Oleg Sheinman

On June 9, 2009, our colleague and dear friend Oleg Sheinman, professor of the Independent University of Moscow, leading research fellow of the Steklov Institute, turned 60.

After graduating from the Moscow mathematical high-school #52 in 1966, Oleg became a student of the department of mechanics and mathematics (“mekh-mat”) of Moscow State (Lomonosov) University. His scientific advisor there was A. A. Kirillov. From that time and until the present day, the representation theory of Lie groups and algebras is Oleg's main mathematical passion and the tool with which he has successfully attacked very different problems.

After graduating Oleg worked at the Central Economics and Mathematics Institute of the Academy of sciences and at the Krzhizhanovski Power Engineering Institute, where he had to master an “adjacent” mathematical specialty: integer-valued programming. His PhD thesis was devoted to this topic.

However, Lie groups and algebras theory remained his guiding star, and after defending his PhD thesis Oleg returned to his favorite subject. A key role in Oleg's scientific path was played by his active participation in S. P. Novikov's seminar on integrable systems and his joint work with I. M. Krichever. Continuing the works of Novikov and Krichever devoted to the algebraic geometry approach to integrable systems, O. Sheinman has developed the theory of the class of infinite-dimensional Lie algebras known as Krichever–Novikov algebras, constructing a full-fledged representation theory for them. These results have constituted the subject of his State Doctor (habilitation) thesis defended at the Steklov Mathematical Institute in 2007.

Krichever–Novikov algebras were also the subject of a series of papers of O. Sheinman written with the German mathematician M. Schlichenmaier. Recently, Oleg turned to a new class of infinite-dimensional Lie algebras also closely connected with integrable systems and Riemann surfaces. These are the algebras of Lax operators that appeared in his joint paper with Krichever published in Functional Analysis and its Applications in 2007.

O. Sheinman is a leading research fellow at the Department of Geometry and Topology of the Steklov Mathematical Institute and a professor of the Independent University of Moscow. Teaching was always a vital necessity for Oleg. He continually gives courses in representation theory and Lie groups and algebras at the Independent University of Moscow and at the Scientific Educational Centre of the Steklov Mathematical Institute. He runs (together with S. M. Natanzon and O. V. Schwarzman) the Seminar on Riemann surfaces, Lie algebras and mathematical physics, one of the oldest and most successful seminars at the IUM.

Sport activities have accompanied Oleg throughout his life: hiking and camping, skiing, table tennis. Thanks to that, Oleg succeeds in keeping a high level of vitality in everything that he does.

We cordially congratulate Oleg with the anniversary and wish him to stay in excellent mathematical and physical shape as long as possible.

V. Buchstaber, S. Gusein-Zade, Yu. Ilyashenko, A. Kirillov, I. Krichever,
S. Natanzon, S. Novikov, A. Sergeev, A. Sossinsky, M. Tsfasman