V. Buchstaber - Publications


Buchstaber V., Panov T.E., Ray N., Toric genera, Accepted to print in AMRN; Preprint, 2009; arXiv:0908.3298.
Buchstaber V., T.E.Panov, Toric Topology, Dobrushin International Conference, Proceedings, Moscow, Russia, 2009, 27--36.
Buchstaber V., Ring of Combinatorial Polytopes and Applications, Mathematisches Forschungsinstitut Oberwolfach, Report No. 01/2009, Toric Geometry, 4 - 10 January, 2009, 14--16.
Buchstaber V., E.Yu.Bunkova, Heat Equation and Families of Two-Dimensional Sigma Functions, Proceedings of the Steklov Institute of Mathematics, v. 266, 2009, 1-28.


Buchstaber V., O.V.Karpov, Tertychniy S.I., Niemeyer J., Kieler O., Modeling of rf-biased overdamped Josephson junctions, J. Appl. Phys., 104, 093910, 2008; Virtual Journal of Applications of Superconductivity, v. November 15, 2008, Issue 10.
Buchstaber V., Lectures on Toric Topology, Toric Topology Workshop, KAIST 2008, Trends in Mathematics, Information Center for Mathematical Sciences, V. 11, N. 1, 2008, 1-55.
Buchstaber V., Leykin D.V., Solution of the problem of differentiation of Abelian functions over parameters for families of (n,s)-curves, Funct. Anal. Appl., 42:4, 2008, 268-278.
Buchstaber V., Ring of Simple Polytopes and Differential Equations, Proceedings of the Steklov Institute of Mathematics, v. 263, 2008, 1-25.
Buchstaber V., Terzic' S., Equivariant complex structures on homogeneous spaces and their cobordism classes, Geometry, Topology, and Mathematical Physics, S.P.Novikov"s seminar: 2006-2007 (V.M.Buchstaber, I.M.Krichever, Eds), Providence (RI), Amer. Math. Soc. Transl., v. 224, ser. 2, 2008, 27-57; arXiv:math. AT/0708.2054 v.1, 15 Aug 2007.
Buchstaber V., Ray N., An Invitation to Toric Topology: Vertex Four of a Remarkable Tetrahedron, Toric topology., Contemp. Math., v. 460, Providence (RI): Amer. Math. Soc., 2008, 1-27; MIMS, 2008.31: http://www.manchester.ac.uk/mims/eprints. http://www.manchester.ac.uk/mims/eprints
Buchstaber V., Face-polynomials of simple polytopes and two-parameter Todd genus, Russian Math. Surveys, v. 63, Issue 3, 2008, 554--556.
Buchstaber V., Rees E.G., Frobenius n-homomorphisms, transfers and branched coverings, Proceeding of the Cambridge Phil. Society, v. 144(1), 2008, 1-12; ArXiv: math.RA/0608120 v. 1, 4 Aug 2006.


Buchstaber V., Panov T., Ray N., "Spaces of polytopes and cobordism of quasitoric manifolds". Moscow Math. Journal 7 (2007), no.2, 219-242. http://arxiv.org/abs/math.AT/0609346
Buchstaber V., The Leonhard Euler Tercentenary. The problem of support for young mathematicians, Newsletter of the EMS, Issue 65, EMS, September 2007, 3-4.
Buchstaber V., Abelian Functions and Singularity Theory, International Conference "Analysis and Singularities", dedicated to the 70th anniversary of V.I. Arnold, Book of abstracts, Steklov Math. Inst., Moscow, August 20 - 24, 2007, 117-118.
Buchstaber V., Koritskaya E.V., The Quasi-Linear Burgers-Hopf Equation and the Stasheff Polytopes, Funct. Anal. Appl., 41:3, 2007, 196-207.
Buchstaber V., Leykin D.V., Differentiation of Abelian functions over its parameters, Russian Math. Surveys, v. 62, Issue 4, 2007, 787-789.
Buchstaber V., Ray N., The Universal Equivariant Genus and Krichever"s Formula, Russian Math. Surveys, v. 62, Issue 1, 2007, 178-180.
Buchstaber V., Panov T.E., Ray N., Spaces of polytopes and cobordism of quasitoric manifolds, Moscow Math. J., v. 7, N. 2, 2007, 219-242; arXiv: Math. AT/0609346.
Buchstaber V., Kolmogorov and Topology, Chapter 1 in the book: "Kolmogorov`s Heritage in Mathematics", edited by E.Charpenter, A.Lesne, N.Nikolski, Springer-Verlag Berlin Heidelberg, 2007.
Buchstaber V., Lazarev A., Dieudonne modules and p-divisible groups asoociated with Morava K-theory of Eilenberg-Mac Lane spaces, Algebraic and Geometric Topology, 7, 2007, 529--564; arXiv:math. AT/0507036 v.1, 2 Jul 2005.


Buchstaber V., Gaifullin A., "Representations of m-valued groups on triangulations of manifolds", Russ. Math. Surv., 2006, 61 (3), 560562 http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=1751&option_lang=rus
Buchstaber V., Karpov O.V., Sherstobitov S.V., Tertychniy S.I., Niemeyer J., Kieler O., Josephson junction parameters for alternating current wave form synthesis, J. Appl. Phys., 100, 093907, 2006.
Buchstaber V., Analogous polytopes, toric manifolds and complex cobordisms, International conference on Toric Topology, Osaka, 29.05. - 03.06.2006.
Buchstaber V., Gaifullin A.A., Representations of m-valued groups on triangulations of manifolds, Russian Math. Surveys 61, Issue 3, 2006, 560-562.
Buchstaber V., Euler characteristic, Dehn-Sommerville characteristics, and their applications, In the book: "Topology in Molecular Biology", Springer Series in Solid-Sciences, v. 150, 2006, 163-176.
Buchstaber V., The n-valued groups: theory and applications, Moscow Math. J., v. 6, N. 1, 2006, 57-84.
Buchstaber V., Krichever I.M., Integrable equations, addition theorems, and the Riemann-Schottky problem, Russian Math. Surveys, 61, Issue 1, 2006, 19-78.
Buchstaber V., Leykin D.V., Functional equations that define multiplication in a continuous Krichever-Novikov basis, Russian Math. Surveys, v. 61, Issue 1, 2006, 165-167.


Buchstaber V., Leykin D.V., Differential and differential-functional equations for sigma-functions, Fourth International Conference on Differential and Functional Differential Equations, Moscow, August 14-21, 2005, Book of abstracts.
Buchstaber V., Jacobi transformations and its applications, International conference on Selected Problems of Modern Mathematics, dedicated to the 200th anniversary of K.G. Jacobi, Kaliningrad, April 4-9, 2005, Book of abstracts.
Buchstaber V., Lazarev A., The Gelfand Transform in Commutative Algebra, Moscow Math. J., v. 5, N. 2, 2005, 311-327.
Buchstaber V., Leykin D.V., Addition laws on Jacobian varieties of plane algebraic curves, Proceedings of the Steklov Math. Inst., v. 251, Issue 4, 2005, 49-120.
Buchstaber V., Leykin D.V., Trilinear functional equations, Russian Math. Surveys, v. 60, Issue 2, 2005, 341-343.
Buchstaber V., Leykin D.V., Hyperelliptic Addition Law, J. Nonlinear Math. Phys., 12, suppl. 1, 2005, 106--123.


