3. Postdoctoral Program - MSRI

mirror symmetry using log geometry and tropical geometry. While at MSRI, Brett Parker
worked on five papers, the first 3 of which he posted on the arXiv: ‘Exploded Manifolds’
- an introductory paper which established basic differential geometry properties of exploded
manifolds, ‘Holomorphic curves in Exploded manifolds: compactness’ - a paper which established
the compactness results necessary for Gromov Witten invariants, ‘DeRham theory of
Exploded Manifolds’, a paper which proved various results needed for defining Gromov Witten
invariants of exploded manifolds using integration of differential forms, ‘Holomorphic curves in
Exploded manifolds: regularity’ - a paper which establishes the regularity results for families
of holomorphic curves necessary for defining Gromov Witten invariants, and ‘Gromov WItten
invariants of exploded manifolds’, in which Gromov Witten invariants of exploded manifolds
are defined.
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 Zrich.
Paolo Rossi
PhD: SISSA - Trieste, 2008 Position prior to MSRI membership: Postdoc at Ecole Polytechnique,
Paris
Position after MSRI membership: postdoc at Institut de Mathematiques de Jussieu, Paris VI
Mentor: Yasha Eliashberg, Alexander Givental
During his stay at MSRI Paolo benefited from the active scientific environment and from
discussions with many experts, among them his mentors Yakov Eliashberg and Alexander
Givental. He also started a very fruitful collaboration with Oliver Fabert about gravitational
descendants in SFT which is still giving results. They wrote a joint paper ”String, dilaton and
divisor equation in Symplectic Field Theory” at MSRI which was submitted to IMRN and is
now at an advanced state of the correction and publication process. From there they went on
the same project and they are already producing the third paper of the series.
Yasha Savelyev
PhD: SUNY Stony Brook, 2008
Position prior to MSRI membership: postdoc at U Mass Amherst
Position after MSRI membership: resumes previous position
Mentor: Leonid Polterovich and Dusa McDuff
While at MSRI, Yasha worked on the paper On Gromov K-Area, and revised Bott periodicity
and stable quantum classes, both now on the arxiv. He gave a well received talk in the research
seminar, and also talked to many people about new ideas, including Hutchings, Teleman,
Givental, Eliashberg, Bukhovsky as well as Polterovich and McDuff.
Van Horn-Morris, Jeremy
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