Photonics

Scattering of electromagnetic waves on periodic dielectric and metal structures. Applications of the operator theory to study resonances and bound states in continuum (Siegert states) in nanophotonic structures. Nonlinear resonant scattering of electromagnetic waves and applications to optical nonlinear effects at the nanoscale. Pseudo-spectral numerical methods in electromagnetic and quantum scattering problems. The objective is to develop theoretical foundations for  amplification  and control of optical nonlinear effects in photonics at the nanoscale which can be used to design photonic devices for all-optical data processing (photonic transistors, switches, and similar).

Modeling of laser-induced plasmas

Theoretical and numerical  methods based on the Navier-Stokes equations to study dynamics of laser-induced plasmas and applications to remote chemical sensing based on the laser-induced breakdown spectroscopy (LIBS).  Methods and numerical algorithms  for optical data processing in LIBS plasmas and plasma diagnostics.

Yang-Mills and gauge theories

Mathematical aspects of quantization of constrained dynamical systems by the path integral method. Geometry of the physical phase space and the orbit space in gauge systems and Yang-Mills theories. Lattice Yang-Mills theories. Topological excitations in lattice  Yang-Mills theories, knot solitons, and applications to non-perturbative dynamics in gauge systems.