Popov, Vladimir Leonidovich

Born September 3, 1946.

In 1969 - graduated from the Faculty of Mechanics and Mathematics of Moscow State University .

In 1972, he defended his thesis, topic: "Stability of the action of algebraic groups and arithmetic of quasihomogeneous varieties."

In 1984 - defended his doctoral dissertation, topic: "Groups, generators, syzygies and orbits in the theory of invariants."

In 1986 - awarded the academic title of professor.

In 2016, he was elected a corresponding member of the RAS .

Specialist in the field of algebra.

The author of 128 scientific works, including 4 monographs.

The main scientific results:

• two classical problems of the theory of invariants are solved: the generalized 14 Hilbert problem posed by M. Nagata in 1965, the main problem of the constructive theory of invariants posed by D. Hilbert in 1893;
• the pioneering results of the theory of embeddings of homogeneous algebraic varieties (including toric and spherical) were obtained, which determined its rapid modern development; a new trend has been created in the theory of invariants, in the framework of which finiteness theorems for actions with a given length of the syzygy chain are proved;
• linear algebraic groups are characterized as automorphism groups of simple finite-dimensional (non-associative) algebras;
• the theory of Cayley groups, discovered in 1846, is constructed; in particular, the problem of D. Moon on the classification of Caelic unimodular groups is solved;
• simple Lie algebras are classified whose field of rational functions is purely transcendental over the field of associated invariants. This result is key in constructing counterexamples to the hypothesis of I. V. Gelfand and A. A. Kirillov on the bodies of partial enveloping algebras;
• answers to Grothendieck Serre's questions about algebraic groups; the problem of classification of discrete groups of motions of a Hermitian affine space generated by affine reflections was posed by A. Borel;
• the old Flat and Tauber conjectures on algebraic groups are proved.

Conducts teaching activities as a professor at the Higher School of Economics , member of the editorial boards of the journals Transformation Groups, Izvestiya RAN, Matematicheskaya Serie, Matematicheskie Zametki, etc.

He previously taught at various foreign institutes and universities.

• Popov, Vladimir Leonidovich on the official website of the RAS
• Popov, Vladimir Leonidovich on the mathematical portal Math-Net.Ru