Integrable systems in Gromov-Witten and symplectic field theory

January 30 to February 3, 2012

at the

American Institute of Mathematics, Palo Alto, California

organized by

Boris Dubrovin, Oliver Fabert, Todor Milanov, and Paolo Rossi

This workshop, sponsored by AIM and the NSF, will be devoted to the relation between symplectic invariants (namely Gromov-Witten and Symplectic Field Theory) and the theory of infinite dimensional integrable systems.

Starting with the formulation of Witten's conjecture in the 90's, which relates the full Gromov-Witten potential of the point with the commuting integrals of the KdV integrable hierarchy, it has become widely known that there is a deep and subtle relation between Gromov-Witten invariants and the theory of integrable systems of Hamiltonian PDEs.

As outlined by Eliashberg in his ICM2006 plenary talk, the integrable systems of rational Gromov-Witten theory of a symplectic manifold very naturally arise in rational Symplectic Field Theory of circle bundles over such symplectic manifold. More in general, after carefully defining a generalization of gravitational descendants, SFT provides a framework that associates an infinite dimensional Hamiltonian system with infinite symmetries to each contact manifold (or more in general stable Hamiltonian structure). Adding higher genera curves provides a quantization of such system.

Recently some progresses have been made in the investigation of the Hamiltonian systems from SFT (in particular by studying the analogue of tautological relations for psi-classes in Symplectic Field Theory). The goal of this workshop is, hence, to bring together experts from the field of symplectic geometry working on SFT and related topics with experts from the field of integrable systems and their relation to Gromov-Witten theory, in order to push this line of research further in many related directions:

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

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