3. Postdoctoral Program - MSRI

Program Report
Symplectic and Contact Geometry and Topology
Year-long program, 2009-10
Organizers:
Y. Eliashberg (Stanford), J. Etnyre (Georgia Tech), E. Ionel (Stanford), D. McDuff
(Barnard), P. Seidel (MIT)
1 Introduction
MSRI has historically played a major role in our general area of mathematics. The first
relevant program took place in 1988/89, just a few years after the invention of Symplectic and
Contact Topology in their modern sense. In the twenty years since then, the field has grown
enormously, and unforeseen connections with other areas of Mathematics and Physics have
been found. By 2009, the time was ripe to reevaluate the achieved progress, and crystallize
new ideas and promising direction of research.
The 2009/10 program in Symplectic and Contact Geometry and Topology, organized by Y.
Eliashberg, J. Etnyre, E. Ionel, D. McDuff and P. Seidel, was designed to
- Promote the cross-pollination of ideas between different areas of symplectic and contact
geometry;
- Help assess and formulate the main outstanding fundamental problems and directions in
the field;
- Lead to new breakthroughs and solutions of some of these main problems;
- Discover new applications of symplectic and contact geometry in mathematics and physics;
- Educate a new generation of young mathematicians, giving them a broader view of the
subject and the capability to employ techniques from different areas in their research.
The program ran in parallel with two tightly related semester-long programs: on Tropical
Geometry in the Fall, and on Homology Theories for Knots and Links in the Spring. Both
fields have close connections to ours, and the presence of experts in these areas was extremely
beneficial. We also benefited from interactions with the UC Berkeley mathematics department
on various levels, from graduate students to faculty members. The resulting productive research
environment led to a number of high-profile results and breakthroughs, as well as starting
developments in new directions.
2 Research Developments
Embedded Contact Homology and related invariants. One of major results obtained during
the program is the proof of a long sought equivalence between Seiberg–Witten–Floer theory,
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