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- Alexander Varchenko

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
51
Citations
12,289
266
World Ranking
735
National Ranking
369

- Algebra
- Mathematical analysis
- Pure mathematics

His primary areas of study are Pure mathematics, Algebra, Mathematical physics, Tensor product and Quantum group. His research brings together the fields of Function and Pure mathematics. As a member of one scientific family, Alexander Varchenko mostly works in the field of Algebra, focusing on Schubert calculus and, on occasion, General linear group, Schubert variety, Enumerative geometry, Schubert polynomial and Real algebraic geometry.

The concepts of his Mathematical physics study are interwoven with issues in Eigenvalues and eigenvectors, Yang–Baxter equation and Differential equation. In his work, Basis, Algebra over a field and Spectrum is strongly intertwined with Combinatorics, which is a subfield of Tensor product. Alexander Varchenko has researched Quantum group in several fields, including Transfer, Representation theory and Verma module.

- Singularities of Differentiable Maps (1180 citations)
- Arrangements of hyperplanes and Lie algebra homology (384 citations)
- Zeta-function of monodromy and Newton's diagram (209 citations)

His main research concerns Pure mathematics, Algebra, Bethe ansatz, Combinatorics and Tensor product. His research integrates issues of Mathematical analysis and Differential equation in his study of Pure mathematics. His Mathematical analysis research focuses on Monodromy and how it relates to Hypergeometric function.

His Algebra research includes elements of Algebra over a field and Filtered algebra. His Bethe ansatz research includes themes of Simple, Eigenvalues and eigenvectors and Conjecture. His Combinatorics study combines topics from a wide range of disciplines, such as Matrix, Variety and Product.

- Pure mathematics (57.78%)
- Algebra (19.72%)
- Bethe ansatz (16.39%)

- Pure mathematics (57.78%)
- Hypergeometric distribution (12.50%)
- Differential equation (13.61%)

His primary scientific interests are in Pure mathematics, Hypergeometric distribution, Differential equation, Combinatorics and Algebra. His Pure mathematics research integrates issues from Cotangent bundle and Flag. His research in Hypergeometric distribution focuses on subjects like Finite field, which are connected to Modulo, Polynomial, Knizhnik–Zamolodchikov equations, Prime number and Space.

His Space research is multidisciplinary, incorporating perspectives in Bethe ansatz, Tensor product and Mathematical physics. His study looks at the relationship between Combinatorics and fields such as Omega, as well as how they intersect with chemical problems. In the subject of general Lie algebra, his work in Verma module is often linked to Projective line, thereby combining diverse domains of study.

- Trigonometric weight functions as K-theoretic stable envelope maps for the cotangent bundle of a flag variety (48 citations)
- Elliptic and K-theoretic stable envelopes and Newton polytopes (26 citations)
- Elliptic and K-theoretic stable envelopes and Newton polytopes (26 citations)

- Algebra
- Pure mathematics
- Mathematical analysis

His primary areas of investigation include Pure mathematics, Flag, Equivariant map, Differential equation and Algebra. His Pure mathematics research incorporates themes from Cotangent bundle, Polynomial and Finite field. The study incorporates disciplines such as Trigonometry, Diagonal, Polytope and Trigonometric functions in addition to Flag.

He combines subjects such as Singular point of a curve, K-theory, Tangent bundle and Braid group with his study of Differential equation. His work on Equivariant cohomology as part of general Algebra research is often related to Context, thus linking different fields of science. Alexander Varchenko interconnects Quantum group, Schubert variety, Combinatorics and Type in the investigation of issues within Equivariant cohomology.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Singularities of Differentiable Maps, Volume 2: Monodromy and Asymptotics of Integrals

S.M. Gusein-Zade;A.N. Varchenko;Alexander N. Varchenko;V.I. Arnold.

**(1988)**

2693 Citations

Singularities of Differentiable Maps

V. I. Arnold;S. M. Gusein-Zade;A. N. Varchenko.

**(1985)**

1965 Citations

Arrangements of hyperplanes and Lie algebra homology

Vadim V. Schechtman;Alexander N. Varchenko.

Inventiones Mathematicae **(1991)**

436 Citations

Newton polyhedra and estimation of oscillating integrals

A. N. Varchenko.

Functional Analysis and Its Applications **(1977)**

354 Citations

Zeta-function of monodromy and Newton's diagram

A. N. Varchenko.

Inventiones Mathematicae **(1976)**

292 Citations

Multidimensional hypergeometric functions and representation theory of lie algebras and quantum groups

A. N. Varchenko.

**(1995)**

193 Citations

Geometry and Classificatin of Solutions of the Classical Dynamical Yang–Baxter Equation

Pavel Etingof;Alexander Varchenko.

Communications in Mathematical Physics **(1998)**

187 Citations

Quasiclassical asymptotics of solutions to the KZ equations

Nicolai Reshetikhin;Alexander Varchenko.

arXiv: High Energy Physics - Theory **(1994)**

172 Citations

Estimate of the number of zeros of an abelian integral depending on a parameter and limit cycles

A. N. Varchenko.

Functional Analysis and Its Applications **(1984)**

155 Citations

Solutions of the Quantum Dynamical Yang–Baxter Equation and Dynamical Quantum Groups

Pavel Etingof;Alexander Varchenko.

Communications in Mathematical Physics **(1998)**

148 Citations

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