Publications (77)
Identities between q-hypergeometric and hypergeometric integrals of different dimensions
V. Tarasov, A. Varchenko
Bispectral and (gl_N, gl_M) Dualities, Discrete Versus Differential
E. Mukhin, V. Tarasov, A. Varchenko
A Selberg Integral Type Formula for an sl_2 One-Dimensional Space of Conformal Blocks
A. Varchenko
The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz
E. Mukhin, V. Tarasov, A. Varchenko
Solutions to the Quantized Knizhnik-Zamolodchikov Equation and the Bethe Ansatz
V. Tarasov, A. Varchenko
Conformal blocks and equivariant cohomology
R. Rimányi, V. Schechtman, A. Varchenko
Intersection cohomology of a rank one local system on the complement of a hyperplane-like divisor
D. Arinkin, A. Varchenko
Elliptic and K-theoretic stable envelopes and Newton polytopes
R. Rimányi, V. Tarasov, A. Varchenko
Cohomology of the complement to an elliptic arrangement
A. Levin, A. Varchenko
Bethe algebra of the gl_{N+1} Gaudin model and algebra of functions on the critical set of the master function
E. Mukhin, V. Tarasov, A. Varchenko
Populations of solutions of the XXX Bethe equations associated to Kac-Moody algebras
E. Mukhin, A. Varchenko
The Determinant of a Hypergeometric Period Matrix
Y. Markov, V. Tarasov, A. Varchenko
Quiver $D$-Modules and Homology of Local Systems over an Arrangement of Hyperplanes
S. Khoroshkin, A. Varchenko
Equivariant Chern-Schwartz-MacPherson classes in partial flag varieties: interpolation and formulae
R. Rimanyi, A. Varchenko
Solutions of Trigonometric KZ Equations satisfy Dynamical Difference Equations
Y. Markov, A. Varchenko
Path count asymptotics and Stirling numbers
K. Petersen, A. Varchenko
Gaudin Hamiltonians generate the Bethe algebra of a tensor power of vector representation of gl_N
E. Mukhin, V. Tarasov, A. Varchenko
Critical points of master functions and flag varieties
E. Mukhin, A. Varchenko
On reality property of Wronski maps
E. Mukhin, V. Tarasov, A. Varchenko
Solutions of the qKZB Equation in Tensor Products of finite dimensional modules over the elliptic quantum group $E_{Ï,η}sl_2$
E. Mukhin, A. Varchenko
BGG resolutions via configuration spaces
M. Falk, V. Schechtman, A. Varchenko
On separation of variables and completeness of the Bethe ansatz for quantum gl_N Gaudin model
E. Mukhin, V. Tarasov, A. Varchenko
On the Gaudin model associated to Lie algebras of classical types
Kang Lu, E. Mukhin, A. Varchenko
Asymptotic Solutions to the Knizhnik-Zamolodchikov Equation and Crystal Base
A. Varchenko
Differential equation for Jacobi-Pineiro polynomials
E. Mukhin, A. Varchenko
The gl_2 Bethe algebra associated with a nilpotent element
E. Mukhin, V. Tarasov, A. Varchenko
Dynamical Gelfand-Zetlin algebra and equivariant cohomology of Grassmannians
R. Rimanyi, A. Varchenko
The Quantized Knizhnik-Zamolodchikov Equation in Tensor Products of Irreducible sl(2)-Modules
E. Mukhin, A. Varchenko
Identities for hypergeometric integrals of different dimensions
V. Tarasov, A. Varchenko
Higher Lame Equations and Critical Points of Master Functions
E. Mukhin, V. Tarasov, A. Varchenko
Conformal blocks in the tensor product of vector representations and localization formulas
R. Rimanyi, A. Varchenko
Multiple orthogonal polynomials and a counterexample to Gaudin Bethe Ansatz Conjecture
E. Mukhin, A. Varchenko
Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator
G. Felder, L. Stevens, A. Varchenko
How to regularize singular vectors and kill the dynamical Weyl group
K. Styrkas, V. Tarasov, A. Varchenko
Cohomology of a flag variety as a Bethe algebra
R. Rimanyi, V. Schechtman, V. Tarasov +1
Determinants of the hypergeometric period matrices of an arrangement and its dual
D. Mukherjee, A. Varchenko
Solutions to the XXX type Bethe ansatz equations and flag varieties
E. Mukhin, A. Varchenko
A remark on sl_2 approximation of the Kontsevich integral of the unknot
S. Tyurina, A. Varchenko
Bethe algebra of Gaudin model, Calogero-Moser space and Cherednik algebra
