Victor Buchstaber

Victor Buchstaber's AcademicInfluence.com Rankings

Victor Buchstaber

Mathematics

#2201

World Rank

#3435

Historical Rank

Measure Theory

#3189

World Rank

#3775

Historical Rank

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Mathematics

Why Is Victor Buchstaber Influential?

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According to Wikipedia, Victor Matveevich Buchstaber is a Soviet and Russian mathematician known for his work on algebraic topology, homotopy theory, and mathematical physics. Work Buchstaber's first research work was in cobordism theory. He calculated the differential in the Atiyah-Hirzebruch spectral sequence in K-theory and complex cobordism theory, constructed Chern-Dold characters and the universal Todd genus in cobordism, and gave an alternative effective solution of the Milnor-Hirzebruch problem. He went on to develop a theory of double-valued formal groups that led to the calculation of cobordism rings of complex manifolds having symplectic coverings and to the explicit construction of what are now known as Buchstaber manifolds. He devised filtrations in Hopf algebras and the Buchstaber spectral sequence, which were successfully applied to the calculation of stable homotopy groups of spheres.

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Victor Buchstaber's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Torus Actions and their Applications in Topology and Combinatorics (2002) (543)
Mathematical Proceedings of the Cambridge Philosophical Society (2008) (467)
Kleinian functions, hyperelliptic Jacobians and applications (1997) (171)
Toric Topology (2012) (121)
Spaces of polytopes and cobordism of quasitoric manifolds (2006) (96)
Torus actions, combinatorial topology, and homological algebra (2000) (96)
Solitons, Geometry, and Topology: On the Crossroad (1997) (89)
Tangential Structures on Toric Manifolds, and Connected Sums of Polytopes (2000) (80)
HYPERELLIPTIC KLEINIAN FUNCTIONS AND APPLICATIONS (1996) (78)
Elliptic Dunkl operators, root systems, and functional equations (1994) (73)
Rational analogs of abelian functions (1999) (68)
Cellular cochain algebras and torus actions (2004) (57)
Uniformization of jacobi varieties of trigonal curves and nonlinear differential equations (2000) (52)
Multivalued groups, their representations and Hopf algebras (1997) (49)
Moment-angle complexes (2002) (48)
Polynomial Lie Algebras (2002) (45)
Integrable correspondences and algebraic representations of multivalued groups (1996) (44)
n-valued Groups: Theory and Applications (2006) (44)
TORUS ACTIONS AND COMBINATORICS OF POLYTOPES (1999) (41)
Solution of the problem of differentiation of Abelian functions over parameters for families of (n, s)-curves (2008) (36)
Multi-dimensional sigma-functions (2012) (36)
Toric Genera (2009) (34)
LECTURES ON TORIC TOPOLOGY (2008) (33)
Ring of simple polytopes and differential equations (2008) (32)
An Invitation to Toric Topology: Vertex Four of a Remarkable Tetrahedron. (2008) (30)
Rings of continuous functions, symmetric products, and Frobenius algebras (2004) (30)
Multivalued Groups, n -Hopf Algebras and n -Ring Homomorphisms (1998) (29)
Topology and geometry of the canonical action of $T^4$ on the complex Grassmannian $G_{4,2}$ and the complex projective space $CP^{5}$ (2014) (29)
Combinatorics of Simplicial Cell Complexes and Torus Actions (2004) (28)
Combinatorial 2-truncated Cubes and Applications (2012) (27)
Polynomial dynamical systems and the Korteweg—de Vries equation (2016) (27)
Holomorphic solutions of the double confluent Heun equation associated with the RSJ model of the Josephson junction (2015) (27)
Geometry, Topology, and Mathematical Physics (2004) (26)
Rotation number quantization effect (2010) (24)
On a remarkable functional equation in the theory of generalized Dunkl operators and transformations of elliptic genera (1996) (23)
Combinatorial algebras and multivalued involutive groups (1996) (22)
Explicit solution family for the equation of the resistively shunted Josephson junction model (2013) (22)
Elliptic formal group laws, integral Hirzebruch genera and Krichever genera (2010) (21)
Toric Topology of the Complex Grassmann Manifolds (2018) (20)
On determinants of modified Bessel functions and entire solutions of double confluent Heun equations (2015) (18)
Frobenius n-homomorphisms, transfers and branched coverings (2006) (17)
Heat Equations in a Nonholomic Frame (2004) (16)
Dieudonné modules and p-divisible groups associated with Morava K -theory of Eilenberg-Mac Lane spaces (2005) (16)
Automorphisms of the solution spaces of special double-confluent Heun equations (2016) (16)
Electrodynamic properties of a Josephson junction biased with a sequence of delta-function pulses (2001) (15)
Fullerenes, Polytopes and Toric Topology (2016) (15)
Infinite-dimensional Lie algebras determined by the space of symmetric squares of hyperelliptic curves (2017) (14)
On monodromy eigenfunctions of Heun equations and boundaries of phase-lock areas in a model of overdamped Josephson effect (2016) (14)
Total positivity, Grassmannian and modified Bessel functions (2017) (13)
A recursive family of differential polynomials generated by the sylvester identity and addition theorems for hyperelliptic Kleinian functions (1997) (13)
Generalized Kramers–Wannier duality for spin systems with non-commutative symmetry (2003) (12)
Manifolds of Isospectral Matrices and Hessenberg Varieties (2018) (12)
Equivariant complex structures on homogeneous spaces and their cobordism classes (2008) (12)
Finite sets of operations sufficient to construct any fullerene from C20 (2016) (11)
Kleinian functions, hyperelliptic Jacobians and applications . Integrable systems with pairwise interactions and functional equations (1997) (11)
Geometry, Topology, and Mathematical Physics: S. P. Novikov’s Seminar: 2006–2007 (2008) (11)
Hyperelliptic Addition Law (2004) (11)
COHOMOLOGICAL RIGIDITY OF MANIFOLDS DEFINED BY RIGHT-ANGLED 3-DIMENSIONAL POLYTOPES (2017) (10)
The dynamics of transients in an overdamped Josephson junction biased by trains of short current pulses with controllable parameters (2003) (9)
Construction of fullerenes (2015) (9)
COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: Moment-angle complexes and combinatorics of simplicial manifolds (2000) (9)
Two-Valued Groups, Kummer Varieties, and Integrable Billiards (2010) (9)
Flag manifolds and the Landweber–Novikov algebra (1998) (9)
Ring of Polytopes, Quasi-symmetric functions and Fibonacci numbers (2010) (8)
Cobordisms, Manifolds with Torus Action, and Functional Equations (2018) (8)
Multidimensional Schrodinger equations with Abelian potentials (2002) (8)
Features of the dynamics of a josephson junction biased by a sinusoidal microwave current (2006) (8)
Multi-variable sigma-functions: old and new results (2018) (7)
Josephson junction parameters for alternating current wave form synthesis (2006) (7)
"Time series analysis and Grassmannians”, Applied problems of Radon transform (1994) (7)
w-function of the KDV hierarchy (2004) (7)
Yang–Baxter maps, Darboux transformations, and linear approximations of refactorisation problems (2020) (6)
Graded lie algebras that define hyperelliptic sigma functions (2002) (6)
The Gelfand transform in commutative algebra (2005) (6)
Torus Actions, Equivariant Moment-Angle Complexes, and Coordinate Subspace Arrangements (1999) (6)
Modeling of rf-biased overdamped Josephson junctions (2008) (5)
Representations of the Klein Group Determined by Quadruples of Polynomials Associated with the Double Confluent Heun Equation (2018) (5)
$\sigma$-функции $(n,s)$-кривых@@@$\sigma$-functions of $(n,s)$-curves (1999) (5)
Torus Actions Determined by Simple Polytopes (2000) (5)
