3. Postdoctoral Program - MSRI

on the group of Hamiltonian diffeomorphisms. Their preprint ”On the Uniqueness of Hofer’s
Geometry” is available on arxiv.org.
Andrew Cotton-Clay
PhD: UC Berkeley, 2009
Position prior to MSRI membership: none
Position after MSRI membership: Benjamin Peirce Lecturer and NSF Postdoctoral Fellow,
Harvard University
Mentor: Denis Auroux
Andrew’s research focused on applications of holomorphic curves to symplectic and contact
geometry, and to geometry and topology, in low dimensions. There are only limited cases in
which we have a thorough understanding of rigid holomorphic curves in symplectizations of
contact or stable Hamiltonian manifolds. In the case of mapping tori over T 2 , and for many
cases for mapping tori over higher genus surfaces, he obtains a complete description of rigid
holomorphic pairs of pants. This has applications to periodic Floer homology, and to the
symplectic field theory of the natural stable Hamiltonian structure on the mapping tori. It
also has connections to number theory, and one may expect applications to contact 3-manifolds
via open books.
Preprints: Holomorphic pairs of pants in mapping tori, preprint
Oliver Fabert
PhD: University of Munich (LMU) 2008
Position prior to MSRI membership: University of Munich (LMU)
Position after MSRI membership: postdoc at Max Planck Institute, Leipzig, Germany
Mentor: Eleny Ionel
Oliver Fabert received his Ph.D. from the University of Munich (LMU) in 2008 under the
supervision of Kai Cieliebak. His dissertation was entitled ”Transversality results and computations
in symplectic field theory” and was in parts written up during his one semester stay at
the Swiss Federal Institute of Technology (ETH) in Zurich, Switzerland while joining Dietmar
Salamons working group. While at MSRI Oliver continued thinking about the transversality
problem for holomorphic curves, mostly together with his mentor Eleny Ionel, as well as
the integrable systems structure that naturally appears in symplectic field theory, where he
continued his joint work with Paolo Rossi. As results of this intensive joint work during his
stay at MSRI they so far wrote two joint papers on ”String, dilaton and divisor equation in
symplectic field theory” (ArXiv preprint 1001.3094) and ”Topological recursion relations in
non-equivariant cylindrical contact homology” (ArXiv preprint 1007.2287). In both papers the
stay at MSRI is greatly mentioned. Together with Joel Fish and Roman Golovko he organized
a working group on Hofer-Wysocki-Zehnders polyfold theory which claims to solve the above
transversality problem in full generality, see also the survey ”Transversality problems in symplectic
field theory and a new Fredholm theory” on the Arxiv (1003.0651). Furthermore he
organized with Paolo Rossi and Dimitri Zvonkine a second (of four) working group exploring
the relation between holomorphic curves and integrable systems. Apart from the people he already
mentioned, he benefitted very much from discussions with many other great researchers
like Yasha Eliashberg, Octav Cornea and Clifford Taubes.
Agnes Gadbled
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