|Degree:||Candidate of Physical and Mathematical Science|
|Research interests:||representation theory of algebras, in particular, decomposition of an operator intoa linear combination of special operators or into a product of operators;representation theory of Braid groups, spectra of weighted graphs, inverseproblems on weighted graphs and matrices; image recognition problems,quantum information theory, frames, and quantum channels|
1. Presidential Grant for Young Scientists, 2004
1. Algebra and geometry, bachelor's, 1 year, lectures and practical classes.
1. When a sum of idempotents or orthoprojections is a multiple of identity (with Yu. S. Samoilenko), Func. Anal. and Appl., 34, no. 4, (2000) 311-313.
2. Scalar operator representable as a sum of projectors (with Yu. S. Samoilenko), Ukrainian Math. Jour., 53, no. 7 (2001) 1116--1133.
3. On decomposition of the identity into a sum of idempotents (with T. Ehrhardt, Yu. Samoilenko and B.Silbermann), Meth. of Func. Anal. and Topology, no. 2,(2001) 1-6.
4. On sums of projections (with S. Kruglyak and Yu. Samoilenko), Func. Anal. and Appl., 36, no. 3, (2002) 182-195.
5. Decomposition of a scalar matrix into a sum of orthogonal projections (with S. Kruglyak and Yu. Samoilenko), Linear Algebra and its Appl. 370, (2003) 217-225.
6. When is a sum of partial reflections equal to a scalar operator (with A. S. Mellit and Yu. S. Samoilenko), Func. Anal. and Appl. 38, no. 2, (2004) 157-160.
7. Every matrix is a linear combination of three idempotents. Linear Algebra and Its Appl. 390, (2004) 137-143.
8. Multicommutators and multianticommutators of orthogonal projections (with V. Mazorchuk), Linear and Multilinear Algebra, 56(6), (2008) 639-646.