I am a professor in the Mathematics Department of the University of North Carolina at Chapel Hill

Education

Moscow State 1971
Ph.D. Moscow State 1974 (Adviser : V. Arnol'd)

How to find me

• My office is Phillips Hall 382. Office phone : (919) 962-9603
• You can email me at varchenko@math.unc.edu

My research interests

Mathematical Physics,Topology,Algebraic Geometry, Combinatorics

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,Funktsional'nyi Analiz i ego Prilozheniya 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. 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", pp. 135-172, Birkhauser, 1990.
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. Hypergeometric Functions and Representation Theory of Lie Algebras and Quantum Groups, Advanced Series in Mathematical Physics, Vol.21, World Scientific, 1995.
13. (joint with V. Tarasov) Completeness of Bethe vectors and Difference Equations with Regular Singular Points, Int. Math. Res. Notices, 1995, No. 13, 637-669.
14. (joint with G. Felder)Algebraic Bethe Ansatz for the elliptic quantum group E(tau,eta)(sl2), Nuclear Physics B 480(1996), 485-503.
15. (joint with V. Tarasov)Geometry of q-hypergeometric functions as a bridge between Yangians and quantum affine algebras, Invent. Math. 128(1997), 501-588.
16. (joint with S. Gussein-Zade)Verlinde algebras and the intersection form on vanishing cycles, Selecta Mathematica, New Series 3(1997), 79-97.