#
Towards Relative Symplectic Field Theory

September 24 to September 28, 2007
at the

American Institute of Mathematics,
San Jose, California

organized by

Kai Cieliebak,
Tobias Ekholm,
Yakov Eliashberg, Kenji Fukaya,
Dennis Sullivan,
and Michael Sullivan

## Original Announcement

This workshop CUNY Graduate Center
and Stanford Mathematical Research Center (MRC) is to understand the structure of relative Symplectic Field Theory (SFT),
discuss and reconcile different
versions of its
algebraic formalism, and to work
towards building rigorous foundations of the theory. There will
also be explored applications of relative SFT to symplectic
and contact topology, as well as low-dimensional topology.
The goal of the SFT project is to uncover algebraic structures
which reflect the topology of the compactified moduli spaces of punctured holomorphic curves
in symplectic manifolds with cylindrical ends.
Its relative counterpart should describe
the topology of the compactified moduli spaces of punctured holomorphic curves with Lagrangian boundary conditions.

Though the SFT project is not yet completed in either absolute or relative case, the involved algebraic structures are much better understood in the absolute case, and the building of the analytic foundations of the theory in the absolute case is well under way. The absolute SFT already led to new invariants of contact and symplectic
manifolds and brought many applications to symplectic and contact
topology. There were also uncovered deep relations to other subjects such as
enumerative algebraic geometry and integrable systems.

On the other hand, relative SFT is still in the period of its infancy. While special cases of the
relative theory have been known for a long time, e.g. Floer homology
for Lagrangian intersections and Legendrian contact homology, the general formulation of a Relative Symplectic Field Theory has not been yet understood.

On the other hand, in the past few years several new fruitful ideas, and in particular,
a link to String Topology were introduced to the subject. As a result, a general picture of Relative SFT is now
emerging. By bringing together the researchers involved in these new
developments, we intend to reconcile different approaches and establish Relative Symplectic Field Theory
in full generality, investigate its relations with
Open String Topology, and discuss applications. There will be also
discussed the current status of the analytic foundations of the theory, and the remaining necessary steps to complete the project.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

A survey article on string topology by Dennis Sullivan.

Papers arising from the workshop: