Varchenko, A. N. (Aleksandr Nikolaevich)
Overview
Works:  51 works in 224 publications in 4 languages and 2,910 library holdings 

Genres:  Conference papers and proceedings Bibliography Educational films Filmed lectures Nonfiction films 
Roles:  Author, Editor, Contributor 
Classifications:  QA614.58, 514.72 
Publication Timeline
.
Most widely held works by
A. N Varchenko
Singularities of differentiable maps by
V. I Arnolʹd(
Book
)
74 editions published between 1985 and 2013 in 3 languages and held by 551 WorldCat member libraries worldwide
... There is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end  they go on for ever like periodic fractions. Zoology, for example, has discovered thirtyfive thousand forms of life ... A.P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, shortwave and saddlepoint asymptotics and geometrical and wave optics)
74 editions published between 1985 and 2013 in 3 languages and held by 551 WorldCat member libraries worldwide
... There is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end  they go on for ever like periodic fractions. Zoology, for example, has discovered thirtyfive thousand forms of life ... A.P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, shortwave and saddlepoint asymptotics and geometrical and wave optics)
Special functions, KZ type equations, and representation theory by
A. N Varchenko(
Book
)
7 editions published in 2003 in English and held by 230 WorldCat member libraries worldwide
7 editions published in 2003 in English and held by 230 WorldCat member libraries worldwide
Geometry of differential equations(
Book
)
8 editions published in 1998 in English and held by 201 WorldCat member libraries worldwide
8 editions published in 1998 in English and held by 201 WorldCat member libraries worldwide
Topics in singularity theory : V.I. Arnold's 60th anniversary collection(
Book
)
8 editions published in 1997 in English and held by 199 WorldCat member libraries worldwide
8 editions published in 1997 in English and held by 199 WorldCat member libraries worldwide
Why the boundary of a round drop becomes a curve of order four by
A. N Varchenko(
Book
)
9 editions published between 1991 and 1992 in English and held by 192 WorldCat member libraries worldwide
9 editions published between 1991 and 1992 in English and held by 192 WorldCat member libraries worldwide
Geometry of qhypergeometric functions, quantum affine algebras and elliptic quantum groups by
V Tarasov(
Book
)
8 editions published between 1997 and 1998 in English and held by 165 WorldCat member libraries worldwide
8 editions published between 1997 and 1998 in English and held by 165 WorldCat member libraries worldwide
Multidimensional hypergeometric functions and representation theory of Lie algebras and quantum groups by
A. N Varchenko(
Book
)
11 editions published in 1995 in English and held by 152 WorldCat member libraries worldwide
This book recounts the connections between multidimensional hypergeometric functions and representation theory. In 1984, physicists Knizhnik and Zamolodchikov discovered a fundamental differential equation describing correlation functions in conformal field theory. The equation is defined in terms of a Lie algebra. Kohno and Drinfeld found that the monodromy of the differential equation is described in terms of the quantum group associated with the Lie algebra. It turns out that this phenomenon is the tip of the iceberg. The KnizhnikZamolodchikov differential equation is solved in multidimensional hypergeometric functions, and the hypergeometric functions yield the connection between the representation theories of Lie algebras and quantum groups. The topics presented in this book are not adequately covered in periodicals
11 editions published in 1995 in English and held by 152 WorldCat member libraries worldwide
