Séance du 4 avril 2014

Lieu : IHP, salle 01

11:00  Jean-François Barraud (Toulouse) :
A Floer fundamental group.

Résumé: I will describe how to derive the fundamental group of a symplectic manifold from Floer theoretic objects. As an application, new, purely homotopic constraints will be given on the number of Conley-Zehnder index 1-n fixed points points of Hamiltonian isotopies.

14:15  Dingyu Yang (IMJ) :

    When is a Kuranishi structure equivalent to a section of a finite dimensional orbifold bundle?
Résumé: A Kuranishi structure is a compatible collection of local sections in finite but not constant dimensions whose zero sets cover a compact metrizable space, such that it allows a compact perturbation theory. It is capable of describing and perturbing moduli spaces of pseudoholomorphic curves in symplectic geometry. The feature of charts and coordinate change among them resembles one from a coherent system of local finite dimensional reductions. This talk will try to make sense of this. It will also touch on how a Kuranishi structure deviates from a section in an orbifold bundle. It will be an informal introduction of author's work on the polyfold--Kuranishi correspondence. The talk should be accessible to general audiences.

16:00  Félix Schmäschke (Bochum) :

   Pearl homology for pairs.

Résumé: I construct a spectral sequence converging to the Floer homology of a
pair of two monotone Lagrangian submanifolds intersecting cleanly. The
notion of a cleanly intersecting Lagrangians is a useful
generalization of transversely intersecting Lagrangians and naturally
arises for instance in situations with present symmetries. The
spectral sequence is obtained via an invariant, which I call pearl
homology for pairs, because it is a direct generalization of the pearl
homology associated to a single monotone Lagrangian as introduced by
Biran and Cornea. As an application, I deduce from the spectral
sequence new obtructions to embeddings of monotone Lagrangian

Prochaines séances: 23/05, 06/06.