**15-25-502.**

**11:00**Erkao Bao (Nantes)

**Semi-global Kuranishi charts and contact homology .**

*Abstract:*Contact homology was proposed and studied by Eliashberg, Givental and Hofer 16 years ago. It is a very powerful tool to distinguish different contact structures. However, the rigorous definition did not come out until last year. In this talk, we will first see that the naive definition does not work because the moduli spaces of J-holomorphic curves that we count to define the differential of contact homology are not transversally cut out. In order to achieve transversality, we will use a simplified version of the Kuranishi perturbation theory, consisting of "semi-global Kuranishi charts". This is a joint work with Ko Honda.

**14:15**Stefan Suhr (Hamburg)

**A Hamiltonian version of a result of Gromoll and Grove**

**.**

*Abstract:*Many problem on closed geodesics in Riemannian manifolds have a reformulation as a symplectic or contact geometric problem. A celebrated result in the theory of Riemannian metrics all of whose geodesics are closed is the theorem of Gromoll and Grove asserting that the geodesics of a Riemannian maetric on the 2-sphere all of whose geodesics are closed are simple closed. This implies especially that all geodesics have a common minimal period. I will explain how generalize this theorem to real Hamiltonian structures, which includes contact structures, on the 3-dimensional real projective space. As a corollary one obtains that for reversible Finsler metrics all geodesics have the same length if they areall closed.

**16:00**Sylvain Courte (Grenoble)

**Generating functions and sheaves for Legendrian links in R^3 .**

*Abstract:*To a (generic) one-parameter family of functions (f_x) on a manifold M we associate the graph of all critical values : this is the front projection of a Legendrian link L in R^3 and (f_x) is called

a generating function for L. Which Legendrian links admit a generating function ? How many up to equivalence? To deal with such questions it is natural to associate to a generating function a sheaf on R^2 microsupported on the Legendrian. We will discuss to what extent this is a bijective correspondence. This is joint work (in progress) with Vivek Shende.

Prochaines séances: 6 janvier (M. Limouzineau, ?, ?), 3 mars (B. Chantraine, ?, ?).

Autre activité symplectique à Paris:

- Séminaire Nantes-Orsay,

- Soutenance d'HDR de Patrick Massot le 12 décembre à 14h, petit amphi du batiment 425, à Orsay.