3. Postdoctoral Program - MSRI

curves in symplectic manifolds. Originally conceived by Eliashberg, Givental and Hofer it is actively
being developed to this day. The talks focused on the algebraic framework of the theory and
the analytic tools needed to define the theory rigorously. In particular, there were several talks on
scale calculus and polyfolds.
Floer homology: Speakers — Mohammed Abouzaid, Peter Albers, Sikimeti M’au, Mark McLean.
There are many variants of Floer theory. These lectures focused on Hamiltonian Floer theory,
Lagrangian Floer theory and symplectic homology. They discussed successes of the theory and
several applications as well as limitations and current challenges within the theory.
Topological aspects: Speakers — Denis Auroux, John Etnyre, Ko Honda, Maksim Maydanskiy. The
introduction of Lefschetz pencils (fibrations) in symplectic geometry and open book decompositions
in contact geometry have transformed many questions in symplectic and contact geometry into
questions with a more topological flavor (especially in dimensions 3 and 4). These connections were
described and many applications were discussed during these lectures. Convex surfaces, another
fundamental topological tool in 3 dimensional contact geometry, were also surveyed.
Applications: Speakers — Octav Cornea, Michael Entov, Victor Ginzburg, Lenny Ng. This series
of lectures consisted in a wide sampling of the many diverse applications of symplectic and contact
geometry and topology to other areas as well as applications of some of the sophisticated machinery
from other lectures being applied to symplectic geometry itself. For example, connections with
invariants of smooth knots in 3-manifolds and applications to quantum mechanics and Hamiltonian
dynamics were discussed, as well as new perspectives on the geometry of Lagrangian submanifolds.
Problem session: Organizer – Lisa Traynor. Participants of the workshop were invited to share
problems that would be good to think about during the coming year. Dusa McDuff began by
introducing a number of intriguing questions including some unknown questions about the connectedness
of some groups of symplectomorphisms. Helmut Hofer urged people to try to construct
bizarre embeddings of ellipsoids since this will help us understand if there are gaps in what SFT can
detect. Mohammed Abouzaid discussed a known theorem that states that a Lagrangian torus inside
T 4 is theoretically equivalent to some linear Lagrangian and then posed the question of whether
this remains true when T 4 is replace by a more general product of Riemann surfaces. Knowledge
about this would have applications to mirror symmetry. Yasha Eliashberg introduced a number of
interesting problems. He urged us to think of some “overly optimistic” conjectures, for example
generalizations of the Arnold conjectures or the statement that every odd dimensional manifold
(with stable almost complex structure) is contact, and then either prove or find counterexamples to
these conjectures. Eliashberg also highlighted an important question about how SFT changes when
a handle is attached to a manifold. Lastly, Octav Cornea introduced a version of symplectic embeddings
relative to to a pair of Lagrangian submanifolds and posed some questions that compare
the maximal “width” of such an embedding to the Hofer distance between the Lagrangians.
Distribution of the funding:
There were many more requests for funding than could be honored. We were able to stretch the
funding quite far since some of the speakers and participants were already at MSRI because of the
earlier Graduate and Connections for Women Workshops. We gave a high priority to requests of
post-docs/young faculty since this workshop provided an excellent opportunity to find new areas of
research at this important time in their career. We had numerous requests from graduate students
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