3. Postdoctoral Program - MSRI

Final Report
Introductory Workshop
Symplectic and contact geometry and topology
August 2009
Organizers:
J. Etnyre (Georgia Institute of Technology)
D. McDuff (Columbia University)
L. Traynor (Bryn Mawr College)
This was the Introductory Workshop for the year long program “Symplectic and contact geometry
and topology” being held during the 2009-2010 academic year. The audience was made up of a
broad array of people including graduate students, post-docs, and established researchers in the
symplectic and contact fields as well as other closely related subjects. The workshop served two
main purposes: (1) to introduce people to a broad swath of the field, and (2) to frame the most
important problems and subareas in order to give some shape to the year long program.
While not able to cover this immense field completely, we focused on four broad areas that will be
the basis for most of the activities during the coming year. We also took into account the request of
the organizers of the Fall Tropical Geometry program to emphasize the kind of holomorphic curves
that could be counted. Specifically we focused on (a) Symplectic field theory, (b) Floer homology, (c)
Topological aspects, and (d) Applications. For each topic we had a blend of mini-courses introducing
the main ideas of the area and a few other talks aimed at exposing the lay of the land and future
directions for the field. In addition we had two very introductory lectures introducing the history
and basic ideas in symplectic and contact geometry and topology. Generous breaks between the
lectures were also built into the workshop to allow the participants time to interact with the speakers
and amongst themselves.
To achieve the broadest possible perspectives on these subjects we asked two experts in each area,
(a)–(d) above, to organize the activities in that area. Specifically we had Y. Eliashberg and H. Hofer
organize the Symplectic field theory talks; M. Abouzaid and P. Albers organize the Floer talks;
D. Auroux and K. Honda organize the topological aspects talks; and L. Traynor and M. Entov
organize the applications talks. This resulted in the selection of a wide variety of speakers, ranging
from well established leaders of the field to several postdocs and junior faculty.
Content of the talks: We will not describe the details of each talk but list the speakers for each
subject area and discuss the main points that were conveyed.
Introductory talks: Speaker — Dusa McDuff. In these, the first two talks of the workshop, the basic
definitions and examples of symplectic structures, contact structure, Hamiltonian flows, etc. were
introduced. The first lecture went on to discuss of some of the questions (such as the Arnold and
Weinstein conjectures) that strongly influenced the development of the field as well as those that
drive much current research. The second lecture described the basic elements of Gromov’s theory
of pseudo-holomorphic curves, since this is the crucial idea behind all current work in the field.
Symplectic field theory: Speakers — Helmut Hofer, Yasha Eliashberg, Paolo Rossi, Katrin Wehrheim.
Symplectic field theory is an elaborate framework for capturing information given by holomorphic
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