3. Postdoctoral Program - MSRI

German Research Foundation
Mentor: Eleny Ionel, Cliff Taubes
Together with G. Noetzel (Leipzig), Sonja started working on a project about n-categories and
higher Morse moduli spaces. Moreover, they interpreted their joint work with D. Salamon
about hyperkaehler Floer homology in terms of infinite dimensional Hamiltonian systems on
the double iterated loop space. Sonja also spent a lot of time discussing certain aspects of
symplectic dynamical systems with many of the senior mathematicians at the MSRI while she
was revising a submitted preprint about homoclinic points and Floer homology. She also spent
some time thinking about the relation between certain cube diagrams and hyperkaehler Floer
homology with Scott Baldridge (LSU), who visited MSRI in January. Sonja also gave talks:
one in the ’Connections for Women workshop’, and two talks each in the Symplectic Research
Seminar, the Postdoc Seminar and the working group on ’Giroux correspondences’.
Preprints: 1) Homoclinic points and Floer homology (submitted; revising) 2) n-categories
and higher Morse moduli spaces (with G. Noetzel) 3) Hyperkaehler Floer theory as infinite
dimensional Hamiltonian system on the iterated loop space and the Maslov index (with G.
Noetzel)
Sonja mentioned: ” I very much liked the Symplectic Year at the MSRI since it provided
ample opportunity to discuss problems directly with the experts. Moreover, I got to know
many people working in symplectic geometry — I feel much more comfortable to write an
email about a mathematical question to a person I know than to somebody whom I only know
from the literature...”
Cagatay Kutluhan
PhD: University of Michigan, 2009
Position prior to MSRI membership: none
Position after MSRI membership: Ritt Assistant Professor at Columbia University
Mentor: Ko Honda, Cliff Taubes
Cagatay Kutluhan received his Ph.D. from the University of Michigan, Ann Arbor in 2009
under the supervision of Daniel M. Burns, Jr. His dissertation was titled “Floer homology
and symplectic forms on S 1 × M 3 .” While at MSRI Cagatay continued thinking about generalizations
of his thesis result as well as related other problems. He also investigated several
constructive methods in contact and symplectic topology and their interplay with gauge theory
and Floer homology. He learned a great deal more about the latter through seminars, working
groups and by direct contact with experts in the field. Moreover, he started a project with
Tolga Etgu and Bulent Tosun during his stay. However, the most exciting progress in his
research took place in the beginning of 2010 when he and his collaborators Yi-Jen Lee and
Clifford Henry Taubes finally figured out how to prove the equivalence of Heegaard Floer homology
and Seiberg-Witten Floer homology. They have already posted two of the five preprints
that prove this equivalence on arXiv in Summer of 2010. After his stay at MSRI, Cagatay
started his position as a Ritt Assistant Professor at Columbia University.
Preprints: HF=HM I : Heegaard Floer homology and Seiberg–Witten Floer homology with
Yi-Jen Lee and Clifford H. Taubes available at arXiv:1007.1979
HF=HM II : Reeb orbits and holomorphic curves for the ech/Heegaard Floer correspondence
with Yi-Jen Lee and Clifford H. Taubes available at arXiv:1008.1595
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