Holomorphic Curves in Contact Geometry
August 4 to 9, 2003
at the
American Institute of Mathematics,
Palo Alto, California
organized by
Yasha Eliashberg
and
John Etnyre
This workshop, sponsored by
AIM and the
NSF, will be devoted to
the development of holomorphic curve
techniques in contact geometry and topology. The advent of
holomorphic curve techniques in contact topology, as exemplified
in Symplectic Field Theory (SFT), and asymptotically holomorphic curve
techniques, in the spirit of Donaldson, has allowed one to use a
diverse set of geometric, analytic and topological tools when
studying contact structures. The goal of this workshop is to
expose, develop and apply these tools.
The workshop will bring together researchers in contact and
symplectic geometry, dynamics, low-dimensional topology and
physics, who will explore connections between the various
approaches people have taken to using holomorphic curves, develop
new holomorphic curve techniques and apply them to various
questions in contact and symplectic geometry and low-dimensional
topology.
The main questions to be addressed concern
- connections between symplectic field theoretic and gauge theoretic
invariants of contact and symplectic manifolds in dimensions
both high and low;
- invariants of a smooth manifold via holomorphic curve invariants
of its unit cotangent bundle;
- the theory of Legendrian submanifolds and its interaction
with the classical knot theory;
- applications of Lefschetz pencil representation of symplectic
manifolds, and open book representation of contact manifolds
for computing of holomorphic curve invariants.
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 there will be
ample time between talks for discussions and for work to be done.
The application deadline for participation in this workshop has passed.
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American Institute of Mathematics.
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AIM Research Conference Center.