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Séance du 13 mai 2016

Lieu: IHP, salle **01 **

**11:00 ** Stéphane Guillermou (Grenoble)
**The three cusps conjecture.**
*Abstract: *Arnol'd's three cusps conjecture is about the fronts of Legendrian
curves in the projectivized cotangent bundle of the 2-sphere. It says that
the front of a generic Hamiltonian deformation of the fiber over a point has
at least three cusps. We will recall some results of the microlocal theory of sheaves of
Kashiwara and Schapira and see how we can use them to prove the conjecture.
**14:15 ** Guogang Liu (Nantes)** **
**On positive loops of loose Legendrian embeddings****.**
*Abstract:* Positive Legendrian/contact isotopies relate to the orderability of the universal cover of contactomorphism groups. In fact, there does not exist positive loops based in any Legendrian.I will explain that for any loose Legendrian there always exists a positive loop based in it. For the case of a loose sphere, I will construct a positive loop by hand. While for the other cases, I will do it by h-principle.

**16:00 ** Peter Uebele (Augsburg)
**Periodic Reeb flows and products in symplectic homology.**
*Abstract:** *F

or contact manifolds with periodic Reeb flow, symplectic
homology can be computed with Morse-Bott methods. The computation
indicates that its chain groups are periodic in the degree. We will
show that, under a certain index assumption, this periodicity also
holds on homology and has a natural explanation in terms of the
pair-of-pants product. This also reveals a good part of the ring
structure of symplectic homology, in particular that it is finitely
generated as a algebra. The proof uses the V-shaped symplectic
homology introduced by Cieliebak-Frauenfelder-Oancea and the action
of a loop of Hamiltonian diffeomorphisms on Floer homology
introduced by Paul Seidel.

Autre activité symplectique à Paris: Séminaire Nantes-Orsay.