Fermi Surfaces. New observable integer-valued quantities. Right definition of the symmetry group for Quasi-Crystals the Quasi-Crystallographic Groups was invented in This approach is different from all other authors who assumed that the rotational part is finite. This result was published later it was included in the article of Le Thang, S. Piunikhin, V. Sadov published in the Russian Mathematical Surveys , vol.
The whole Family of Hyperelliptic Jacobian Varieties is Unirational with specific effectively written polinomial formulas in the space C n. The complete solution of the inverse finite-gap periodic problem Dubrovin-Novikov, Solution of Inverse Spectral Problem for the purely potential periodic operators with algebraic Fermi-Curve, Prym theta-functions, Novikov-Veselov equation and Hierarchy The Big Norm Problem for rapidly decreasing 2D operators, its solution for the "levels below the ground state" based on the Generalized Analytical Functions Grinevich-Novikov, Complete solution for the case of Elliptic Curve rank 2.
Krichever-Novikov Equation The difference higher rank commuting operators Krichever-Novikov, , New ideas are proposed how to calculate the Topological Charge through the inverse spectral data Dubrovin-Novikov, Complete Solution of the Topological Charge Problem, its calculation in terms of the inverse spectral algebro-geometrical data Grinevich-Novikov, Evolution of Multivalued Functions in the Witham Metod for KdV, numerical studies and formulation of boundary conditions, the influence of viscosity Avilov, Novikov, Krichever, Fourier Series and Riemann Surfaces. Krichever-Novikov bases and algebra's, the almost graded multiplication property Recent results: The continious analogs of Fourier bases on Riemann Surfaces, Indefnite Hilbert Spaces and finite-gap operators with singularities Grinevich-Novikov, , The String Equation as an algebraic object: the Painleve'-I equation can be presented as an equation on the module space of the elliptic curves , with P.
Cyclic, Semicyclic and Quasicyclic Laplace Chains for the 2D Schroedinger operators in periodic magnetic field and potential, the operators with pair of infinitely degenerate exactly solvable energy levels Novikov-Veselov, It turns out that it is a 2D ''Burgers Hierarchy''. Magnetic Pauli Operators was constructed on that base with Grinevich and Mironov, Discretization of Differential-geometrical Connection on the Triangulated Manifolds and linear difference triangle operators.
Integrable Soliton Systems on the trivalent tree, fourth order selfadjoint operators and Laplace Transformations. Krichever-Novikov, Cohomology of the Steenrod algebra. Nauk SSSR, , v. Some problems in the topology of manifolds connected with the theory of Thom spaces. On embedding simply-connected manifolds in Euclidean space. On the diffeomorphisms of simply-connected manifolds.
Smooth manifolds of a general homotopy type, Intern. Homotopy properties of Thom complexes. Homotopy properties of the group of diffeomorphisms of a sphere. Informatsii Akad. Nauk SSSR, , Homotopically equivalent smooth manifolds, I. Foliations of codimension 1 on manifolds, Dokl. Foliations of codimension 1, Dokl. Smooth foliations on three-dimensional manifolds , Uspekhi Mat.
Nauk, , v. Main trends of algebraic topology and algebraic geometry, Uspekhi Mat. Pyatetskii-Shapiro and I. Gorki mathematical seminar on homotopic topology June , Uspekhi Mat. Vishik and M. New ideas in algebraic topology K-theory and its applications. Uspekhi Mat. Homotopic and topological invariance of certain rational classes of Pontryagin. Topological invariance of rational Pontryagin classes. Differentiable sphere bundles , Izv.
Rational Pontryagin classes, Homeomorphism and homotopy type of closed manifolds I. Structures on manifolds, Proc.
The topology of foliations , Trudy Moskov. Obshch, , v. On manifolds with free Abelian fundamental group and their applications. The translation has been made by AMS in , s.
Wolf prize in mathematics ( vol. 2)
This article also has been translated recently in the Topological Library v 2. As far as I know the work of Siebenmann mentioned in the footnote at the page 38 never has been published Traces of elliptic operators on submanifolds and K-theory, Dokl. Elliptic operators and submanifolds, Dokl. The Cartan-Serre theorem and intrinsic homology. Pontryagin classes, the fundamental group and some problems of stable algebra. Kirillow, D. Fuks and I. Operation rings and spectral sequences of Adams type in extraordinary cohomology theories, U-cobordisms and K-theory, Dokl.