Baskakov I.V., Buchstaber V., Panov T., "Cellular cochain algebras and torus actions". Russian Math. Surveys 59 (2004), no.3, 562-563; arXiv:math.AT/0407189.
Buchstaber V., Panov T., "Combinatorics of simplicial cell complexes, and torus actions". Proceedings of the Steklov Institute of Mathematics, vol. 247, 2004, pp.33-49.
Buchstaber V., Panov T., "Toricheskie deistiviya v topologii i kombinatorike" (Torus Actions in Topology and Combinatorics, in Russian). MCCME, Moscow, 2004, 272 pages. http://www.mccme.ru/publications/2004.html
Buchstaber V., Kolmogorov et la Topologie, L`heritage de Kolmogorov en mathematiques, Editions Berlin, Paris, 2004, 151-162.
Buchstaber V., Panov T.E., Combinatorics of simplicial cell complexes, and torus actions, Proceedings of the Steklov Math. Inst., v. 247, 2004, 1-17.
Buchstaber V., Leykin D.V., Heat Equations in a Nonholonomic Frame, Funct. Anal. Appl., 38:2, 2004, 88-101.
Buchstaber V., Baskakov I.V., Panov T.E., Cellular cochain algebras and torus actions, Russian Math. Surveys, v. 59, Issue 3, 2004, 562-563.
Buchstaber V., Lazarev A.Yu., The discrete Gel"fand transformation and its dual, Russian Math. Surveys, v. 59, Issue 1, 2004, 184-186.
Buchstaber V., Rees E.G., Rings of continuous functions, symmetric products, and Frobenius algebras, Russian Math. Surveys, v. 59, Issue 1, 2004, 125-145.
Buchstaber V., Panov T.E., Torus actions in topology and combinatorics, Mosk. Tsentr Nepr. Mat. Obraz., Moscow, 2004, 272 pp. (in Russian).
Buchstaber V., Shorina S.Yu., w-Function of the KdV Hierarchy, Geometry, Topology, and Mathematical Physics, S.P.Novikov`s seminar: 2002-2003 (V.M.Buchstaber, I.M.Krichever Eds), Providence (RI), Amer. Math. Soc. Transl., v. 212, ser. 2, 2004, 41--46.
Buchstaber V., Interview with Sergey P. Novikov, Geometry, Topology, and Mathematical Physics, S.P.Novikov`s seminar: 2002-2003 (V.M.Buchstaber, I.M.Krichever Eds), Amer. Math. Soc. Transl., v. 212, ser. 2, Providence (RI), 2004, 25--40.


Buchstaber V., Leykin D.V., Pavlov M.V., Egorov`s hydrodynamic chains, Chazy equation and group SL(2,C), Funct. Anal. Appl., 37:4, 2003, 251-262.
Buchstaber V., Polynomial Lie algebras and versal deformations, Meeting: Singularities, Obervwolfach, 21 27 September, 2003.
Buchstaber V., Shorina S.Yu., The w-Function of a Solution the g-th Stationary KdV Equation, Russian Math. Surveys, v. 58, Issue 4, 2003, 780-781.
Buchstaber V., Kolmogorov, cohomology and cobordisms, Intern. conf. "Kolmogorov and contemporary mathematics", Book of abstracts, Moscow, June 16 - 21, 2003.
Buchstaber V., Monastyrsky M.I., Generalized Kramers-Wannier duality for spin systems with non-commutative symmetry, J. Phys. A, 36, N. 28, 2003, 7679--7692.
Buchstaber V., Shorina S.Yu., Commuting multidimensional third-order differential operators defining a KdV hierarchy, Russian Math. Surveys, v. 58, Issue 3, 2003, 610-612.
Buchstaber V., T.E.Panov, Torus actions,equivariant moment-angle complexes, coordinate subspace arrangements, Math. Sci. (New York), 113, N. 4, 2003, 558-568; arXiv: math. AT/9912199.


Buchstaber V., Panov T., "Torus Actions and Their Applications in Topology and Combinatorics". University Lecture Series, vol.24, American Mathematical Society, Providence, RI, 2002 (152 pages). http://www.ams.org/bookstore?fn=20&arg1=ulectseries&ikey=ULECT-24
Buchstaber V., Rees E.G., The Gelfand map and symmetric products, Selecta Math. (N.S.), 8, N. 4, 2002, 523-535.
Buchstaber V., Algebraic varieties of solutions of two-dim Lame type equations, Intern. conf. "Differential and functional differential equations", Book of abstracts, Moscow, August 11 - 17, 2002, 19-20.
Buchstaber V., Leykin D.V., Polynomial Lie algebras, Functional Anal. Appl., 36:4, 2002, 267-280.
Buchstaber V., Enolskii V.Z., Leykin D.V., Eilbeck J.C., Salerno M., Multidimensional Schrodinger equation with Abelian potential, J. Math. Phys., v. 43, N. 6, 2002, 2858--2881.
Buchstaber V., Leykin D.V., Graded Lie algebras defining hyperelliptic sigma-functions, Doklady Math. Sci., 66, 4:2, 2003, 87-90.
Buchstaber V., Leykin D.V., Lie algebras associated with sigma-functions and versal deformations, Russian Math. Surveys, v. 57, Issue 3, 2002, 584-586.
Buchstaber V., Rees E.G., Applications of Frobenius n-homomorphisms, Russian Math. Surveys, v. 57, Issue 1, 2002, 148-149.
Buchstaber V., Panov T.E., Torus actions and their applications in topology and combinatorics, University Lecture Series, v. 24, AMS, Providence (RI), 2002, 152 pp.


