In 1969 he graduated from the Faculty of Mechanics and Mathematics of
Moscow State University. In 1972 he received his
Candidate of Sciences degree (PhD) with thesis Стабильность действия алгебраических групп и арифметика квазиоднородных многообразий (Stability of the action of algebraic groups and the arithmetic of quasi-homogeneous varieties). In 1984 he received his Russian
Doctor of Sciences degree (habilitation) with thesis Группы, образующие, сизигии и орбиты в теории инвариантов (Groups, generators, syzygies and orbits in the theory of invariants). He is a member of the
Steklov Institute of Mathematics and a professor of the
National Research University – Higher School of Economics. and in 2008–2010 he was a core member of the panel for Section 2, "Algebra" of the Program Committee for the 2010 International Congress of Mathematicians (
Hyderabad, India). In 1987 he published a proof of a conjecture of
Claudio Procesi and Hanspeter Kraft. In 2006, with Nicole Lemire and
Zinovy Reichstein, Popov published a solution to a problem posed by Domingo Luna in 1973. == Awards ==