The main research directions

Development of simplicially-lattice models for effective computer representation, storage, conversion and generation of combinatorially-topological nature objects.

Development of tools for interactive and automatic operating modes on the computer with combinatorially-topological objects.

Development of special, VRML based tools for combinatorially-topological objects visualisation, for using in combinatorial topology and algebraic geometry researches, training courses and so on..

The common approach based on researches published in following works:

Alexandrov P.S. Combinatorial topology.
Pontryagin L.S. Foundations of combinatorial topology.
Novikov S.P. Topology.
Gelfand I.M. Lectures on linear algebra.
George E. Andrews The Theory of Partitions.
Vershik A. M., Okounkov A. Yu. A New Approach to the Representation Theory of the Symmetric Groups. II
Manin Yuri I. Classical computing, quantum computing, and Shor’s factoring algorithm.
Stanley R.P. Enumerative combinatorics.