Orbits, invariant and covariant functions for the reductive algebraic groups acting on affine varieties. Representations of quivers.

Graduated, postgraduated student, and Ph.D. at the Moscow State University, department of mathematics and mechanics (advisor prof.  E. B. Vinberg). I participate in the seminar on Algebraic groups and Invariant Theory of E. B. Vinberg and A. L. Onischik at MSU and in research on the subject of this seminar. I collaborate in the educational programs of the Moscow Independent University.

• On non-connected simple linear groups with a free algebra of invariants // Izvestiya Math., 60 (1996), 811–856.
• On algebras of invariants and codimension 1 Luna strata for non-connected groups // Geometriae Dedicata, 72 (1998), 189–215.
• On representations of $SL_n$ with algebras of invariants being complete intersections // Journal of Lie Theory, 11 (2001), 207–229.
• On spherical representations of quivers and generalized complexes // Transformation groups, 7, no. 1 (2002), 87–106.
• First fundamental theorem for covariants of classical groups // Advances in Math., to appear.

• Lomonosov Moscow State University
• Independent University of Moscow
• Moscow Mathematical Society