Lieu : IHP, salle 314
11:00 Johan Bjorklund (IMJ) :
Legendrian contact homology in the product of a real line with a punctured Riemann surface.
Résumé: Ekholm, Etnyre and Sullivan has defined Legendrian contact homology in
manifolds on the form PxR where P is an exact symplectic manifold. In
the case where P is a surface the Riemann mapping theorem enables a
combinatorial description.
We give a combinatorial description of the Legendrian differential
graded algebra associated to a Legendrian knot in PxR, where P is a
punctured Riemann surface. If time allows we will show that in any
homology class there are examples of Legendrian knots which are smoothly
isotopic but not Legendrian isotopic.
14:15 Margherita Sandon (Montréal & CNRS) :
Homologie de Floer pour les points translatés.
Résumé: In 2011 I proposed a contact version of the Arnold conjecture, based on the notion of translated points of contactomorphisms. I will now discuss a work in progress to prove this conjecture for all contact manifolds, by constructing a Floer homology theory for translated points. I will also discuss why I expect this Floer homology theory to provide a perfect tool to study contact rigidity phonomena such as orderability, non-squeezing and existence of bi-invariant metrics on the contactomorphism group.
16:00 Tony Rieser (Haifa) :
Coisotropic capacities and non-squeezing for relative
symplectic embeddings
Résumé: We introduce a notion of symplectic capacity relative to a
coisotropic submanifold of a symplectic manifold, and we define a
modification of the Hofer-Zehnder capacity and show it provides an
example. As a corollary, we obtain a non-squeezing theorem for
symplectic embeddings relative to coisotropic constraints.
Prochaines séances: 07/03 (M. Zavidovique, A. Oancea, ?), 04/04 (?,?,?)
