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
Mathematical modeling and analysis of bioprocesses; mathematical applications in management of nonlinear systems, economics, risk assessment, etc. Mathematical biology, modeling of infectious and chronic diseases, population dynamics.
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.
Mathematical modelling with applications in biology and onclogy, dynamical systems and applications, numerical analysis, harmonic analysis.
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.
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.
Numerical methods, Approximation theory.
Application of geometrical methods in control theory, Mathematical applications in biosciences, economic and etc.