Algebraic integrability of Schroedinger operators in many dimensions, bispectral problem and Huygens' Principle. Hamiltonian formalism, action-angle variables and Riemann surfaces. Integrable Lagrangian systems with discrete time. Theory of multi-valued groups and iterated correspondences. Integrable systems in geometry and topology.
Integrable gradient flows.
Solvable algebraic and functional equations. To appear in Journal of Mathematical Physics. On geometry of a special class of solutions to generalised WDVV equations. Algebro-geometric Poisson brackets for the difference operators and Volterra system. An introductory course on the qualitative theory of ordinary differential equations on the plane and on calculus of variations.