I am working in the theory of differential equations, more precisely in partial differential equations (PDE), CNN modeling of complex nonlinear partial differential equations arising from applications in mathematical physics, in biology, in ecology, in mechanics etc. Member of EU-MATHS-IN

Developing Logo microworlds and models for integrating the learning and the creative processes: Methodological issues of using Information Technology in teaching Mathematics, Languages, Music, Science, Arts; Applying Informatics and ICT in Primary and Secondary School;  Methodological support of projects for implementing the Inquiry Based Learning in Primary and Secondary School;

Computer algebra (algorithms, systems and applications),Information Modeling.

Computational Lexicography, Corpus Linguistics, Contrastive Linguistics (esp. the Comparison of Slavic Languages), Ukrainian Studies, Traditional and Computational Dialectology, Semantic Web, Formal Modelling of Semantic Phenomena, Databases and Quantitative Methods in Linguistics, E-learning Systems and Content Development, Web Design and Computer Graphics, Modelling of Linguistic Information-Retrieval Systems.

Levy processes, functionals based on Levy processes, spectral theory of non-selfadjoint Markov processes, Brownian motion in random environment  

Probability and Stochastic Processes. Specifically: Probability distributions, Characterizations, Moment Problems, Stochastic Differential Equations, Counterexamples in Probability, Probability in Other Branches of Mathematics  

Discrete Mathematics, Programming languages, parallel and distributed computing, cloud computing, information aggregation and retrieval.

1) Image and Video Processing: MPEG-21, MPEG-7, MPEG-4, SIFT. 2) Computer graphics: OPEN GL, Color theory, Java 2D and Java 3D, Maya, 3ds MAX 3) Medical imaging: Magnetic Resonance Images analysis, Segmentation, 3D reconstruction, Functional MRI 4) Game design:  LUA, XNA, Python, Sonics, Game generators: Blitz, I7, Game Factory, Inscape, Torque, Yoyo, Unity, Alice. 5) Multimedia Systems: Semantic web technology. Ontology. W3C's Web Ontology Language (OWL), Resource Description Framework (RDF), Content based image retrieval (CBIR). Digital Libraries. 6) Data Base Systems: Models 7) Information Retrieval and Data mining:  Association Rule mining, Classification - tree-based approaches, Neural Networks, Clustering basics, statistical approaches, Neural-net. Fuzzy Sets and Systems. Expert Systems. 8) Web technology: Web2.0 tools. Ajax, Web Map Server (WMS), Web Feature Server (WFS), XML (Extensible Markup Language), RSS, RDF (Resource Description Framework), Web 2.0 mash-ups, Java Script, Java Applets, MySQL and PHP, PERL, ASP.Net. Electronic comers.