This book recounts the connections between multidimensional hypergeometric functions and representation theory. In 1984, physicists Knizhnik and Zamolodchikov discovered a fundamental differential equation describing correlation functions in conformal field theory. The equation is defined in terms of a Lie algebra. Kohno and Drinfeld found that the monodromy of the differential equation is described in terms of the quantum group associated with the Lie algebra. It turns out that this phenomenon is the tip of the iceberg. The KnizhnikZamolodchikov differential equation is solved in multidimensional hypergeometric functions, and the hypergeometric functions yield the connection between the representation theories of Lie algebras and quantum groups. The topics presented in this book are not adequately covered in periodicals
Singularities of functions, wave fronts, caustics and multidimensional integrals by
V. I Arnolʹd(
Book
)
1 edition published in 2012 in English and held by 40 WorldCat member libraries worldwide
1 edition published in 2012 in English and held by 40 WorldCat member libraries worldwide
Singularités des applications différentiables by
V. I Arnolʹd(
Book
)
24 editions published in 1986 in French and Undetermined and held by 39 WorldCat member libraries worldwide
24 editions published in 1986 in French and Undetermined and held by 39 WorldCat member libraries worldwide
Classification des points critiques, des caustiques et des fronts d'onde by
V. I Arnolʹd(
Book
)
2 editions published in 1986 in French and held by 39 WorldCat member libraries worldwide
2 editions published in 1986 in French and held by 39 WorldCat member libraries worldwide
Monodromie et comportement asymptotique des intégrales by
V. I Arnolʹd(
Book
)
2 editions published in 1986 in French and held by 36 WorldCat member libraries worldwide
2 editions published in 1986 in French and held by 36 WorldCat member libraries worldwide
Osobennosti different︠s︡iruemykh otobrazheniĭ : monodromii︠a︡ i asimptotiki integralov by
V. I Arnolʹd(
Book
)
15 editions published between 1982 and 2004 in Russian and Undetermined and held by 25 WorldCat member libraries worldwide
15 editions published between 1982 and 2004 in Russian and Undetermined and held by 25 WorldCat member libraries worldwide
Osobennosti different︠s︡iruemykh otobrazheniĭ by
V. I Arnolʹd(
Book
)
in Russian and held by 22 WorldCat member libraries worldwide
in Russian and held by 22 WorldCat member libraries worldwide
Monodromy and asymptotics of integrals by
V. I Arnolʹd(
Book
)
4 editions published between 1988 and 2012 in English and held by 17 WorldCat member libraries worldwide
4 editions published between 1988 and 2012 in English and held by 17 WorldCat member libraries worldwide
Multidimensional hypergeometric functions and their appearance in conformal field theory, algebraic ktheory, algebraic geometry,
etc by
A. N Varchenko(
Visual
)
2 editions published in 1990 in English and held by 11 WorldCat member libraries worldwide
2 editions published in 1990 in English and held by 11 WorldCat member libraries worldwide
Pochemu granit︠s︡a krugloĭ kapli prevrashchaetsi︠a︡ v inversnyĭ obraz ėllipsa by
A. N Varchenko(
Book
)
4 editions published in 1995 in Russian and held by 8 WorldCat member libraries worldwide
4 editions published in 1995 in Russian and held by 8 WorldCat member libraries worldwide
Collected works by
V. I Arnolʹd(
Book
)
3 editions published between 2009 and 2013 in English and held by 2 WorldCat member libraries worldwide
"Vladimir Arnold is one of the greatest mathematical scientists of our time. He is famous for both the breadth and the depth of his work." "At the same time he is one of the most prolific and outstanding mathematical authors. This first volume of his Collected Works focuses on representations of functions, celestial mechanics, and KAM theory."Jacket
3 editions published between 2009 and 2013 in English and held by 2 WorldCat member libraries worldwide
"Vladimir Arnold is one of the greatest mathematical scientists of our time. He is famous for both the breadth and the depth of his work." "At the same time he is one of the most prolific and outstanding mathematical authors. This first volume of his Collected Works focuses on representations of functions, celestial mechanics, and KAM theory."Jacket
