Academic Staff

Information security and cryptography, secret sharing schemes and their applications. crowd computing, crowdsourcing and gamification

Information modeling of telecommunication systems, generalized networks, intuitionistic fuzzy sets

Numerical methods, Approximation theory, Data compression.

Complex differential geometry, algebraic geometry, global analysis.

Coding Theory: covering radii of codes, optimal codes, decoding, Computer communications: error control performance of codes, Combinatorics, Algorithms.

Programming languages, Methodology of programming, Geometric computations and algorithms, Education in programming.

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.

Infinite-dimensional topology, Geometric Tomography/Topology, Geometry of Banach spaces, Convexity, Topological vector spaces, Selection theory.

Mathematical modeling and computer simulation of multiphase flows with heat and mass transfer and bioprocesses.

Fractional calculus; Fractional differential and integral equations: operator-theoretical approach, qualitative properties of solutions. Convolutional calculus: Duhamel-type representations for nonlocal boundary-value problems.

Nonsmooth analysis, differential inclusions, optimal control

Coding theory - optimal codes, equidistant codes, Data protection - steganography, watermarking, Information technologies -interdisciplinary methods, Databases, Semantic Web, Multimedia Digital Libraries and Content Management Systems, Methods of preservation and presentation of cultural heritage, Digitalization.

Branching stochastic processes, limit theorems, statistical inferences, application of branching models in epidemiology, demography and population dynamics.

Mathematical modeling of biological processes, Bifurcation analysis of dynamical system, Computer simulations of biological models

Cryptology, coding theory, discrete mathematics.

Algebra (Linear Algebra in Euclidean Space, Group Theory, Finite Fields), Geometry (Codes and Designs in Polynomial Metric Spaces), Combinatorics (Spherical Designs, Designs in Projective Spaces), Coding Theory (Coding Limits, Optimal Codes), Cryptography.

Combinatorial algorithms and codes - isomorphism, generation and classification algorithms, coding theory - code boundaries, optimal codes, code automorphisms, algebra, finite fields, cryptography.

The research interests of Dr. Boyadzhiev include: the comparison principle for systems of elliptic and parabolic differential equations; PDEs, including both cooperative, and non-cooperative systems; movement of waves in a solid body - in particular, the use of characteristics to track the path of seismic waves from an earthquake source to reception stations; development of methods for choosing the optimal solution of nonlinear vapor problem in mathematical modelling of Earth structure; deterministic models in geophysics and financial markets.

Deep learning, neural networks

Algebra: Linear Algebra in Euclidean Spaces, Finite Fields; Geometry: Codes and Designs in Polynomial Metric Spaces, Packings and Coverings; Combinatorics: Orthogonal Arrays, t-Designs, Strongly Regular Graphs, Association Schemes – Spherical Designs, Designs in Projective Spaces; Coding Theory: Bounds for Codes, Optimal Codes.

Decision Support Software Systems, DSSS in Disaster Management, Collaborative Software Systems, Project Management, Virtual Communities, Software Engineering Process.

Dynamic educational environments, teacher training in dynamic mathematical software, inquiry-based learning in mathematics

Algebra.

Implementing ICT in education; dynamic learning environments; spatial intelligence; math art; fun mathematics.

Algebra: Theory of Associative Rings: fields; field extensions; Galois theory - maximal p-extensions, absolute Galois groups; central simple algebras; Brauer groups of fields - structure and invariants; valuation theory. Number Theory - local class field theory.

(Complex) algebraic geometry, (nonabelian) Hodge theory and mathematical physics.

Group algebras and Abel groups, modules and associative rings, algebraic theory of matrices.

Operations research, Stochastic optimization

Тheoretical and Contrastive Linguistics, Typology, Semantics, Evaluative Morphology, Aspectology, Writing Systems, Quantitative Methods in Linguistics, Computational Morphology, Computational Lexicography, Methodology of Linguistics.

Cryptology, combinatorial optimization and algorithms

Bioinformatics

Approximations of derivatives, approximations for the fractional integral, numerical methods

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.

