Séance du vendredi 04 octobre 2013

Lieu : IHP, salle 05

11:00 Jean Gutt (Bruxelles & Paris) :

  On Ekeland minimal number of periodic Reeb orbits on some hypersurfaces in R^2n.

Résumé: In 1986 Ekeland proved, using variational techniques, a lower bound on the minimal number of periodic Reeb orbits on convex hypersurfaces pinched between two spheres S(r) and S(R) with R²< 2r². The convex assumption was replaced by a weaker condition, namely that the scalar product of the exterior normal vector of the hypersurface at the point z with z is greater than r. This was done by Berestycki, Lasry, Mancini and Ruf. We shall show how to recover this result using a homological framework.

14:00 Maksim Maydanskiy (IMJ) :

  Floer-theoretically essential tori in geometrically-empty Stein surfaces.

Résumé: We call exact symplectic manifold  geometrically empty if it contains no compact exact Lagrangian submanifolds. One way to show that a symplectic manifold is empty is to show that its symplectic cohomology vanishes. However, the converse is not true. We show that every Stein surface in a certain natural family (which also appears in Fintushel-Stern rational blowdown construction, for example) is geometrically empty, but has non-vanishing symplectic cohomology. The proof hinges on a Floer homology computation for certain monotone tori in Lefschetz fibrations. This is joint work with Yankı Lekili.

Prochaines séances: 8/11 (B. Chantraine, J. Evans, V. Vertesi) et 6/12 (C. Wendl, A. Ritter, ?)