E. Mukhin, V. Tarasov, A. Varchenko
Three sides of the geometric Langlands correspondence for gl_N Gaudin model and Bethe vector averaging maps
E. Mukhin, V. Tarasov, A. Varchenko
Small Elliptic Quantum Group $e_{tau,γ}(sl_N)$
V. Tarasov, A. Varchenko
Bethe algebra and algebra of functions on the space of differential operators of order two with polynomial solutions
E. Mukhin, V. Tarasov, A. Varchenko
Special functions, conformal blocks, Bethe ansatz, and SL(3,Z)
G. Felder, A. Varchenko
Resonance relations, holomorphic trace functions and hypergeometric solutions to qKZB and Macdonald-Ruijsenaars equations
K. Styrkas, A. Varchenko
Schubert calculus and representations of general linear group
E. Mukhin, V. Tarasov, A. Varchenko
Bispectral and $(\glN,\glM)$ Dualities
E. Mukhin, V. Tarasov, A. Varchenko
Multiplication Formulas for the Elliptic Gamma Function
G. Felder, A. Varchenko
The Euler adic dynamical system and path counts in the Euler graph
K. Petersen, A. Varchenko
Dynamical differential equations compatible with rational qKZ equations
V. Tarasov, A. Varchenko
On the new form of Bethe ansatz equations and separation of variables in the $sl_3$ Gaudin model
E. Mukhin, V. Schechtman, V. Tarasov +1
Reality property of discrete Wronski map with imaginary step
E. Mukhin, V. Tarasov, A. Varchenko
Cohomology classes of conormal bundles of Schubert varieties and Yangian weight functions
R. Rimanyi, V. Tarasov, A. Varchenko
Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra
V. Gorbounov, R. Rimanyi, V. Tarasov +1
Partial flag varieties, stable envelopes and weight functions
R. Rimanyi, V. Tarasov, A. Varchenko
Norms of eigenfunctions to trigonometric KZB operators
E. Jensen, A. Varchenko
Unitarity of SL(2)-conformal blocks in genus zero
E. Looijenga, A. Varchenko
Difference Equations Compatible with Trigonometric KZ Differential Equations
V. Tarasov, A. Varchenko
Critical points of functions, sl_2 representations, and Fuchsian differential equations with only univalued solutions
I. Scherbak, A. Varchenko
Duality for Knizhnik-Zamolodchikov and Dynamical Equations
V. Tarasov, A. Varchenko
Spaces of quasi-exponentials and representations of gl_N
E. Mukhin, V. Tarasov, A. Varchenko
Quantization of the space of conformal blocks
E. Mukhin, A. Varchenko
Extended Joseph polynomials, quantized conformal blocks, and a q-Selberg type integral
R. Rimányi, V. Tarasov, A. Varchenko +1
Differential Equations Compatible with KZ Equations
G. Felder, Y. Markov, V. Tarasov +1
Bethe Algebra of Homogeneous XXX Heisenberg Model Has Simple Spectrum
E. Mukhin, V. Tarasov, A. Varchenko
A generalization of the Capelli identity
E. Mukhin, V. Tarasov, A. Varchenko
Selberg Type Integrals Associated with $sl_3$
V. Tarasov, A. Varchenko
Trigonometric weight functions as K-theoretic stable envelope maps for the cotangent bundle of a flag variety
R. Rimanyi, V. Tarasov, A. Varchenko
Poincare-Birkhoff-Witt expansions of the canonical elliptic differential form
G. Felder, R. Rimanyi, A. Varchenko
Combinatorics of rational functions and Poincare-Birkhoff-Witt expansions of the canonical U(n-)-valued differential form
R. Rimanyi, L. Stevens, A. Varchenko
Critical points of master functions and the mKdV hierarchy of type A^2_2
A. Varchenko, T. Woodruff, D. Wright
Bethe subalgebras of the group algebra of the symmetric group
E. Mukhin, V. Tarasov, A. Varchenko
Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors
V. Schechtman, H. Terao, A. Varchenko
Functorial properties of the hypergeometric map
E. Mukhin, A. Varchenko
Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety
V. Tarasov, A. Varchenko
Bethe eigenvectors of higher transfer matrices
E. Mukhin, V. Tarasov, A. Varchenko
Spaces of quasi-exponentials and representations of the Yangian Y(gl_N)
E. Mukhin, V. Tarasov, A. Varchenko
On algebraic equations satisfied by hypergeometric solutions of the qKZ equation
E. Mukhin, A. Varchenko