Dynamical systems, Applications in mathematical modeling of bioprocesses, Computer-oriented numerical analysis.

Numerical methods for nonlinear partial differential equations – finite element and finite difference methods; algorithms and scientific software; Numerical analysis of nonlinear and spectral problems in hydrodynamics, quantum mechanics, nonlinear heat - conducting medium; Numerical investigation of solutions to generalized Boussinesq’s type equations; Global solvability or finite time blow up of Cauchy problem for generalized Boussinesq’s type equations.

Artificial intelligence and logic programming; transliterations and keyboard layouts.

I carry out research mostly in the field of approximation theory. In the recent years I have been particularly interested in establishing a precise and useful characterization of the rate of convergence of various approximation processes generated either by linear operators or by non-linear as best (weighted) approximation by algebraic or trigonometric polynomials. My research also includes interpolation, (generalized) Fourier expansions, orthogonal polynomials, quadrature formulae, multipliers, application of Fourier analysis in approximation theory, and functional analysis.

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.

Software Quality, Agile Methodologies, Education on Informatics.

String theory, AdS/CFT correspondence, lattice gauge theories, Monte Carlo simulations, financial mathematics.

Informatics, mathematical modeling, chemistry, ICT.

Internet of things, artificial intelligence, intelligent service recommendation for mobile users, Internet tomography

Non-commutative algebra and applications for quantum groups, non-commutative geometry, symbolic computation

Complex Geometry and Analysis, Hodge Theory, Non-commutative Geometry, Homological Mirror Symmetry

Numerical solution of partial differential equations, Finite elements, Multilevel methods.

Modeling in financial mathematics, valuation and calibration of financial derivatives; numerical methods for partial and ordinary differential equations with applications in computational and quantitative finance, mathematical and computer modeling of natural and anthropogenic phenomena such as: transfer of pollutants in air and water environment; population dynamics of honey bees; spread of infectious diseases

Numerical methods; Approximation theory; Spline-functions; Interpolation and approximation by radon projection data; Aproximating harmonic functions through Radon projections; Low rank approximations.

Research interests: Information searching systems; Digitization of cultural heritage, research of digital and physical accessibility of museums; ICT and educational programs in museums

Soliton theory, Soliton interactions.

Digital Libraries and Services.

Temporal logic, probability logic, real-time systems, model checking, formal methods and theoretical computer science in general.

Stability of nonlinear waves, nonlinear dispersive equations, inverse scattering theory

Nonlinear Subdivision; Normal multi-scale transforms for curves and surfaces; Image and Signal Processing; Mathematical Modeling; Constrained Optimization; Primal-Dual Algorithms and their Parallel implementation.

Representation theory of Lie algebras and Lie groups, applications to Invariant theory, infinite-dimensional Lie algebras, momentum maps, geometric quantization and applications to physics.

Implementing algorithms for computing Pade approximations and their generalizations as a software application.

Digital Signal Processing and Analysis in Speech and Audio Signals; Machine Learning; Data Hiding Using Speech and Audio Signals; Acoustics; Psychoacoustics and Architectural Acoustic Analysis

Information systems, information modelling, distributed systems, numerical methods.

Algebra.

Differential Equations, Dynamical Systems, Mathematical Physics.

Modal logic, Boolean function complexity.

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.

Fields of interest/ expertise:
• Theoretical and mathematical physics; quantum field theory; field-theoretical methods in condensed-matter theory;
• Algorithms for large system modelling and analysis;
• Mathematical biology: biocomputing; modelling of biomolecular structure and dynamics; immunoinformatics; protein folding
• High-performance computing
• History and philosophy of physics

My mathematical work is primary connected with the approximation theory. Other areas of interest are varying fields of analysis, analytic number theory, numerical methods and mathematical modeling. I am also interested in the theory and application of the electoral systems, election conduct and observation.

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.

Data Mining, Image Retrieval, Data Bases, Information Systems, applied in areas such as: Digitization of Cultural Heritage, Disaster Risk Management, Analysis of Economical Processes, Education.

