

The main direction of my research is the construction of the curvaturetype differential invariants for a wide class of geometric structures on manifolds with applications to a) equivalence of nonholonomic vector distributions, subRiemannian structures, CR (Cauchy Riemann) structures, fields of cones, ordinary and partial differential equations; b) optimality properties of extremals of optimal control problems; c) statefeedback equivalence of control systems; d) qualitative study of Hamiltonian systems. The approach is based on the study of differential geometry of curves in Grassmannians, Lagrange Grassmannians, and spaces of flags. Among other topics of my research are 1) projective/affine equivalence of subRiemannian metrics and inverse optimal control problem ; 2) Gromov's hprinciple for vector distribution (global existence of distributions with prescribed differential properties); 3) nonsmooth Morse theory with applications to Mathematical Physics; 4) invariant description of flat control systems; 5) subRiemannian LaplaceBeltrami operator. 
