Sergey Natanzon

S.M. Natanzon is 60. His early mathematical exercises were supervised by E.B. Dynkin in the famous Moscow mathematical school #2. Natanzon graduated from the faculty of mechanics and mathematics (mekh-mat) of the Moscow State University where he joined Vinberg's seminar. Prof. E.B. Vinberg guided Natanzon in his student work on Fuchsian groups. Starting there, Natanzon became one of the best contemporary experts in Fuchsian groups, moduli spaces of algebraic curves (both real and complex), Hurwitz spaces, and their applications to integrable systems and 2D topological field theory.

Natanzon's numeruous results include

transparent and rigorous construction of the Teichmüller space T by canonical hyperbolic 4g-gons. The construction provides managable coordinates on T;

description of super-Fuchsian groups;

classification of topological G-actions on Riemann surfaces for certain finite groups G. Analytically, this is the question of the number of irreducible components of the loci of curves possessing G-symmetry in the moduli space;

generalization of the classical Lüroth connectedness theorem for generic functions to the case of functions with prescribed ramification over a single point;

construction of real 2-zone soliton solutions to integrable hierarchies;

construction of a beautiful compactification of Hurwitz spaces;

construction of an Arf invariant of plane curves;

classification of topological invariants of real forms of complex curves; investigation of ovoids of Riemann surfaces;

wide-ranging investigation of integrable hierarchies including their applications to effectivisation of the Riemann Theorem on conformal maps;

construction of a new example of topological field theory, called the Klein Topological Field Theory;

explicit formulas for certain solutions to WDVV equations,

The wide scope of Sergey Natanzon's mathematical interests and his personal attraction makes him a prized advisor for talented students (some of them have become well-known already) and an eagerly desired collaborator, working jointly with researchers from Russia, Sweden, United States, Portugal, France, Spain, and Great Britain.

For many years Natanzon is a permanent professor of the Independent University of Moscow, an organizer of the research seminar “Lie algebras, Riemann surfaces, and mathematical physics”, contributing a great deal to teaching beginners and advanced students, writing remarkable books for them, and supervising their research. We cordially congratulate Sergey and wish him many happy returns of the day.

S. Gusein-Zade, Yu. Ilyashenko, G. Kabatiansky,
S. Lando, A. Sergeev, O. Sheinman,
O. Schwarzman, M. Tsfasman, E. Vinberg