Igor Zelenko


Published and accepted papers  on-line
Preprints on-line
Papers in preparation   
Detailed CV (last updated: December 12,  2022)
Short CV
Some recent beamer presentations
Video-recordings of some recent talks/lecture series
Working Seminar in Geometric Control  
Workshop on Equivalence, invariants, and symmetries of vector distributions  and related structures : from Cartan to Tanaka and beyond , IHP, Paris, France, December 10-12, 2014
Workshop on "Geometry of vector distributions and etc"   , SISSA, Trieste, Italy December 13-15, 2006
 PhD Thesis (ps-file)

Igor Zelenko
Department of Mathematics

Texas A&M Univerisity,
Blocker 601J,
College Station, TX 77843-3368, USA;
e-mail:  zelenko@math.tamu.edu
fax: +1-979-845-6028 

The main direction of my research is the construction of the curvature-type differential invariants  for  a wide class of  geometric structures on manifolds with applications to

a) equivalence of nonholonomic vector distributions,  sub-Riemannian structures,  CR (Cauchy -Riemann) structures, fields of cones,  ordinary and partial differential equations;

b) optimality properties of extremals of optimal control problems;

c) state-feedback 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  sub-Riemannian metrics and inverse optimal control problem ;

2) Gromov's  h-principle 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) sub-Riemannian Laplace-Beltrami operator.