Geometric analysis: Sobolev spaces theory. Quasiconformal analysis. Geometric measure theory. Analysis on metric measure spaces.
Functional analysis: Sobolev spaces, global analysis: analysis on manifolds and L2-cohomology, geometrical theory of functions: quasi-conformal mappings, chemical engineering science.
Partial differential equations, geometric measure theory
Besov spaces, sobolev spaces.
Set theoretic topology, functional analysis, topological groups.