Studying varieties of parabolic subgroups of Chevalley groups as well
as that of their incidence geometries, association schemes, their fusions
and related groups. This direction is closely connected with algebraic
coding theory. One of the applied accomplishments is the discovery a new
infinite family of distance regular graphs.
Algorithms for effective computations of intersectional indices of the corresponding Hecke algebras, Bruhat decompositions, small Shubert cells, based on the idea of embedding of varieties into corresponding Lie algebra.
Extremal graph theory. Applications of Group Theory ( certain factorizations of groups, free products, amalgamated products, buildings) to the following problems:
Wreath products of groups and its application.
Groups of biregular transformations of affine varieties and correspondent algebras Lie.
Theory and statistics of random fields. Spectral and correlation theory of random processes and fields.
Random fields with independent increments .
Stationary stochastic processes. Second order stochastic processes. Time series analysis.
Stochastic in finance and social sciences.
Asymptotic behaviour of solutions of difference and differential equations and its stochastic analogues in a Banach space. Such equations adequately describe a behaviour of real dynamical systems.
Study of linear relations, boundary problems for operator-differential equations in a Hilbert space.
Problems of Mathematical Education.
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