Abstract and axiomatic recursion theory; Romanization of Cyrillized languages and re-Romanization of English; Antarctic place naming, geographic surveying and mapping; foreign and security policy, European and Atlantic integration; self-determination, minority rights, immigration policies.
Combinatorial and computational ring theory, noncommutative algebra, algebras with polynomial identity, automorphisms and derivations of polynomial and free algebras, commutative and noncommutative invariant theory, group representations, theory of symmetric functions, group algebras, and coding theory.
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.
Numerical methods, Approximation theory, Data compression.
