Differential Geometry and its connections to Algebraic Geometry, Complex Analysis and Theoretical Physics

Lie theory, reductive and semisimple Lie groups, linear representations and actions on manifolds. Geometry of flag varieties. Geometric Invariant Theory.

Stability of nonlinear waves, nonlinear dispersive equations, inverse scattering theory

Differential, algebraic and symplectic geometry, topology and mathematical physics.

Several complex variables

Differential geometry of Riemannian manifolds, differential geometry of surfaces and hypersurfaces in Euclidean or Minkowski spaces, local theory of surfaces in pseudo-Euclidean spaces with neutral metric.

Infinite-dimensional topology, Geometric Tomography/Topology, Geometry of Banach spaces, Convexity, Topological vector spaces, Selection theory.

Fractional calculus; Fractional differential and integral equations: operator-theoretical approach, qualitative properties of solutions. Convolutional calculus: Duhamel-type representations for nonlocal boundary-value problems.