Hydrodynamics, bifurcation theory, and algebraic geometry, 19651972 by
V. I Arnolʹd(
)
1 edition published in 2013 in English and held by 0 WorldCat member libraries worldwide
This book features the collected works of Vladimir Arnold, one of the great mathematical scientists of our time. This volume focuses on hydrodynamics, bifurcation theory, and algebraic geometry
1 edition published in 2013 in English and held by 0 WorldCat member libraries worldwide
This book features the collected works of Vladimir Arnold, one of the great mathematical scientists of our time. This volume focuses on hydrodynamics, bifurcation theory, and algebraic geometry
MULTIDIMENSIONAL HYPERGEOMETRIC FUNCTIONS THE REPRESENTATION THEORY OF LIE ALGEBRAS AND QUANTUM GROUPS by
A. N Varchenko(
)
2 editions published in 1995 in English and held by 0 WorldCat member libraries worldwide
4.5 Twosided Hochschild complexes connected with a discriminantal configuration4.6 Algebraic interpretation of the abstract complexes X.(Cn k) and Q.(Cn k) of a discriminantal configuration; 4.7 Geometric interpretation of complexes C.(+Uqn'_; M; 2; +A)A and C.*(+Uqn'_; M; 2; u)A defined in (4.5); 4.8 Symmetrization; 4.9 Proof of Theorem (4.7.5); 5. Quasiisomorphism of twosided Hochschild complexes to suitable onesided Hochschild complexes; 5.1 Onesided Hochschild complexes connected with a discriminantal configuration
2 editions published in 1995 in English and held by 0 WorldCat member libraries worldwide
4.5 Twosided Hochschild complexes connected with a discriminantal configuration4.6 Algebraic interpretation of the abstract complexes X.(Cn k) and Q.(Cn k) of a discriminantal configuration; 4.7 Geometric interpretation of complexes C.(+Uqn'_; M; 2; +A)A and C.*(+Uqn'_; M; 2; u)A defined in (4.5); 4.8 Symmetrization; 4.9 Proof of Theorem (4.7.5); 5. Quasiisomorphism of twosided Hochschild complexes to suitable onesided Hochschild complexes; 5.1 Onesided Hochschild complexes connected with a discriminantal configuration
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Related Identities
 Arnolʹd, V. I. (Vladimir Igorevich) 19372010 Honoree Author Editor
 GuseĭnZade, S. M. (Sabir Medzhidovich) Author Contributor
 Khovanskiĭ, A. G. Editor
 Vasilʹev, V. A. 1956 Contributor Editor
 Etingof, P. I. (Pavel I.) 1969 Author
 Arnolʹd, V. I. (Vladimir Igorevich) 19372010
 Sosinskiĭ, A. B. (Alekseĭ Bronislavovich) Translator
 Tarasov, V. (V. O.) Author
 Arnold, V. I. Author
 Kotli︠a︡r, V. S. (Vladimir Semenovich)
Useful Links
Associated Subjects
Affine algebraic groups Algebra Arnolʹd, V. I.(Vladimir Igorevich), Bifurcation theory Boundary value problems Catastrophes (Mathematics) Celestial mechanics Cell aggregationMathematics Critical point theory (Mathematical analysis) Curves, Elliptic Differentiable mappings Differential algebra Differential equations Differential equations, Partial Fluid dynamicsMathematical models Functions, Special Geometry, Algebraic Geometry, Differential Global analysis (Mathematics) Global differential geometry Holomorphic mappings Hydrodynamics Hypergeometric functions Integral equationsAsymptotic theory KacMoody algebras KnizhnikZamolodchikov equations Mathematics Monodromy groups Quantum groups Representations of groups Representations of Lie algebras Representations of quantum groups Singularities (Mathematics) Topological groups Topology
Alternative Names
Alexander Nikolajewitsch Wartschenko
Alexander Nikolajewitsch Wartschenko russischUSamerikanischer Mathematiker
Alexander Varchenko Russian mathematician
Alexander Varchenko Russisch wiskundige
Varčenko, A. N.
Varčenko, Aleksandr Nikolaevič
Varčenko, Aleksandr Nikolaevič 1949
Varchenko, A.
Varchenko, A. 1949
Varchenko, A.N.
Varchenko, A. N. 1949
Varchenko, Aleksandr 1949
Varchenko, Aleksandr Nikolaevich.
Varchenko, Aleksandr Nikolaevich 1949
Varchenko, Alexander.
Varchenko, Alexander 1949
Varchenko, Alexandre Nikolaevich
Wartschenko, Alexander Nikolajewitsch 1949
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