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Séance du 15 septembre 2017

Lieu: IHP, salle 201

**11:00 ** Umut Varolgunes (MIT)** **
**Mayer-Vietoris sequence for relative symplectic cohomology. **
*Abstract:* I will first recall the definition of an invariant that assigns to any
compact subset K of a closed symplectic manifold M a module SH_M(K) over
the Novikov ring. I will go over the case of M=two sphere to illustrate
various points about the invariant.
Finally, I will state the Mayer-Vietoris property and explain under
what conditions it holds.
* *

** **
**14:15 **Doris Hein (Freiburg)
** **
**Local invariant Morse theory and applications in Hamiltonian dynamics.*** *
*Abstract:* Local homology is a useful tool to study periodic orbits. For example, the key to the existence of infinitely many periodic orbits of Hamiltonian systems are properties of the local Floer homology of one special orbit. I will discuss a discrete version of this invariant constructed using local invariant Morse homology of a discrete action function. The construction is very geometric and relies on a hands-on description of invariant local Morse homology. The resulting local homology can be interpreted as an invariant of germs of Hamiltonian systems or of closed Reeb orbits. It has properties similar to those of local Floer homology in the symplectic setting and probably similar applications in dynamics.

**16:00 ** Noémie Legout (Orsay) ** **
**Products in Floer theory for Lagrangian cobordisms.**
** ***Abstract: *Chantraine, Dimitroglou-Rizell, Ghiggini and Golovko have defined the Cthulhu complex, a Floer complex for Lagrangian cobordisms. The acyclicity of this complex permits to rely the Legendrian contact homologies of the positive and negative Legendrian ends of the cobordism and the singular homology of the cobordism through various long exact sequences. In this talk, I will recall briefly the definitions of Legendrian contact homology and Cthulhu complex, and I will explain how to define products on a subcomplex of the Cthulhu complex..

Prochaines séances: 6/10 (Gutt, Pedroza, Vaintrob), 10/11 (Näf, Siefring, ? ), 2/12 (? , ? , ? )

Autre activité symplectique à Paris:

- Séminaire Nantes-Orsay,