3. Postdoctoral Program - MSRI

of the theory via webs and foams modulo local relations and presented some of its
features (for example, its functoriality under tangle cobordisms).
After the talks, the participants held an informal panel discussion about academic
issues, including those that might be of specific interest to women. The panelists
included Shelly Harvey (Rice), Joanna Kania-Bartoszynska (NSF), Gordana
Matic (University of Georgia), Dusa McDuff (Barnard), and Olga Plamenevskaya
(Stony Brook). There was a brief disagreement among participants as to whether
discrimination against women in mathematics is a current concern; however, most of
the discussion was very friendly and included a lot of advice to younger mathematicians
on topics such as job search, grant applications and research presentations.
The panelists and more senior participants also answered a lot of questions about
life in academia.
The day concluded with a very nice dinner, sponsored by MSRI, at a local Thai
restaurant. The dinner provided an excellent opportunity for female participants
to chat in an informal atmosphere.
The second day began with a beautiful talk by Shelly Harvey (Rice), who gave an
overview of knot concordance results. She started with basic definitions, pictures,
and a few classical theorems, and then described a few modern tools in knot concordance,
including higher signatures, n-solvable filtrations, Heegaard Floer homology
and Khovanov homology.
Gordana Matic (University of Georgia) gave the next talk, focusing on contact
topology. She gave basic definitions and described the central questions in contact
topology, then explained how to build Heegaard Floer contact invariants from an
open book decomposition, and concluded with several applications.
In the afternoon, Vera Vertesi (MSRI) continued the discussion about contact
topology, defining Legendrian and transverse knots in contact manifolds. She described
several different invariants of these knots coming from Heegaard Floer homology,
and then explained how these invariants are related.
Joan Licata (Stanford) also spoke on Legendrian knots, but from a quite different
perspective. Her focus was on invariants, originating in contact homology and
symplectic field theory, that take the form of a differential graded algebra. In certain
simple cases, these invariants admit a combinatorial description; Joan discussed
some known results for knots in S 3 and explained how to extend these ideas to
knots in lens spaces.
Ina Petkova (Columbia) returned to the subject of knot concordance in her talk,
discussing how the new bordered Floer homology technology of Lipshitz, Ozsváth,
and D. Thurston can be used to give concordance information about cable knots.
The final talk of the conference was given by Cinem Onaran (Oberwolfach). She
talked about the interplay between Legendrian knots and open book decompositions,
outlining some interesting results concerning overtwisted contact structures
and loose knots, and also explaining how Heegaard Floer invariants may be used
to detect restrictions on the genus of open books compatible with certain contact
structures.
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