Logics for space and time, modal logic.

Databases; Information Systems; IT Services.

Variational analysis

Algebra.

Riemannian and almost Hermitian manifolds, theory of submanifolds, differential geometry of surfaces in a 3-dimensional and in a 4-dimensional Euclidean or pseudo-Euclidean space.

Differential, algebraic and symplectic geometry, topology and mathematical physics.

General topology (set-valued mappings), Functional analysis.

Biomedical information processing, mathematical methods for extracting useful signal from high intensity background noise

Fractional Calculus, Special Functions, Integral Transforms, Differential Equations.

Differential inclusions, Differential equations, Optimal control, Optimization, Decision making support systems.

(equivariant) (stable) homotopy theory, topological modular forms

Coding theory, query problems, covering problems.

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.

Algebra, Semigroup Theory, Transformation Semigroups, Universal Algebra, Clone Theory, Varieties of algebraic structures, discrete functions.

General Topology, Functional Analysis, Cardinal Invariants.

Algebras with polynomial identities, Integrable equations

Теория на кодирането и приложението й в кодова модулация, водни знаци и флаш-памети.

Operations research.

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.

Iinformation modelling, OLAP, big data, neural networks.

Application of geometrical methods in control theory, Mathematical applications in biosciences, economic and etc.

Non-linear elliptic and parabolic equations and systems appearing in geometry, physics and engineering: e.g. the minimum surface equation, the equation of Monge-Ampere, the equation of anisotopic diffusion in the theory image clarification, viscose solutions, diffraction problems of equations with non-continuous coefficients and others.

Functional Analysis; Approximation theory.

Numerical methods, Approximation theory.

Didactical models, didactical technologies, individual educational trajectories, gifted education, context education, building competences, integrated education, Socratic method.

Type-theoretic approaches to information theory and information processing, Dependent-Type Theory of Situated Information, Type-Theory of Algorithms, Recursion Theory, Computational Syntax, Automata Theory, Computational Semantics, Computational Syntax-Semantics Interface, Computational Linguistics, Type-Theoretic Grammars, Constraint Based Lexicalized Grammar (CBLG), Artificial Intelligence

Digitization, Semantic Web, Ethnology, Folklore Studies, Culture Anthropology, Communities and Identities, Ethno-statistics, Museums and Archives, Digital Libraries.

Coding theory, computer algebra, high performance computing.

Software Technologies; Software Quality Requirements; Comparative Analysis; Software Development Models; Software Project Management.

Interval analysis, Numerical methods with verification, Algebraic properties of intervals, errors, convex bodies, stochastic numbers etc., Hausdorff approximations, Mathematical modeling in biology, enzyme kinetics, microbial growth, synaptic transmission, special relativity.

Representations of Lie and Hecke algebras; Group algebras and differential and difference equations associated with quantum mechanics and mathematical physics.

Discrete optimization, Bioinformatics, Drug design.

Differential geometry of Riemannian manifolds, differential geometry of surfaces and hypersurfaces in Euclidean or Minkowski spaces, local theory of surfaces in pseudo-Euclidean spaces with neutral metric.

Modelling, simulation, cybersecurity, operations research, computer sciences, computer assisted exercises, crisis/emergency management.

Data Mining, Knowledge Retrieval, Data Bases, Information systems, ERP-systems, Software and Web Design applied in areas such as: Analysis and Management of Economical and Natural Processes.

Web-based learning environments, e-learning, adaptive learning, personalization of learning, virtual worlds and virtual learning, serious games, MOOC, digitization of cultural, historical and scientific heritage.

Several complex variables, Analysis on complex and almost complex manifolds, Complex differential geometry, Twistor theory.

Random Combinatorial Structures, Asymptotic Enumeration, Limit Theorems.

