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SUMMARY:A generating function for higher Floer products and infinite-dimen
 sional integrable systems - Oliver Fabert\, Augsburg
DTSTART:20120229T160000Z
DTEND:20120229T173000Z
UID:TALK34573@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:Floer theory (of symplectomorphisms) is a well-established too
 l in symplectic topology and can be viewed as a generalization of Gromov-W
 itten theory. On the other hand\, it has been well-known for more than 20 
 years that there is a deep connection between Gromov-Witten theory and the
  theory of integrable PDE. Generalizing this relation\, in this talk I wil
 l show that from the Floer theory of a general symplectomorphism one still
  obtains a (generally infinite-dimensional) Hamiltonian system with infini
 tely many symmetries. Instead of following the classical path using Froben
 ius manifolds and bihamiltonian structures\, the main idea is to use sympl
 ectic field theory. The computation of the sequences of commuting descenda
 nt Hamiltonians involves a generating function (with weights) of all highe
 r Floer products (corresponding to Gromov-Witten invariants with more than
  3 points)\, which is an invariant of the symplectomorphism after passing 
 to SFT homology.
LOCATION:MR13
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