Quantum Josephson D/A converter driven by trains of short 2/spl pi/-pulses (2002) (4)
Moment-angle complexes and polyhedral products for convex polytopes (2010) (4)
Upper and lower bound theorems for graph-associahedra (2010) (4)
Polynomial Hamiltonian integrable systems on symmetric powers of plane curves (2018) (4)
$(2n,k)$-manifolds and applications (2014) (4)
KdV hierarchies and quantum Novikov's equations (2021) (4)
Explicit algebraic description of hyperelliptic Jacobians on the basis of the Klein σ-functions (1996) (4)
The space of symmetric squares of hyperelliptic curves and integrable Hamiltonian polynomial systems on $\bbbR^4$ (2017) (3)
Toric genera of homogeneous spaces and their fibrations (2011) (3)
Topology, Geometry, Integrable Systems, and Mathematical Physics (2014) (3)
Lie Algebras of Heat Operators in a Nonholonomic Frame (2019) (3)
Quantum digital ac waveform synthesizer based on pulse-width modulation method (2008) (3)
Characteristic expansions and multiplicative addition theorems (1996) (3)
Embeddings of moment-angle manifolds and sequences of Massey products. (2018) (3)
Combinatorics of Simplicial Cell Complexes (2004) (3)
COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: Mathematical models of the dynamics of an overdamped Josephson junction (2008) (3)
Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3 (2018) (3)
Toric Topology of Stasheff Polytopes (2007) (2)
Analytical and number-theoretical properties of the two-dimensional sigma function (2020) (2)
Application of Multivariate Statistical Analysis for the Detection of Structural Changes in the Series of Monitoring Data (1991) (2)
Sigma Functions and Lie Algebras of Schrödinger Operators (2020) (2)
XXIX Workshop on Geometric Methods in Physics (2010) (2)
A pr 2 01 9 The foundations of ( 2 n , k )-manifolds (2019) (2)
AN INDEX OF AN EQUIVARIANT VECTOR FIELD AND ADDITION THEOREMS FOR PONTRJAGIN CHARACTERISTIC CLASSES (2000) (2)
Addition Theorems, Formal Group Laws and Integrable Systems (2010) (2)
Spectral clustering of combinatorial fullerene isomers based on their facet graph structure (2019) (2)
A quantum digital ac-voltage synthesizer based on pulse-width modulation of the Josephson junction bias current (2009) (2)
DOUBLE COBORDISM, FLAG MANIFOLDS AND QUANTUM DOUBLES (1996) (2)
Combinatorics of simple polytopes and differential equations (2008) (2)
Toric Topology. Chapter 2: Combinatorial structures (2011) (2)
A statistical model of background air pollution frequency distributions (1991) (2)
Victor Enolski (1945–2019) (2020) (1)
The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications (2017) (1)
Direct families of polytopes with nontrivial Massey products (2018) (1)
Многообразие решений уравнения $\displaystyle[\frac{\partial^2}{\partial u_1\partial u_2}-6\wp_{1,2}(u_1,u_2)+E]\psi=0$@@@The manifold of solutions of the equation $[\dfrac{\partial^2}{\partial u_1\partial u_2}-6\wp_{1,2}(u_1,u_2)+E]\psi=0$ (2001) (1)
Operations and quantum doubles in complex oriented cohomology theory (1999) (1)
COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: Face-polynomials of simple polytopes and the two-parameter Todd genus (2008) (1)
The orbit spaces $G_{n,2}/T^n$ and the Chow quotients $G_{n,2}\!/\!/(\mathbb{C} ^{\ast})^{n}$ of the Grassmann manifolds $G_{n,2}$ (2021) (1)
Toric Topology and Applications (2015) (1)
Complex cobordism classes of homogeneous spaces (2007) (1)
Heat Equations and Sigma Functions (2009) (1)
LIE-HOPF ALGEBRAS AND LOOP HOMOLOGY OF SUSPENSION SPACES (2010) (1)
Statistical Analysis of Long Term Trends in Atmospheric CO2 Concentration at Baseline Stations (1988) (1)
The problem of differentiation of an Abelian function over its parameters (2006) (1)
Abelian Functions and Singularity Theory (2007) (1)
An exploratory analysis of long‐term trends in atmospheric CO2 concentrations (1991) (1)