Information modeling through multidimensional data cubes and issues related to data sparsity in the model, big data, data warehouses, data quality

Inquiry-based learning in mathematics

Several complex variables

Nonparametric statistics.

e-Learning, Virtual reality, 3D, Serious Games, Gamification, Interactive Learning Resources

Research, projects and developments in the field of statistical analysis techniques for IDS, coding theory, probability models, digital competences, mathematical and soft skills, e-learning, adaptive learning in web-based environments, personalization of learning and ICT-based approaches to improve learners' ability to learn.

Functional Programming; Computer Algebra Systems; Knowledge Based Systems; Information Retrieval; Semantic Technologies.

Semantic Web, Digital Libraries and Content Management Systems, Programming, Databases, Digitalization, Digital Graphics

Probabilistic forecasting, computational statistics, mathematical analysis

Biostatistics, bioinformatics.

Extreme value theory, Random processes, Limit theorems, Insurance risk theory, Finance mathematics.

Fractional Calculus, Special Functions, Integral Transforms, Differential Equations.

Multimedia Digital Libraries Services: Annotation and Semantic Indexing of Digital Objects, Metadata Management, Tools and Techniques for Navigation, Preview, Group, and Selection to Digital Objects/Collections and their Descriptions, Personalized and Adaptive Access to the Digital Content, etc., e-Learning Technologies and Standards, New Information Technologies and Environments for Distance Learning, Multimedia and Language Technologies, Knowledge and Semantic Web Technologies.

Mathematical Linguistics and Knowledge Processing, Human Language Technologies, Information Society Technologies, Knowledge Technologies and Management, Semantic WEB services, Semantic Information Processing, Digital Libraries and Content Management Systems, Algorithmics, Theory of Computation, Discrete Mathematics.

Partial differential equations, Microlocal analysis, Spectral theory, Scattering theory, Dynamical systems.

My research has been in the area of arc and jet schemes, motivic integration, and their applications to singularities, such as Nash problem. Also, I am working in topology of complements of algebraic sets, including generalizations of Zariski - van Kampen theorem for higher homotopy groups, and hyperplane arrangements. Recently started my interest in applications of singularities of differentiable maps to medical imaging.

The main research interests and publications of Peter Popivanov are in partial differential equations - linear and nonlinear micro-local analysis nonelliptic border problems and global solvability, hipoellipticity, propagation of singularities of weakly nonlinear hyperbolic equations and systems and applications in mechanics and geometry.

Numerical and algebraic methods for problems with uncertain (interval) data; Linear algebraic systems involving (non)linear dependencies between interval parameters: methods, software tools, applications; Algebraic extensions (http://www.math.bas.bg/~epopova/directed.html) of the classical interval space; Software tools for problems with uncertain data and/or result verification; Interaction between computer algebra and interval computations; Dynamic and interactive web-accessible mathematical computations and graphics (webComputing) (http://cose.math.bas.bg/webComputing/); Standards for floating-point arithmetic and computer interval arithmetic; Statistical data analysis.

General and set-theoric topology, monotone properties realized through coverings, generalizations of paracompactness, combinatorial geometry, theory of the continuums, real and complex analysis.

Algebraic geometry and commutative algebra, and their interactions with deformation theory and singularity theory.

Partial differential equations and applications: Solvability and hypoellipticity for pseudodifferential operators with multiply characteristics; Scattering theory for hyperbolic equations and systems for moving obstacles; Nonlinear degenerate parabolic equations; BIEM for systems of elasticity in the domains with cracks.

Ethnology, Folklore studies, Culture Anthropology, Linguistics, Computational Linguistics, Digital Libraries.

Mathematical modelling with applications in biology and onclogy, dynamical systems and applications, numerical analysis, harmonic analysis.

Operations research (Optimization, Variation Analysis, Game Theory), Functional analysis (Banach Space Geometry, Convex Analysis, Monotone Operators), General Topology (Topological Methods in Optimization and Variation Analysis, Set-valued mappings).

Functional analysis, Differential inclusions, Optimal control.

Accessibility: standards and legislation; documents, software, web interfaces and content; assistive technologies; people with disabilities and technology; practical applications.