Buchstaber V., Symmetric powers as algebraic variety, Conference "Fundamental mathematics today", Dedicated to the 10th anniversary of the Independent University of Moscow, Programme and abstracts, Moscow, December 26 - 29, 2001, 11.
Buchstaber V., Leykin D.V., The manifold of solutions of the two-dimensional analogue of the two-zone Lame equation, Russian Math. Surveys, v. 56, Issue 6, 2001, 1155-1157.
Buchstaber V., Rees E.G., A constructive proof of the generalized Gelfand isomorphism, Functional Anal. Appl., v. 35, N. 4, 2001, 257-260.
Buchstaber V., Integrable nonlineal differential equations and uniformization of universal spaces of Jacobians, Intern. conf. "Differential equations and related topics", Book of abstracts, Moscow, May 22 - 27, 2001, 78.
Buchstaber V., Ray N., Tangential Structures on Toric Manifolds and Connected Sums of Polytopes, Int. Math. Res. Notices, N. 4, 2001, 193--219; arXiv: Math AT/0010025.


Buchstaber V., Panov T., "Torus actions, equivariant moment-angle complexes and coordinate subspace arrangements". Journal of Math. Sciences 113 (2003), no. 4, 558-568; arXiv:math.AT/9912199. http://arxiv.org/abs/math.AT/9912199
Buchstaber V., Panov T., "Torus actions determined by simple polytopes". In: "Geometry and Topology: Aarhus" (K.Grove, I.H.Madsen, and E.K.Pedersen, eds.). Contemporary Mathematics, vol.258, American Mathematical Society, Providence, RI, 2000, pp.33-46.
Buchstaber V., Panov T., "Moment-angle complexes and combinatorics of simplicial manifolds". Russian Math. Surveys 55 (2000), no.3, 576-579. http://higeom.math.msu.su/people/taras/#publ
Buchstaber V., Panov T., "Torus actions, combinatorial topology and homology algebra". Russian Math. Surveys 55 (2000), no.5, 825-921; arXiv:math.AT/0010073. http://arxiv.org/abs/math.AT/0010073
Buchstaber V., Leykin D.V., Enolskii V.Z., Uniformization of Jacobi manifolds of trigonal curves, and nonlinear differential equations, Functional Anal. Appl., 34:3, 2000, 159-171.
Buchstaber V., Panov T.E., Torus actions, combinatorial topology and homological algebra, Russian Math. Surveys, v. 55, Issue 5, 2000, 825-921.
Buchstaber V., Botvinnik B.I., Novikov S.P., Yuzvinskii S.A., Algebraic aspects of the theory of multiplications in complex cobordism theory, Russian Math. Surveys, v. 55, Issue 4, 2000, 613-633.
Buchstaber V., Panov T.E., Moment-angle complexes and combinatorics of simplicial manifolds, Russian Math. Surveys, v. 55, Issue 3, 2000, 567-569.
Buchstaber V., K.E.Feldman, The index of an equivariant vector field and addition theorems for Pontryagin characteristic classes, Izv. Math. 64:2, 2000, 223-247.
Buchstaber V., T.E.Panov, Torus action determined by simple polytopes, "Geometry and Topology: Aarhus" (K.Grove, I.Madsen and E.Pedersen, eds), Contemporary Mathematics 258 AMS, Providence, RI, 2000, 33-46.


Buchstaber V., Panov T., "Torus actions and combinatorics of polytopes". Proceedings of the Steklov Institute of Mathematics, vol. 225, 1999, pp.87-120; arXiv:math.AT/9909166. http://arxiv.org/abs/math.AT/9909166


Buchstaber V., Panov T., "Algebraic topology of manifolds defined by simple polytopes". Russian Math. Surveys 53 (1998), no.3, 623-625. http://higeom.math.msu.su/people/taras/#publ