Methods of algebraic topology from the point of view of cobordism theory. Adams operators and fixed points. Homotopic and differential topology history of mathematics in the Fatherland, Naukova Dumka, Kiev , , v. Pontryagin classes, the fundamental group and some problems of stable algebra , in Essays on Topology and Related Topics.
Algebraic construction and properties of Hermitian analogues of K-theory over ring with involution from the viewpoint of Hamiltonian formalism. Applications to differential topology and the theory of characteristic classes, I. Algebraic construction and properties of Hermitian analogues of K-theory over rings with involution from the viewpoint of Hamiltonian formalism.
Applications to differential topology and the theory of characteristic classes, II. Analogues hermitiens de la K-theorie, Actes Congr. Math Nice , Gauthier-Villars, Paris , , vol. Formal groups, power systems, and Adams operators. Formal groups and their role in the apparatus of algebraic topology , Uspekhi Mat. Buchstaber and A. On some characteristics of cosmological models , Zh. A necessary reconstruction of mathematical education, Priroda, , N 2, Singularities of the cosmological model of the Bianchi IX type according to the qualitative theory of differential equations , Zh.
A periodic problem for the Korteweg-de Vries equations, I. Funktsional Anal. Periodic and conditionally periodic analogues of the many soliton solutions of the Korteweg-de Vries equations , Zh. A periodic problem for the Korteweg-de Vries and Sturm-Liouville equations. Their connection with algebraic geometry, Dokl.
Qualitative theory of homogeneous cosmological models, Trudy Sem. The connection between the Hamiltonian formalisms of stationary and nonstationary problems, Functional Anal. Non-linear equations of Korteweg-de Vries type, finite zone linear operators, and Abelian varieties , Uspekhi Mat. Dubrovin and V. The Schroedinger equation in a periodic field and Riemann surfaces, Dokl.
Dubrovin and I. Homogeneous models in general relativity theory and gas dynamics , Uspekhi Mat. Algebraic topology, Encyclopedia of Mathematics, , vol. Methods of algebraic geometry in contemporary mathematical physics, Math. Reviews,, with V. Drinfel'd, I. Krichever and Yu. Problems in geometry, Moscow State University , M. Mishchenko, Yu. Solov'ev and A.
I, Funktsional Anal. A method of solving the periodic problem for the Korteweg-de Vries equation and a generalization of it, Proc. All-Union Conf. Petrovskii on his seventy-fifth birthday, Moscow State University , M. Algebraic geometry and mathematical physics, Proc.
Modern geometry. Methods and applications, Nauka, Moscow , with B. Dubrovin and A. Holomorphic fiberings and non-linear equations. Finite zone solutions of rank 2, Dokl. Solutions to the Ginzburg-Landau equations for planar textures in superfluid He-3, Comm. Golo and M. Methods of qualitative theory of dynamics systems in general relativity theory, Non-linear waves, Nauka, Moscow , , with O. Holomorphic bundles over algebraic curves and nonlinear equations. The theory of solitons and method of the inverse problem, Nauka, Moscow , with V.
Zakharov, S. Manakov, and L. P Pitaevskii. Ground states of a two-dimensional electron in a periodic magnetic field. Ground states in a periodic field. Magnetic Bloch functions and vector bundles. A method of solving the periodic problem for the KdV equations and its generalization, in Solitons, ed R. Bullough and P. Linear operators and integrable Hamiltonian systems, Proc.
Helsinki , Helsinki, Multivalued functions and functionals. An analogue of the Morse theory, Dokl. Periodic solutions of the Kirchhoff equations for the free motion of a rigid body in a fluid and the extended Lyusternik-Shnirel'man-Morse theory. Variational methods and periodic solutions of equations of Kirchhoff type. II, Funktsional Anal. Bloch functions in a magnetic field and vector bundles. Typical dispersion relations and their quantum numbers, Dokl. Kirchhoff type equations and many-valued functions and functionals. Analogue of the Morse-Lyusternik-Shnirel'man theory and periodic orbits in a magnetic field, Report to the I.