Igor Zelenko


Published and accepted papers  on-line
Preprints on-line
Papers in preparation   
Some recent talks   
Detailed CV (last updated: February 22, 2021)
Short CV
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
Associate Professor,
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) state-feedback equivalence of control systems;

b) equivalence of nonholonomic vector distributions, fields of cones,  ordinary and partial differential equations;

c) optimality properties of extremals of optimal control problems;

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) geodesic (projective) equivalence of  sub-Riemannian metrics ;

2) invariant description of flat control systems;

3) sub-Riemannian Laplace-Beltrami operator.