Cyclic homology and symplectic topology

November 9 to November 13, 2009

at the

American Institute of Mathematics, Palo Alto, California

organized by

Mohammed Abouzaid, Eleny Ionel, Lenhard Ng, and Paul Seidel

This workshop, sponsored by AIM and the NSF, will be devoted to a significant ongoing development on the interface between algebra and geometry through the realization that the ``closed string'' invariants of symplectic and contact manifolds, obtained by counting periodic orbits,can often be thought of algebraically as versions of Hochschild homology and cyclic homology. The relevant algebraic techniques originated outside symplectic topology (for instance, see the work of Goodwillie and Jones on free loop space cohomology), but the connection has become increasingly close with the development of string topology and symplectic field theory (see recent work of Godin and Cohen on one side, and of Latschev and Cieliebak on the other).

This workshop will bring together specialists on the symplectic and algebraic sides with the primary purposes of understanding this emerging picture. We expect to discuss implications for the structure of symplectic invariants, as well as concrete geometric applications. Two specific issues ofinterest will be

  1. conjectures of Seidel describing symplectic homology as Hochschild homology, in the context of Lefschetz fibrations;
  2. recent work of Bourgeois-Ekholm-Eliashberg which constructs an exact sequence for contact homology under critical handle attachments.

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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