Mathematics
My mathematical research interests are mainly focused around two topics (suggested by my PhD adviser Prof. Volodymyr Makarov):
Study of direct, inverse or nonlocal problems for evolution equations in Banach space
Function-Discrete methods for nonlinear boundary value problems.
Aside from work on the mentioned mathematical topics I devote a considerable amount of time to work on various applications of the developed numerical methods and their effective implementation using modern coding techniques and paradigms. Such efforts are mainly directed towards the development of fully discrete hybrid numerical methods for ecological, physical and financial models. To synthesize these hybrid methods I use a combination of spectral methods based on a Dunford-Cauchy integral representation for time discretization along with various space approximation methods.
Physics
I also have certain scientific interests in physics. Mainly they are related to the field of multi-scale physical phenomena in quantum heterostructures with applications to photonics and quantum computing. I got acquainted with the field whilst obtaining my Masters Degree at Wilfrid Laurier University. In the Masters Thesis I discovered that the majority of works where Effective Mass Theory is used to determine electronic band-structure of some crystalline semiconductor materials are based on fundamentally wrong assumptions.
Software development
To supply my theoretical work with numerical examples and data I do a lot of coding. My primary software project is called PamPeRO. It is targeted on the creation of a portable and computationally effective parallel implementation of hybrid methods for evolutionary problems. While working on this project I try to use modern programming concepts of C++ language utilizing existent mathematical software whenever possible. The comprehensive list of codes can be found under the Codes section.