Algebraically integrable quadratic dynamical systems (2012) (1)
The n-valued groups: results and prospectives (2005) (0)
Relationships Between Hyperelliptic Functions of Genus 2 and Elliptic Functions (2021) (0)
International Conference on Toric Topology Programme of Talks (2006) (0)
Half-dimensional torus actions (2015) (0)
Classification of $\mathbb{C}P^2$-multiplicative Hirzebruch genera (2015) (0)
XXIX Workshop on Geometric Methods in Physics : 27 June-3 July 2010, Białowieża, Poland (2010) (0)
Front Matter for Volume 1307 (2010) (0)
Hopf algebras and homotopy invariants (2010) (0)
Two-Valued Groups, Kummer Varieties, and Integrable Billiards (2018) (0)
Polytopes and Hopf algebras (2010) (0)
Differential-algebraic solutions of the heat equation (2014) (0)
Embedding theorems for quasitoric manifolds (2015) (0)
To the memory of Selim Grigor'evich Krein (2018) (0)
Cohomology rings of subspace arrangement complements (2002) (0)
A ug 2 00 9 TORIC GENERA (2009) (0)
Infinite-dimensional Lie algebras determined by the space of symmetric squares of hyperelliptic curves (2017) (0)
Geometry and combinatorics of polytopes (2015) (0)
Boris Nikolaevich Chetverushkin (on his 70th birthday) (2014) (0)
Resolution of Singularities of the Orbit Spaces $$G_{n,2}/T^n$$ (2020) (0)
Back Matter for Volume 1307 (2010) (0)
Circle actions on toric manifolds and their applications (2005) (0)
Spaces of polytopes , and cobordisms of toric manifolds (2012) (0)
Classification of involutive commutative two-valued groups (2023) (0)
Asymptotic properties of Arnold tongues and Josephson effect (2019) (0)
Ring of polytopes and the Rota-Hopf algebra (2010) (0)
Formal group laws and Hirzebruch genera (2015) (0)
Kolmogorov and topology (2007) (0)
XXIX workshop on geometric methods in physics, Bia\lowie\Dza Poland, June 27 -- July 3, 2010. Selected papers based on the presentations at the workshop. (2010) (0)
A ug 2 00 7 COMPLEX COBORDISM CLASSES OF HOMOGENEOUS SPACES (0)
Mikhail Semenovich Agranovich (2018) (0)
Partially framed manifolds and loop spaces on the group (2020) (0)
Rostislav Ivanovich Grigorchuk (on his sixtieth birthday) (2013) (0)
Cohomology of moment-angle complexes and combinatorics of triangulated manifolds (2002) (0)
Commutative and homological algebra of simplicial complexes (2002) (0)
Yurii Grigor'evich Borisovich (obituary) (2008) (0)
Towards the theory of (2n,k)-manifolds: primary examples (2014) (0)
Topology, Geometry, and Dynamics (2021) (0)
Toric and quasitoric manifolds (2002) (0)
Combinatorial algebra of face rings (2015) (0)
Moment-angle complexes and applications (2008) (0)
Toric varieties and manifolds (2015) (0)
Anatolii Moiseevich Vershik (on his 80th birthday) (2014) (0)
Bordism and cobordism (2015) (0)
Commutative and homological algebra (2015) (0)
Topology and combinatorics of simplicial complexes (2002) (0)
Cluster-Permutohedra and Submanifolds of Flag Varieties with Torus Actions (2022) (0)
Toric Topology. Chapter 1: Geometry and combinatorics of polytopes (2011) (0)
A T ] 2 0 M ay 2 00 0 MOMENT-ANGLE COMPLEXES AND COMBINATORICS OF SIMPLICIAL MANIFOLDS (2022) (0)
Euler Characteristic, Dehn–Sommerville Characteristics, and Their Applications (2007) (0)
Theta divisors and permutohedra (2022) (0)
Differentiation of Genus $4$ Hyperelliptic Functions (2019) (0)
On the scientific works of Dmitry Alexandrovich Popov (2020) (0)
Homotopy theory of polyhedral products (2015) (0)
Vladimir Abramovich Rokhlin and algebraic topology (2021) (0)
Torus actions and complex cobordism (2015) (0)
Krichever-Novikov continuous basis for plane algebraic curves (2005) (0)
Some Mathematical Approaches to Modeling Dynamic Processes in the Environment (1990) (0)
Hyperelliptic Sigma Functions and Adler–Moser Polynomials (2021) (0)
Toric Topology. Chapter 3: Commutative and homological algebra of face rings (2011) (0)

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