Alexander Varchenko
| Alexander Varchenko | |
|---|---|
 |
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| Born |
February 6, 1949 Russia |
| Fields | Mathematics |
| Institutions | University of North Carolina |
| Alma mater | Moscow State University |
| Doctoral advisor | V. I. Arnold |
| Known for | Varchenko's theorem |
Alexander Nikolaevich Varchenko (Russian: Александр Николаевич Варченко, born February 6, 1949 in Krasnodar, Soviet Union) is a Soviet and Russian mathematician working in geometry, topology, combinatorics and mathematical physics.
From 1964 to 1966 Varchenko studied at the Moscow Kolmogorov boarding school No. 18 for gifted high school students, where A. N. Kolmogorov and Ya. A. Smorodinsky were lecturing mathematics and physics. Varchenko graduated from Moscow State University in 1971. He was a student of V. I. Arnold. Varchenko defended his Ph.D. thesis Theorems on Topological Equisingularity of Families of Algebraic Sets and Maps in 1974 and Doctor of Science thesis Asymptotics of Integrals and Algebro-Geometric Invariants of Critical Points of Functions in 1982. From 1974 to 1984 he was a research scientist at the Moscow State University, in 1985–1990 a professor at the Gubkin Institute of Gas and Oil, and since 1991 he has been the Ernest Eliel Professor at the University of North Carolina at Chapel Hill.
Varchenko was an invited speaker at the International Congresses of Mathematicians in 1974 in Vancouver (section of algebraic geometry) and in 1990 in Kyoto (a plenary address). In 1973 he received the Moscow Mathematical Society Award.
In 1971, Varchenko proved that a family of complex quasi-projective algebraic sets with an irreducible base form a topologically locally trivial bundle over a Zariski open subset of the base. This statement, conjectured by O.Zariski, had filled up a gap in the proof of Zariski’s theorem on the fundamental group of the complement to a hypersurface published in 1937. In 1973, Varchenko proved R.Thom's conjecture that a germ of a generic smooth map is topologically equivalent to a germ of a polynomial map and has a finite dimensional polynomial topological versal deformation, while the non-generic maps form a subset of infinite codimension in the space of all germs.
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