3. Postdoctoral Program - MSRI

example Gadbled, Mandini, Ma’u, Hohloch, Sandon, Chang. There were certainly enough
women at MSRI to create a vibrant atmosphere in which one’s gender was not an issue.
We also tried to encourage participation by other underrepresented groups. For example, several
African American mathematicians participated at various workshops during the program.
8 Synergistic activities
One of the keys to the success of our program was the interaction with the parallel programs. It
is clear from the above description that we had significant interactions between the programs.
The overlap extended back into the planning stages where the organizers discussed postdoc
applications with the organizers of the parallel programs, resulting in several postdocs that were
in some sense joint between the programs (sometimes with joint funding, sometimes without).
For example: David Shea Vela-Vick and Vera Vertesi were joint with the Homology Theories
of Knots and Links program and Brett Parker was joint with the Tropical Geometry program.
In addition, several of the senior personnel were considered joint between the programs. Some
notable examples of this are Ko Honda and Cliff Taubes.
A prime example of the interactions between the programs was the “Sutured Manifolds and
the Contact Category” informal working group, where deep connections between sutured
Heeegaard-Floer theory (represented by the HTKL program) and contact geometry (represented
by the SCGT program) were explored. Very related to this was Vincent Colin, Paolo
Ghiggini and Ko Honda’s, and independently Cagatay Kutluhan, Yi-Jen Lee and Clifford
Henry Taubes’, breakthrough concerning the equivalence of Embedded Contact Homology and
Heegaard-Floer Homology (and hence Seiberg–Witten–Floer Homology, via earlier work of
Taubes and Hutchings). This beautiful work establishes the long conjectured equivalence of
Seiberg-Witten Floer Homology and Heegaard-Floer Homology using subtle ideas form symplectic
and contact geometry.
These are just a few of the many collaborations between the programs. Other example can
be discerned from the discussions above concerning the work of the postdocs, the seminars,
working groups and research highlights.
9 Nuggets and breakthrough
In the last 10 years, a lot of effort in low-dimensional topology has been directed towards
understanding relations between different homology theories that are defined using completely
different tools and ideas. For instance, the Seiberg-Witten homology theory, mathematically
constructed by Kronheimer and Mrowka, uses some physical ideas from gauge theory; while
two other theories, the Heegaard homology theory of Ozsváth and Szabó, and the Embedded
Contact Homology Theory of Hutchings and Taubes, are based on ideas from symplectic geometry
(Lagrangian intersection theory and holomorphic curves). Each of these approaches has
its advantages, tools and corollaries. It was long conjectured that all these theories coincide.
It is a major success of the current program, in interaction with the concurrent program on
Homology Theories for Knots and Links, that this equivalence has been finally established.
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