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Séance du 2 octobre 2015

Lieu: IHP, salle 201** **

**11:00 ** Alexander Fauck (Berlin)
**Rabinowitz-Floer homology and exotic contact structures****. **
*Abstract:* Filled contact structures are contact structures which come with a
compact symplectic filling. Examples include the unit cotangent bundles
of compact differentiable manifolds, which are filled by the unit ball
bundle. Around 2000,
Ustilovsky showed that there are infinitely many different fillable
contact structures on the standard sphere S^{2n-1} for n greater
then 2. In my talk, I present how one could obtain a similar result on
other manifolds with the help of Rabinowitz-Floer
homology. This is a Floer-type invariant for filled contact manifolds,
which in general depends on the filling but can nevertheless be used to
distinguish contact structures in explicit examples .

**14:15 ** Fabian Ziltener (Utrecht)
**Leafwise fixed points for C**^{^0}-small Hamiltonian flows and local coisotropic Floer homology**. **
*Abstract: *Consider a symplectic manifold (M,\omega), a closed coisotropic submanifold N of M, and a Hamiltonian diffeomorphism \phi on M. A leafwise fixed point for \phi is a point x\in N that under \phi is mapped to its isotropic leaf. These points generalize fixed points and Lagrangian intersection points. The main result of this talk will be that \phi has a leafwise fixed point, provided that it is the time-1-map of a Hamiltonian flow whose restriction to N stays C^{^0}-close to the inclusion of N into M. This result is optimal in the sense that the C^{^0}-condition cannot be replaced by the assumption that \phi is Hofer-small.
The method of proof of this result leads to a local coisotropic version of Floer homology.
**16:00 ** Zach Sylvan (Zurich)
**Gluing Fukaya categories of pumpkin domains. **
*Abstract:* I'll define a new symplectic object called a pumpkin domain and
construct its Fukaya category, which simultaneously generalizes the
wrapped Fukaya category of a Liouville domain and the Fukaya-Seidel
category of a Lefschetz fibration. Pumpkin domains come with a natural
geometric gluing operation, which at the level of Fukaya categories
corresponds to a certain pushout. After describing this, I'll give some
simple applications and a conjectural connection to Legendrian contact
homology.

Prochaines
séances: 06/11 (J. Pardon, Jonny Evans, ?), 04/12 (G. Cazassus, A. Chiodo. O. Fabert)
Autre activité symplectique à Paris: Ecole thématique à Orsay (14-16 octobre), groupe de travail faisceaux.