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 and the question of their integrability arises. As in Gromov-Witten theory, the study of the topological meaning of gravitational descendants yelds new differential equations for the SFT-potential (this part is a work in progress with O. Fabert).

Lecture #13907

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