Alexander Varchenko

Selected publications

  1. Algebro-geometrical equisingularity and local topological classification of smooth mappings, Proc. Int. Cong. Math. Vancouver 1 (1975), 427-432

  2. Newton polyhedra and estimations of oscillatory integrals, Functional Analysis and its Applications 10:3 (1976), 175-196

  3. On the semicontinuity of the spectra and estimates from above of the number of singular points of a projective hypersurface, Doklady Akademii Nauk USSR 270:6 (1983), 1294-1297

  4. (joint with V.I.Arnol'd and S.M.Gusein-Zade) "Singularities of Differential Maps, Vol. I", Nauka, Moscow (1982); Birkhauser (1985)

  5. An estimate of the number of zeros of real abelian integrals depending on a parameter and limiting cycles, Funktsional'nyi Analiz i ego Prilozheniya 18:2 (1984), 1-13; Functional Analysis and its Applications (English translation of FAP) 18 (1984), 98-108

  6. (joint with V.I.Arnol'd and S.M.Gusein-Zade) "Singularities of Differential Maps. Vol. II", Nauka, Moscow, 1984; Birkhauser 1988.

  7. (joint with A.A.Beilinson, A.B.Goncharov, and V.V.Schechtman) Aomoto dilogarithms, mixed Hodge structures and motivic cohomology of pairs of triangles on the plane, in "The Grothendieck Festschrift, vol. I" (1990) 135-172, Birkhauser

  8. Beta-function of Euler, Vandermonde determinant, Legendre equation, and critical values of linear functions of configuration of hyperplanes, I,Izvestiya Akademii Nauk USSR, seriya Matematicheskaya, 53:6 (1989), 1209-1235

  9. (joint with V.Schechtman) Arrangements of hyperplanes and Lie algebra homology, Invent. Math. 106 (1991), 139-194

  10. Multidimensional hypergeometric functions in Conformal Field Theory, Algebraic K-Theory, Algebraic Geometry, Proc. ICM-90, vol. I, 281-300

  11. (joint with P.Etingof) Why the boundary of a round drop becomes a curve of order four, University Lecture Series, vol. 3, AMS (1992)

  12. (joint with B.Blok) Topological Conformal Field Theories and Flat Coordinates, Intern. Journal of Modern Physics A, Vol. 7 (1992), 1467-1490

  13. Hypergeometric Functions and Representation Theory of Lie Algebras and Quantum Groups, Advanced Series in Mathematical Physics, Vol.21, World Scientific (1995)

  14. (joint with V.Tarasov) Completeness of Bethe vectors and Difference Equations with Regular Singular Points, Int. Math. Res. Notices No. 13 (1995), 637-669; math.q-alg/9504011, 1-20

  15. (joint with G.Felder) Algebraic Bethe Ansatz for the elliptic quantum group E(tau,eta)(sl2), Nuclear Physics B 480 (1996), 485-503; math.q-alg/9605024, 1-18

  16. (joint with V.Tarasov) Geometry of q-hypergeometric functions as a bridge between Yangians and quantum affine algebras, Invent. Math. 128 (1997), 501-588; math.q-alg/9604011, 1-66

  17. (joint with S.Gussein-Zade) Verlinde algebras and the intersection form on vanishing cycles, Selecta Mathematica, New Series 3 (1997), 79-97

  18. (joint with P.Etingof) Solutions of the quantum dynamical Yang-Baxter equation and dynamical quantum groups, CMP 196 (1998), 591-640; math.q-alg/9708015, 1-55

  19. (joint with G.Felder) The elliptic gamma function and $SL(3,Z)\ltimes Z^3$, Adv. Math. 156 (2000), 44-76; math.QA/9907061, 1-27

  20. (joint with V.Tarasov) Difference Equations Compatible with Trigonometric KZ Differential Equations, IMRN, No.15 (2000), 801--829; math.QA/0002132, 1-23

  21. (joint with E.Mukhin) Critical points of master functions and flag varieties, math.QA/0209017, 1-49

  22. (joint with V.Tarasov) Selberg Integrals Associated with $sl_3$, math.QA/0302148, 1-11

  23. (joint with V.Tarasov) "Identities for Hypergeometric Integrals of Different Dimensions," math.QA/0305224, 1-9

  24. "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.

  25. (joint with E. Mukhin, V. Tarasov) "The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz," math.AG/0512299, 1-18

  26. (joint with E. Mukhin, V. Tarasov) "Schubert calculus and representations of a general linear group," math.QA/0711.4079, 1-32
Here is the complete publication list

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