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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, ?)