3. Postdoctoral Program - MSRI

Final Report
Symplectic and Contact Topology and Dynamics:
Puzzles and Horizons
March 2010
Organizers:
Paul Biran (Tel Aviv University and ETH-Zürich), John Etnyre (Georgia Institute of Technology),
Helmut Hofer (Courant Institute), Dusa McDuff (Barnard College),
Leonid Polterovich (Tel Aviv University and University of Chicago )
Summary:
This was the third workshop associated with the “Symplectic and contact geometry and topology”
program being held during the 2009-2010 academic year (one more workshop will take place in
May, which is sponsored by the Hayashibara foundation and will have an interdisciplinary focus;
there is also another related workshop in May, but that is not officially affiliated with the program).
Purpose: The workshop focused on recent progress on central problems in symplectic and contact
topology and Hamiltonian dynamics, such as: rigidity of Lagrangian submanifolds; algebra/topology/geometry
of symplectomorphism and contactomorphism groups; exotic symplectic
and contact structures; and existence of periodic orbits of Hamiltonian systems and Reeb flows. It
explained applications of the “large machines” such as Floer Theory, Symplectic Field Theory and
Fukaya categories, as well as showing where these machines do not yet provide satisfactory answers.
Special attention was paid to articulating new problems and directions, as well as to explaining
interactions between symplectic and contact topology and other fields.
Distribution of funding: There were many more requests for funding than could be accomodated.
We were able to stretch the given resources quite far, since some of the speakers and participants
were already at MSRI as participants in the SCGT program. We gave a high priority to requests
from advanced graduate students and beginning researchers, who could benefit most from the
exposure to latest results in the field. Limited funding was provided for more senior researchers
whose presence would add variety and depth to the workshop. We were able to support a large
number of mathematicians at all levels from underrepresented groups.
Some highlights and impact: The workshop started with Taubes’ talk on his work with Hutchings,
solving the chord conjecture in dimension three (both Taubes and Hutchings were program
members while this work was being done). Another notable breakthrough was completed during
the workshop itself, since that allowed all collaborators to meet: the proof that �ECT = � HF , announced
by Honda on the penultimate day. Many participants emphasized having highly productive
discussions during the workshop, which advanced their own research.
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