  Infinite dimensional Hamiltonian systems appear naturally in the rich
algebraic structure of Symplectic Field Theory. Carefully defining a
generalization of gravitational descendants and adding them to the picture, one
can produce an infinite number of symmetries of such systems . As in
Gromov-Witten theory, the study of the topological meaning of gravitational
descendants yields new differential equations for the SFT Hamiltonian, where
the key point is to understand the dependence of the algebraic constructions on
choices of auxiliary data like contact form, cylindrical almost complex
structure, abstract perturbations, differential forms and coherent collections
of sections used to define gravitational descendants.
