What is he best known for?
The fields of study he is best known for:
- 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.
His most cited work include:
- 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)
What are the main themes of his work throughout his whole career to date?
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.
He most often published in these fields:
- Pure mathematics (57.78%)
- Algebra (19.72%)
- Bethe ansatz (16.39%)
What were the highlights of his more recent work (between 2014-2021)?
- Pure mathematics (57.78%)
- Hypergeometric distribution (12.50%)
- Differential equation (13.61%)
In recent papers he was focusing on the following fields of study:
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.
Between 2014 and 2021, his most popular works were:
- 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)
In his most recent research, the most cited papers focused on:
- 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.
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