Publications

Selected publications

  1. Varchenko, A. Algebro-geometrical equisingularity and local topological classification of smooth mappings, Proc. ICM-74 in Vancouver, vol. 1 (1975), 427-432
  2. Varchenko, A. Newton polyhedra and estimates of oscillatory integrals, (Russian) Funkcional. Anal. i Priložen. 10 (1976), no. 3, 13–38
  3. Varchenko, A. Zeta-function of monodromy and Newton’s diagram. Invent. Math. 37 (1976), no. 3, 253–262
  4. Varchenko, A. Semicontinuity of the spectrum and an upper bound for the number of singular points of the projective hypersurface. (Russian) Dokl. Akad. Nauk SSSR 270 (1983), no. 6, 1294–1297
  5. Arnolʹd, V. I.; Guseĭn-Zade, S. M.; Varchenko, A. N.  Singularities of Differential Maps, Vol. I, Nauka, Moscow 1982; Birkhauser 1985, Vol. II,  Nauka, Moscow, 1984; Birkhauser 1988
  6. Varchenko, A An estimate of the number of zeros of real abelian integrals depending on a parameter and limiting cycles,  Funktsional. Anal. i Prilozhen. 18 (1984), no. 2, 14–25, Functional Analysis and its Applications (English translation of FAP) 18 (1984), 98-108
  7. Beĭlinson, A. A.; Goncharov, A. B.; Schechtman, V. V.; Varchenko, A. N. Aomoto dilogarithms, mixed Hodge structures and motivic cohomology of pairs of triangles on the plane. The Grothendieck Festschrift, Vol. I, 135–172, Progr. Math., 86, Birkhäuser Boston, Boston, MA, 1990.
  8. Varchenko, A. N.; Gelʹfand, I. M. Heaviside functions of a configuration of hyperplanes. (Russian) Funktsional. Anal. i Prilozhen. 21 (1987), no. 4, 1–18, 96. 
  9. Varchenko, A. N.; Giventalʹ, A. B. The period mapping and the intersection form. (Russian) Funktsional. Anal. i Prilozhen. 16 (1982), no. 2, 7–20, 96.
  10. Varchenko, A. Beta-function of Euler, Vandermonde determinant, Legendre equation, and critical values of linear functions of configuration of hyperplanes, I, Izvestiya Akademii Nauk USSR, seriya Matem., 53:6 (1989), 1209-1235
  11. Schechtman, Vadim V.; Varchenko, Alexander N. Arrangements of hyperplanes and Lie algebra homology. Invent. Math. 106 (1991), no. 1, 139–194
  12. Varchenko, A. Multidimensional hypergeometric functions in Conformal Field Theory, Algebraic K-Theory, Algebraic Geometry, Proc. ICM-90 in Kyoto, vol. I, 281-300
  13.  Varchenko, A. N.; Ètingof, P. I.  Why the boundary of a round drop becomes a curve of order four, University Lecture Series, 3. American Mathematical Society, Providence, RI, 1992. viii+72
  14. Blok, B.; Varchenko, A. Topological Conformal Field Theories and Flat Coordinates,  Internat. J. Modern Phys. A 7 (1992), no. 7, 1467–1490
  15. Varchenko, A. Hypergeometric Functions and Representation Theory of Lie Algebras and Quantum Groups, Advanced Series in Mathematical Physics, Vol.21, World Scientific (1995)
  16. Reshetikhin, Nicolai; Varchenko, Alexander Quasiclassical asymptotics of solutions to the KZ equations. Geometry, topology, & physics, 293–322, Conf. Proc. Lecture Notes Geom. Topology, IV, Int. Press, Cambridge, MA, 1995,  293–322,  arXiv:hep-th/9402126
  17. Felder, Giovanni; Varchenko, Alexander Integral representation of solutions of the elliptic Knizhnik-Zamolodchikov-Bernard equations. Internat. Math. Res. Notices 1995, no. 5, 221–233 arXiv:hep-th/9502165
  18. Felder, Giovanni; Varchenko, Alexander On representations of the elliptic quantum group Eτ,η(sl2), Comm. Math. Phys. 181 (1996), no. 3, 741–761, arXiv:q-alg/9601003
  19. Felder, Giovanni; Varchenko, Alexander Algebraic Bethe ansatz for the elliptic quantum group Eτ,η(sl2). Nuclear Phys. B 480 (1996), no. 1-2, 485–503, arXiv:q-alg/9605024
  20. Varchenko, A. N.; Tarasov, V. O.  Jackson integral representations for solutions of the Knizhnik-Zamolodchikov quantum equation. (Russian) Algebra i Analiz 6 (1994), no. 2, 90–137; translation in St. Petersburg Math. J. 6 (1995), no. 2, 75–313,  arXiv:hep-th/9311040
  21. Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.   Differential equations compatible with KZ equations. Math. Phys. Anal. Geom. 3 (2000), no. 2, 139–177, arXiv:math/0001184 
  22. Tarasov, V.; Varchenko, A.  Geometry of q-hypergeometric functions as a bridge between Yangians and quantum affine algebras, Invent. Math. 128 (1997), no. 3, 501–588, arXiv:q-alg/9604011
  23. Gusein-Zade, S. M.; Varchenko, A. Verlinde algebras and the intersection form on vanishing cycles. Selecta Math. (N.S.) 3 (1997), no. 1, 79–97, arXiv:hep-th/9610058 
  24. Etingof, Pavel; Varchenko, Alexander  Geometry and classification of solutions of the classical dynamical Yang-Baxter equation. Comm. Math. Phys. 192 (1998), no. 1, 77–120,  arXiv:q-alg/9703040 
  25. Felder, Giovanni; Varchenko, AlexanderThe elliptic gamma function and SL(3,Z)⋉Z3. Adv. Math. 156 (2000), no. 1, 44–76, arXiv:math/9907061
  26. Tarasov, V.; Varchenko, A. Duality for Knizhnik-Zamolodchikov and dynamical equations. The 2000 Twente Conference on Lie Groups (Enschede). Acta Appl. Math. 73 (2002), no. 1-2, 141–154,  arXiv:math/0112005
  27. Mukhin, E.; Varchenko, A. Critical points of master functions and flag varieties. Commun. Contemp. Math. 6 (2004), no. 1, 111–163, arXiv:math/0209017 
  28. Tarasov, V.; Varchenko, A. Selberg-type integrals associated with sl3. Lett. Math. Phys. 65 (2003), no. 3, 173–185, arXiv:math/0302148
  29. Tarasov, V.; Varchenko, A.  Identities for hypergeometric integrals of different dimensions. Lett. Math. Phys. 71 (2005), no. 2, 89–99,  arXiv:math/0305224
  30. Varchenko, A. Special functions, KZ type equations, and representation theory. CBMS Regional Conference Series in Mathematics, 98. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2003. viii+118 pp.
  31. Mukhin, E.; Tarasov, V.; Varchenko, A. The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz. Ann. of Math. (2) 170 (2009), no. 2, 863–881,  arXiv:math/0512299
  32. Mukhin, E.; Tarasov, V.; Varchenko, A. Schubert calculus and representations of the general linear group. J. Amer. Math. Soc. 22 (2009), no. 4, 909–940, arXiv:0711.407    
  33. Gorbounov, V.; Rimányi, R.; Tarasov, V.; Varchenko, A.  Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra. J. Geom. Phys. 74 (2013), 56–86, arXiv:1204.5138

