3. Postdoctoral Program - MSRI

Ma’u, Sikimeti
McLean, Mark
Parker, Brett
Sikimeti received her Ph.D. from Rutgers University in 2008 under the
supervision of Christopher Thomas Woodward. Her dissertation was
titled “The Multiplihedra in Lagrangian Floer Theory”. While at MSRI,
Sikimeti worked on analytical and algebraic aspects of Quilted Floer
theory. During the Fall 2009, she completed “Gluing
Pseudoholomorphic Quilted Disks,” and in the Spring of 2010 she
completed “Quilted strips, graph associahedra, and A-infinity n-modules
and nearly completed “A-infinity bimodules for Lagrangian
correspondences.” According to Sikimeti, “the biggest benefit [of her
membership at MSRI] was the networking aspect, getting to know people
who work in the field, being able to talk to them in person. Another
benefit was finding out the interesting directions people are moving
towards now and getting lots of new ideas for one‟s own research.”
After her stay at MSRI, Sikimeti took a postdoctoral fellowship position
at Barnard College.
Mark received his Ph.D. from the University of Cambridge in 2008.
Mark spent his time at MSRI working on two papers on symplectic
homology. The first paper “A Spectral sequence for symplectic
homology” constructs a spectral sequence converging to symplectic
homology of a Lefschetz fibration whose E1 pages are Floer homology
groups of the monodromy symplectomorphism of this Leftchetz
fibration; this is then used to prove a theorem about fixed points of
certain symplectomorphisms. The second paper, “The growth rate of
symplectic homology and applications” proved several properties of an
invariant of Louiville domains called the growth rate of symplectic
homology. Mark used growth rates to show that the unit cotangent
bundle of a rational hyperbolic manifold is not Stein fillable by a smooth
affine variety. Mark also has a growth rate criterion for infinitely many
Reeb orbits and a sketch of a computability result which will be written
up in a third paper. After his stay at MSRI, Mark resumed to this
previous position as a postdoc at MIT.
Brett Parker received his Ph.D. from Stanford in 2005 under the
supervision of Yakov Eliashberg. His dissertation was titled
“Holomorphic curves in Lagrangian torus fibrations”. In his time at
MSRI, Brett worked on holomorphic curve theory in a new category
called the category of exploded manifolds which has applications to
symplectic topology and is related to tropical geometry. Brett's postdoc at
MSRI allowed him to explain his approach to tropical geometry to many
members of the Tropical Geometry program and to understand
connections to Mark Gross and Berndt Siebert's approach to tropical
geometry and mirror symmetry using Log geometry. He also understood
the connection between the exploded semialgebra, which he works with,
and Oleg Viro's multiple valued fields operations. Brett's participation in
the symplectic and contact geometry and topology program allowed him
to explain to symplectic topologists how exploded manifolds are useful
in symplectic topology and to benefit from the collective expertise of the
other members of that program that work with holomorphic curves. After
his stay at MSRI, Brett took up a postdoctoral research position at the
University of Zürich.
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