- Nonlinear equations of mathematical physics
- Mathematical biology
- Modeling of biofilms and analysis: new class of degenerate parabolic equations
- Model and dimension reduction in dynamical systems with application in biology
- Homogenization approach in PDE and related questions in the life sciences
- Higher order models arising in Physics and Biology
- Chaotic dynamics, topological and Kolmogorov's entropy
- Infinite dimensional dynamical systems and their global Attractors
- Upscaling, Optimization and Design of chemical reactors
- Topological methods and its applications
- Rate-indepentent processes and its applications
- Local and global bifurcation based on the degree theories
- Homological degree theory in the category of quasiruled (Fredholm) manifolds
- Geometrical properties of nonlinear mappings related to (pseudo)differential operators