34. Eric M. Rains, Yi Sun, Alexander Varchenko, Affine Macdonald conjectures and special values of Felder-Varchenko functions , arXiv:1610.01917, 1-43

35. V. Schechtman, A. Varchenko, Solutions of KZ differential equations modulo $p$, arXiv:1707.02615, 1-23

36. Vitaly Tarasov, Alexander Varchenko, q-Hypergeometric solutions of quantum differential equations, quantum Pieri rules, and Gamma theorem, arXiv:1710.03177, 1-47

37. Vitaly Tarasov, Alexander Varchenko, Equivariant quantum differential equation, Stokes bases, and K-theory for a projective space, arXiv:1901.02990, 1-19

38. Richárd Rimányi, Andrey Smirnov, Alexander Varchenko, Zijun Zhou, Three-Dimensional Mirror Self-Symmetry of the Cotangent Bundle of the Full Flag Variety , arXiv:1906.00134, 1-22

39. Igor Krichever, Alexander Varchenko, Incarnations of XXX $\widehat{\frak{sl}_N}$ Bethe equations and integrable hierarchies , arXiv:1907.12198, 1-57

40. Giordano Cotti, Alexander Varchenko, Equivariant quantum differential equation and $qKZ$ equations for a projective space: Stokes bases as exceptional collections, Stokes matrices as Gram matrices, and B-Theorem , arXiv:1909.06582, 1-77

41. Richárd Rimányi, Alexander Varchenko, The F_p Selberg Integral , arXiv:2011.14248, 1-77

Here is the complete publication list

My list of publications in MathSciNet: http://ams.rice.edu/