My scientific interests are in the field of numerical methods for solving differential and integral equations, in particular - the methods of finite differences, finite elements, boundary elements, as well as their application to the mathematical models of physical and industrial processes.
Approximations by rational functions in the complex plane: Pade approximation, best rational approximation, orthogonal polynomials, rate of approximation; complex analysis, potential theory, numerical analysis, mathematical modelling.
General topology (set-valued mappings), Functional analysis.
Algebraic geometry: surface theory, Algebra: associative algebras, theory of finite group representations, Artin braid group representations, Combinatorics: census problems. Mathematical Chemistry: isomerism in organic cemistry, Mathematical Economics: sets of preferences, utility functions.
Dynamical systems, Applications in mathematical modeling of bioprocesses, Computer-oriented numerical analysis.
Research and investigations in the field of Mathematical, Computational, Contrastive and Corpus Linguistics, Knowledge Representation, Human Language Technologies, Artificial Intelligence, Discrete Mathematics. Basic results include creation of digital language resources & tools with a focus on Bulgarian: development of TEI-compliant lexical specifications for encoding and processing of digital corpora and lexica, comparable and multilingual corpora (parallel, annotated, and aligned) – MTE Bulgarian-English, Bulgarian-Polish, Bulgarian-Slovak, and Bulgarian-Polish-Lithuanian, lexical databases for integrated multilingual resources and mono- and bilingual digital dictionaries.
Soliton theory, Soliton interactions.
Numerical solution of partial differential equations, Finite elements, Multilevel methods.
Non-commutative algebra and applications for quantum groups, non-commutative geometry, symbolic computation
Measurements and assessment in education; Comparative, assessment and diagnostic studies in mathematics education; IT in education; Didactics of mathematics; Extracurricular mathematics activities for gifted and talented students from 4th to 12th grade; Combinatorial mathematics, combinatorial geometry.
